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

Percentage Accurate: 89.2% → 98.0%

Time: 12.0s

Alternatives: 20

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: 89.2% 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

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x\_m}{\left(y - z\right) \cdot \left(t - z\right)}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -2.5 \cdot 10^{-305}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{y - z}}{t - z}\\ \end{array} \end{array} \end{array} \]

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 z) (- t z)))))
   (* x_s (if (<= t_1 -2.5e-305) t_1 (/ (/ 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 t_1 = x_m / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -2.5e-305) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x_m / ((y - z) * (t - z))
    if (t_1 <= (-2.5d-305)) then
        tmp = t_1
    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 t_1 = x_m / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -2.5e-305) {
		tmp = t_1;
	} 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):
	t_1 = x_m / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= -2.5e-305:
		tmp = t_1
	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)
	t_1 = Float64(x_m / Float64(Float64(y - z) * Float64(t - z)))
	tmp = 0.0
	if (t_1 <= -2.5e-305)
		tmp = t_1;
	else
		tmp = Float64(Float64(x_m / 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)
	t_1 = x_m / ((y - z) * (t - z));
	tmp = 0.0;
	if (t_1 <= -2.5e-305)
		tmp = t_1;
	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_] := 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, -2.5e-305], t$95$1, N[(N[(x$95$m / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -2.49999999999999993e-305

   1. Initial program 98.0%

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

   if -2.49999999999999993e-305 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 85.8%

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

   3. Taylor expanded in x around 0 85.8%

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

      1. associate-/l/ 96.6%

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

   5. Simplified 96.6%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \leq -2.5 \cdot 10^{-305}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x\_m}{z}}{z - t}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{x\_m}{y - z}}{t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+127}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \end{array} \]

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 z) (- z t))))
   (*
    x_s
    (if (<= y -2.3e-38)
      (/ (/ x_m y) (- t z))
      (if (<= y 4.2e-175)
        t_1
        (if (<= y 1.45e-59)
          (/ (/ x_m (- y z)) t)
          (if (<= y 4e-27)
            t_1
            (if (<= y 1.15e+127)
              (/ x_m (* (- y 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 t_1 = (x_m / z) / (z - t);
	double tmp;
	if (y <= -2.3e-38) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 4.2e-175) {
		tmp = t_1;
	} else if (y <= 1.45e-59) {
		tmp = (x_m / (y - z)) / t;
	} else if (y <= 4e-27) {
		tmp = t_1;
	} else if (y <= 1.15e+127) {
		tmp = x_m / ((y - 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) :: t_1
    real(8) :: tmp
    t_1 = (x_m / z) / (z - t)
    if (y <= (-2.3d-38)) then
        tmp = (x_m / y) / (t - z)
    else if (y <= 4.2d-175) then
        tmp = t_1
    else if (y <= 1.45d-59) then
        tmp = (x_m / (y - z)) / t
    else if (y <= 4d-27) then
        tmp = t_1
    else if (y <= 1.15d+127) then
        tmp = x_m / ((y - 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 t_1 = (x_m / z) / (z - t);
	double tmp;
	if (y <= -2.3e-38) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 4.2e-175) {
		tmp = t_1;
	} else if (y <= 1.45e-59) {
		tmp = (x_m / (y - z)) / t;
	} else if (y <= 4e-27) {
		tmp = t_1;
	} else if (y <= 1.15e+127) {
		tmp = x_m / ((y - 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):
	t_1 = (x_m / z) / (z - t)
	tmp = 0
	if y <= -2.3e-38:
		tmp = (x_m / y) / (t - z)
	elif y <= 4.2e-175:
		tmp = t_1
	elif y <= 1.45e-59:
		tmp = (x_m / (y - z)) / t
	elif y <= 4e-27:
		tmp = t_1
	elif y <= 1.15e+127:
		tmp = x_m / ((y - 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)
	t_1 = Float64(Float64(x_m / z) / Float64(z - t))
	tmp = 0.0
	if (y <= -2.3e-38)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (y <= 4.2e-175)
		tmp = t_1;
	elseif (y <= 1.45e-59)
		tmp = Float64(Float64(x_m / Float64(y - z)) / t);
	elseif (y <= 4e-27)
		tmp = t_1;
	elseif (y <= 1.15e+127)
		tmp = Float64(x_m / Float64(Float64(y - 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)
	t_1 = (x_m / z) / (z - t);
	tmp = 0.0;
	if (y <= -2.3e-38)
		tmp = (x_m / y) / (t - z);
	elseif (y <= 4.2e-175)
		tmp = t_1;
	elseif (y <= 1.45e-59)
		tmp = (x_m / (y - z)) / t;
	elseif (y <= 4e-27)
		tmp = t_1;
	elseif (y <= 1.15e+127)
		tmp = x_m / ((y - 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_] := Block[{t$95$1 = N[(N[(x$95$m / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -2.3e-38], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-175], t$95$1, If[LessEqual[y, 1.45e-59], N[(N[(x$95$m / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 4e-27], t$95$1, If[LessEqual[y, 1.15e+127], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]), $MachinePrecision]]

Derivation

1. Split input into 5 regimes

2. if y < -2.30000000000000002e-38

   1. Initial program 86.8%

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

   3. Taylor expanded in x around 0 86.8%

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

      1. associate-/l/ 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in y around inf 84.0%

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

   if -2.30000000000000002e-38 < y < 4.2e-175 or 1.45000000000000008e-59 < y < 4.0000000000000002e-27

   1. Initial program 91.6%

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

   3. Taylor expanded in x around 0 91.6%

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

      1. associate-/l/ 93.2%

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

   5. Simplified 93.2%

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

   6. Taylor expanded in y around 0 79.3%

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

      1. associate-*r/ 79.3%

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

      2. mul-1-neg 79.3%

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

   8. Simplified 79.3%

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

   if 4.2e-175 < y < 1.45000000000000008e-59

   1. Initial program 99.8%

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

      1. associate-/r* 99.9%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around inf 89.5%

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

      1. un-div-inv 89.5%

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

   7. Applied egg-rr 89.5%

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

   if 4.0000000000000002e-27 < y < 1.1500000000000001e127

   1. Initial program 89.7%

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

   3. Taylor expanded in t around inf 67.3%

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

   if 1.1500000000000001e127 < y

   1. Initial program 72.9%

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

      1. associate-/l/ 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in t around inf 70.0%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-175}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-27}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+127}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-175}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z - t}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{x\_m}{y - z}}{t}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-21}:\\ \;\;\;\;\frac{x\_m}{t - z} \cdot \frac{-1}{z}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+106}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

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 -4.5e-43)
    (/ (/ x_m y) (- t z))
    (if (<= y 8.2e-175)
      (/ (/ x_m z) (- z t))
      (if (<= y 1.35e-59)
        (/ (/ x_m (- y z)) t)
        (if (<= y 1.9e-21)
          (* (/ x_m (- t z)) (/ -1.0 z))
          (if (<= y 9e+106) (/ x_m (* (- y 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 <= -4.5e-43) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 8.2e-175) {
		tmp = (x_m / z) / (z - t);
	} else if (y <= 1.35e-59) {
		tmp = (x_m / (y - z)) / t;
	} else if (y <= 1.9e-21) {
		tmp = (x_m / (t - z)) * (-1.0 / z);
	} else if (y <= 9e+106) {
		tmp = x_m / ((y - 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 <= (-4.5d-43)) then
        tmp = (x_m / y) / (t - z)
    else if (y <= 8.2d-175) then
        tmp = (x_m / z) / (z - t)
    else if (y <= 1.35d-59) then
        tmp = (x_m / (y - z)) / t
    else if (y <= 1.9d-21) then
        tmp = (x_m / (t - z)) * ((-1.0d0) / z)
    else if (y <= 9d+106) then
        tmp = x_m / ((y - 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 <= -4.5e-43) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 8.2e-175) {
		tmp = (x_m / z) / (z - t);
	} else if (y <= 1.35e-59) {
		tmp = (x_m / (y - z)) / t;
	} else if (y <= 1.9e-21) {
		tmp = (x_m / (t - z)) * (-1.0 / z);
	} else if (y <= 9e+106) {
		tmp = x_m / ((y - 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 <= -4.5e-43:
		tmp = (x_m / y) / (t - z)
	elif y <= 8.2e-175:
		tmp = (x_m / z) / (z - t)
	elif y <= 1.35e-59:
		tmp = (x_m / (y - z)) / t
	elif y <= 1.9e-21:
		tmp = (x_m / (t - z)) * (-1.0 / z)
	elif y <= 9e+106:
		tmp = x_m / ((y - 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 <= -4.5e-43)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (y <= 8.2e-175)
		tmp = Float64(Float64(x_m / z) / Float64(z - t));
	elseif (y <= 1.35e-59)
		tmp = Float64(Float64(x_m / Float64(y - z)) / t);
	elseif (y <= 1.9e-21)
		tmp = Float64(Float64(x_m / Float64(t - z)) * Float64(-1.0 / z));
	elseif (y <= 9e+106)
		tmp = Float64(x_m / Float64(Float64(y - 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 <= -4.5e-43)
		tmp = (x_m / y) / (t - z);
	elseif (y <= 8.2e-175)
		tmp = (x_m / z) / (z - t);
	elseif (y <= 1.35e-59)
		tmp = (x_m / (y - z)) / t;
	elseif (y <= 1.9e-21)
		tmp = (x_m / (t - z)) * (-1.0 / z);
	elseif (y <= 9e+106)
		tmp = x_m / ((y - 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, -4.5e-43], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e-175], N[(N[(x$95$m / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-59], N[(N[(x$95$m / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 1.9e-21], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+106], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]), $MachinePrecision]

Derivation

1. Split input into 6 regimes

2. if y < -4.50000000000000025e-43

   1. Initial program 86.9%

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

   3. Taylor expanded in x around 0 86.9%

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

      1. associate-/l/ 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in y around inf 84.2%

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

   if -4.50000000000000025e-43 < y < 8.19999999999999997e-175

   1. Initial program 91.3%

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

   3. Taylor expanded in x around 0 91.3%

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

      1. associate-/l/ 91.9%

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

   5. Simplified 91.9%

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

   6. Taylor expanded in y around 0 82.1%

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

      1. associate-*r/ 82.1%

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

      2. mul-1-neg 82.1%

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

   8. Simplified 82.1%

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

   if 8.19999999999999997e-175 < y < 1.3499999999999999e-59

   1. Initial program 99.8%

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

      1. associate-/r* 99.9%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around inf 89.5%

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

      1. un-div-inv 89.5%

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

   7. Applied egg-rr 89.5%

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

   if 1.3499999999999999e-59 < y < 1.8999999999999999e-21

   1. Initial program 92.9%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 72.2%

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

   if 1.8999999999999999e-21 < y < 8.9999999999999994e106

   1. Initial program 90.6%

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

   3. Taylor expanded in t around inf 69.6%

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

   if 8.9999999999999994e106 < y

   1. Initial program 74.8%

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

      1. associate-/l/ 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in t around inf 72.4%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 6 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-175}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{-1}{z}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+95} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+123}\right):\\ \;\;\;\;\frac{\frac{x\_m}{t - z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{t\_1}\\ \end{array} \end{array} \end{array} \]

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 (* (- y z) (- t z))))
   (*
    x_s
    (if (or (<= t_1 -1e+95) (not (<= t_1 5e+123)))
      (/ (/ x_m (- t z)) (- y z))
      (/ x_m 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 = (y - z) * (t - z);
	double tmp;
	if ((t_1 <= -1e+95) || !(t_1 <= 5e+123)) {
		tmp = (x_m / (t - z)) / (y - z);
	} else {
		tmp = x_m / 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 = (y - z) * (t - z)
    if ((t_1 <= (-1d+95)) .or. (.not. (t_1 <= 5d+123))) then
        tmp = (x_m / (t - z)) / (y - z)
    else
        tmp = x_m / 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 = (y - z) * (t - z);
	double tmp;
	if ((t_1 <= -1e+95) || !(t_1 <= 5e+123)) {
		tmp = (x_m / (t - z)) / (y - z);
	} else {
		tmp = x_m / 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 = (y - z) * (t - z)
	tmp = 0
	if (t_1 <= -1e+95) or not (t_1 <= 5e+123):
		tmp = (x_m / (t - z)) / (y - z)
	else:
		tmp = x_m / 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(y - z) * Float64(t - z))
	tmp = 0.0
	if ((t_1 <= -1e+95) || !(t_1 <= 5e+123))
		tmp = Float64(Float64(x_m / Float64(t - z)) / Float64(y - z));
	else
		tmp = Float64(x_m / 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 = (y - z) * (t - z);
	tmp = 0.0;
	if ((t_1 <= -1e+95) || ~((t_1 <= 5e+123)))
		tmp = (x_m / (t - z)) / (y - z);
	else
		tmp = x_m / 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[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[Or[LessEqual[t$95$1, -1e+95], N[Not[LessEqual[t$95$1, 5e+123]], $MachinePrecision]], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x$95$m / t$95$1), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -1.00000000000000002e95 or 4.99999999999999974e123 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 83.8%

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

      1. associate-/l/ 99.3%

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

   3. Simplified 99.3%

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

   if -1.00000000000000002e95 < (*.f64 (-.f64 y z) (-.f64 t z)) < 4.99999999999999974e123

   1. Initial program 98.1%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -1 \cdot 10^{+95} \lor \neg \left(\left(y - z\right) \cdot \left(t - z\right) \leq 5 \cdot 10^{+123}\right):\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x\_m}{t}}{y}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -0.00082:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-109}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+39} \lor \neg \left(t \leq 1.02 \cdot 10^{+104}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(-t\right)}\\ \end{array} \end{array} \end{array} \]

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 t) y)))
   (*
    x_s
    (if (<= t -0.00082)
      t_1
      (if (<= t 1.4e-109)
        (/ x_m (* z (- y)))
        (if (or (<= t 7.8e+39) (not (<= t 1.02e+104)))
          t_1
          (/ x_m (* 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 t_1 = (x_m / t) / y;
	double tmp;
	if (t <= -0.00082) {
		tmp = t_1;
	} else if (t <= 1.4e-109) {
		tmp = x_m / (z * -y);
	} else if ((t <= 7.8e+39) || !(t <= 1.02e+104)) {
		tmp = t_1;
	} else {
		tmp = x_m / (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) :: t_1
    real(8) :: tmp
    t_1 = (x_m / t) / y
    if (t <= (-0.00082d0)) then
        tmp = t_1
    else if (t <= 1.4d-109) then
        tmp = x_m / (z * -y)
    else if ((t <= 7.8d+39) .or. (.not. (t <= 1.02d+104))) then
        tmp = t_1
    else
        tmp = x_m / (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 t_1 = (x_m / t) / y;
	double tmp;
	if (t <= -0.00082) {
		tmp = t_1;
	} else if (t <= 1.4e-109) {
		tmp = x_m / (z * -y);
	} else if ((t <= 7.8e+39) || !(t <= 1.02e+104)) {
		tmp = t_1;
	} else {
		tmp = x_m / (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):
	t_1 = (x_m / t) / y
	tmp = 0
	if t <= -0.00082:
		tmp = t_1
	elif t <= 1.4e-109:
		tmp = x_m / (z * -y)
	elif (t <= 7.8e+39) or not (t <= 1.02e+104):
		tmp = t_1
	else:
		tmp = x_m / (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)
	t_1 = Float64(Float64(x_m / t) / y)
	tmp = 0.0
	if (t <= -0.00082)
		tmp = t_1;
	elseif (t <= 1.4e-109)
		tmp = Float64(x_m / Float64(z * Float64(-y)));
	elseif ((t <= 7.8e+39) || !(t <= 1.02e+104))
		tmp = t_1;
	else
		tmp = Float64(x_m / Float64(z * Float64(-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)
	t_1 = (x_m / t) / y;
	tmp = 0.0;
	if (t <= -0.00082)
		tmp = t_1;
	elseif (t <= 1.4e-109)
		tmp = x_m / (z * -y);
	elseif ((t <= 7.8e+39) || ~((t <= 1.02e+104)))
		tmp = t_1;
	else
		tmp = x_m / (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_] := Block[{t$95$1 = N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t, -0.00082], t$95$1, If[LessEqual[t, 1.4e-109], N[(x$95$m / N[(z * (-y)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 7.8e+39], N[Not[LessEqual[t, 1.02e+104]], $MachinePrecision]], t$95$1, N[(x$95$m / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if t < -8.1999999999999998e-4 or 1.39999999999999989e-109 < t < 7.8000000000000002e39 or 1.02e104 < t

   1. Initial program 85.7%

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

   3. Taylor expanded in z around 0 48.8%

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

      1. associate-/r* 57.5%

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

      2. div-inv 57.6%

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

   5. Applied egg-rr 57.6%

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

      1. un-div-inv 57.5%

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

   7. Applied egg-rr 57.5%

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

   if -8.1999999999999998e-4 < t < 1.39999999999999989e-109

   1. Initial program 92.2%

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

      1. associate-/l/ 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in t around 0 76.3%

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

      1. associate-*r/ 76.3%

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

      2. neg-mul-1 76.3%

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

   7. Simplified 76.3%

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

   8. Taylor expanded in z around 0 46.8%

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

      1. associate-*r/ 46.8%

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

      2. mul-1-neg 46.8%

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

      3. *-commutative 46.8%

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

   10. Simplified 46.8%

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

   if 7.8000000000000002e39 < t < 1.02e104

   1. Initial program 90.2%

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

      1. associate-/l/ 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in t around inf 62.4%

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

   6. Taylor expanded in y around 0 57.1%

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

      1. associate-*r/ 57.1%

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

      2. mul-1-neg 57.1%

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

   8. Simplified 57.1%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.00082:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-109}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+39} \lor \neg \left(t \leq 1.02 \cdot 10^{+104}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x\_m}{z} \cdot \frac{1}{z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-83}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+41}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{-z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 -2e+43)
      t_1
      (if (<= z 1.15e-83)
        (/ (/ x_m t) y)
        (if (<= z 4.3e+41) (/ (/ x_m y) (- z)) 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 <= -2e+43) {
		tmp = t_1;
	} else if (z <= 1.15e-83) {
		tmp = (x_m / t) / y;
	} else if (z <= 4.3e+41) {
		tmp = (x_m / y) / -z;
	} 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 <= (-2d+43)) then
        tmp = t_1
    else if (z <= 1.15d-83) then
        tmp = (x_m / t) / y
    else if (z <= 4.3d+41) then
        tmp = (x_m / y) / -z
    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 <= -2e+43) {
		tmp = t_1;
	} else if (z <= 1.15e-83) {
		tmp = (x_m / t) / y;
	} else if (z <= 4.3e+41) {
		tmp = (x_m / y) / -z;
	} 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 <= -2e+43:
		tmp = t_1
	elif z <= 1.15e-83:
		tmp = (x_m / t) / y
	elif z <= 4.3e+41:
		tmp = (x_m / y) / -z
	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 <= -2e+43)
		tmp = t_1;
	elseif (z <= 1.15e-83)
		tmp = Float64(Float64(x_m / t) / y);
	elseif (z <= 4.3e+41)
		tmp = Float64(Float64(x_m / y) / Float64(-z));
	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 <= -2e+43)
		tmp = t_1;
	elseif (z <= 1.15e-83)
		tmp = (x_m / t) / y;
	elseif (z <= 4.3e+41)
		tmp = (x_m / y) / -z;
	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, -2e+43], t$95$1, If[LessEqual[z, 1.15e-83], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 4.3e+41], N[(N[(x$95$m / y), $MachinePrecision] / (-z)), $MachinePrecision], t$95$1]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -2.00000000000000003e43 or 4.30000000000000024e41 < z

   1. Initial program 83.4%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 83.9%

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

      1. associate-*r/ 83.9%

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

      2. neg-mul-1 83.9%

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

   7. Simplified 83.9%

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

      1. div-inv 83.9%

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

      2. add-sqr-sqrt 36.8%

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

      3. sqrt-unprod 56.2%

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

      4. sqr-neg 56.2%

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

      5. sqrt-unprod 30.3%

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

      6. add-sqr-sqrt 55.9%

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

      7. sub-neg 55.9%

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

      8. add-sqr-sqrt 30.5%

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

      9. sqrt-unprod 62.1%

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

      10. sqr-neg 62.1%

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

      11. sqrt-unprod 36.6%

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

      12. add-sqr-sqrt 76.1%

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

   9. Applied egg-rr 76.1%

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

   10. Taylor expanded in y around 0 74.4%

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

   if -2.00000000000000003e43 < z < 1.14999999999999995e-83

   1. Initial program 90.4%

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

   3. Taylor expanded in z around 0 62.9%

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

      1. associate-/r* 71.7%

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

      2. div-inv 71.7%

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

   5. Applied egg-rr 71.7%

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

      1. un-div-inv 71.7%

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

   7. Applied egg-rr 71.7%

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

   if 1.14999999999999995e-83 < z < 4.30000000000000024e41

   1. Initial program 99.5%

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

      1. associate-/l/ 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in t around 0 44.5%

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

      1. associate-*r/ 44.5%

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

      2. neg-mul-1 44.5%

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

   7. Simplified 44.5%

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

   8. Taylor expanded in z around 0 36.7%

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

      1. associate-*r/ 36.7%

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

      2. mul-1-neg 36.7%

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

      3. *-commutative 36.7%

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

   10. Simplified 36.7%

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

   11. Taylor expanded in x around 0 36.7%

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

       1. mul-1-neg 36.7%

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

       2. associate-/r* 36.9%

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

       3. distribute-neg-frac2 36.9%

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

   13. Simplified 36.9%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-83}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+41}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x\_m}{z \cdot \left(y + z\right)}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+168}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z} \cdot \frac{1}{z}\\ \end{array} \end{array} \end{array} \]

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 (* z (+ y z)))))
   (*
    x_s
    (if (<= z -6.2e+14)
      t_1
      (if (<= z 1.2e-36)
        (/ x_m (* (- y z) t))
        (if (<= z 2.35e+168) t_1 (* (/ x_m z) (/ 1.0 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 / (z * (y + z));
	double tmp;
	if (z <= -6.2e+14) {
		tmp = t_1;
	} else if (z <= 1.2e-36) {
		tmp = x_m / ((y - z) * t);
	} else if (z <= 2.35e+168) {
		tmp = t_1;
	} else {
		tmp = (x_m / z) * (1.0 / 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 / (z * (y + z))
    if (z <= (-6.2d+14)) then
        tmp = t_1
    else if (z <= 1.2d-36) then
        tmp = x_m / ((y - z) * t)
    else if (z <= 2.35d+168) then
        tmp = t_1
    else
        tmp = (x_m / z) * (1.0d0 / 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 / (z * (y + z));
	double tmp;
	if (z <= -6.2e+14) {
		tmp = t_1;
	} else if (z <= 1.2e-36) {
		tmp = x_m / ((y - z) * t);
	} else if (z <= 2.35e+168) {
		tmp = t_1;
	} else {
		tmp = (x_m / z) * (1.0 / 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 / (z * (y + z))
	tmp = 0
	if z <= -6.2e+14:
		tmp = t_1
	elif z <= 1.2e-36:
		tmp = x_m / ((y - z) * t)
	elif z <= 2.35e+168:
		tmp = t_1
	else:
		tmp = (x_m / z) * (1.0 / 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(z * Float64(y + z)))
	tmp = 0.0
	if (z <= -6.2e+14)
		tmp = t_1;
	elseif (z <= 1.2e-36)
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	elseif (z <= 2.35e+168)
		tmp = t_1;
	else
		tmp = Float64(Float64(x_m / z) * Float64(1.0 / 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 / (z * (y + z));
	tmp = 0.0;
	if (z <= -6.2e+14)
		tmp = t_1;
	elseif (z <= 1.2e-36)
		tmp = x_m / ((y - z) * t);
	elseif (z <= 2.35e+168)
		tmp = t_1;
	else
		tmp = (x_m / z) * (1.0 / 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[(z * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -6.2e+14], t$95$1, If[LessEqual[z, 1.2e-36], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e+168], t$95$1, N[(N[(x$95$m / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2e14 or 1.2e-36 < z < 2.3499999999999998e168

   1. Initial program 89.8%

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

      1. associate-/l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 77.3%

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

      1. associate-*r/ 77.3%

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

      2. neg-mul-1 77.3%

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

   7. Simplified 77.3%

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

      1. div-inv 77.3%

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

      2. associate-/l* 73.4%

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

      3. add-sqr-sqrt 37.5%

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

      4. sqrt-unprod 52.2%

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

      5. sqr-neg 52.2%

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

      6. sqrt-unprod 21.4%

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

      7. add-sqr-sqrt 49.0%

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

      8. sub-neg 49.0%

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

      9. add-sqr-sqrt 38.4%

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

      10. sqrt-unprod 57.8%

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

      11. sqr-neg 57.8%

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

      12. sqrt-unprod 19.4%

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

      13. add-sqr-sqrt 67.8%

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

   9. Applied egg-rr 67.8%

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

       1. associate-/r* 67.8%

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

       2. associate-*r/ 67.8%

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

       3. *-rgt-identity 67.8%

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

       4. +-commutative 67.8%

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

   11. Simplified 67.8%

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

   if -6.2e14 < z < 1.2e-36

   1. Initial program 92.7%

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

   3. Taylor expanded in t around inf 77.8%

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

   if 2.3499999999999998e168 < z

   1. Initial program 68.7%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 90.0%

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

      1. associate-*r/ 90.0%

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

      2. neg-mul-1 90.0%

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

   7. Simplified 90.0%

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

      1. div-inv 90.1%

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

      2. add-sqr-sqrt 28.5%

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

      3. sqrt-unprod 61.7%

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

      4. sqr-neg 61.7%

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

      5. sqrt-unprod 48.4%

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

      6. add-sqr-sqrt 66.5%

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

      7. sub-neg 66.5%

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

      8. add-sqr-sqrt 0.0%

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

      9. sqrt-unprod 68.7%

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

      10. sqr-neg 68.7%

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

      11. sqrt-unprod 84.9%

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

      12. add-sqr-sqrt 85.0%

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

   9. Applied egg-rr 85.0%

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

   10. Taylor expanded in y around 0 85.0%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{z \cdot \left(y + z\right)}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+168}:\\ \;\;\;\;\frac{x}{z \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-211}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-109}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+123}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

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 (<= t -1.2e-211)
    (/ x_m (* y (- t z)))
    (if (<= t 8.8e-109)
      (/ x_m (* z (- z y)))
      (if (<= t 3.3e+123) (/ x_m (* (- y 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 (t <= -1.2e-211) {
		tmp = x_m / (y * (t - z));
	} else if (t <= 8.8e-109) {
		tmp = x_m / (z * (z - y));
	} else if (t <= 3.3e+123) {
		tmp = x_m / ((y - 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 (t <= (-1.2d-211)) then
        tmp = x_m / (y * (t - z))
    else if (t <= 8.8d-109) then
        tmp = x_m / (z * (z - y))
    else if (t <= 3.3d+123) then
        tmp = x_m / ((y - 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 (t <= -1.2e-211) {
		tmp = x_m / (y * (t - z));
	} else if (t <= 8.8e-109) {
		tmp = x_m / (z * (z - y));
	} else if (t <= 3.3e+123) {
		tmp = x_m / ((y - 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 t <= -1.2e-211:
		tmp = x_m / (y * (t - z))
	elif t <= 8.8e-109:
		tmp = x_m / (z * (z - y))
	elif t <= 3.3e+123:
		tmp = x_m / ((y - 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 (t <= -1.2e-211)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (t <= 8.8e-109)
		tmp = Float64(x_m / Float64(z * Float64(z - y)));
	elseif (t <= 3.3e+123)
		tmp = Float64(x_m / Float64(Float64(y - 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 (t <= -1.2e-211)
		tmp = x_m / (y * (t - z));
	elseif (t <= 8.8e-109)
		tmp = x_m / (z * (z - y));
	elseif (t <= 3.3e+123)
		tmp = x_m / ((y - 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[t, -1.2e-211], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.8e-109], N[(x$95$m / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e+123], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if t < -1.2000000000000001e-211

   1. Initial program 88.0%

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

   3. Taylor expanded in y around inf 59.9%

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

      1. *-commutative 59.9%

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

   5. Simplified 59.9%

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

   if -1.2000000000000001e-211 < t < 8.7999999999999997e-109

   1. Initial program 90.4%

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

      1. associate-/l/ 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in t around 0 79.8%

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

      1. associate-*r/ 79.8%

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

      2. neg-mul-1 79.8%

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

   7. Simplified 79.8%

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

      1. frac-2neg 79.8%

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

      2. div-inv 79.8%

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

      3. distribute-frac-neg 79.8%

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

      4. remove-double-neg 79.8%

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

      5. sub-neg 79.8%

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

      6. distribute-neg-in 79.8%

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

      7. add-sqr-sqrt 40.7%

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

      8. sqrt-unprod 59.9%

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

      9. sqr-neg 59.9%

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

      10. sqrt-unprod 22.4%

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

      11. add-sqr-sqrt 50.7%

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

      12. add-sqr-sqrt 28.3%

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

      13. sqrt-unprod 61.3%

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

      14. sqr-neg 61.3%

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

      15. sqrt-unprod 39.1%

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

      16. add-sqr-sqrt 79.8%

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

   9. Applied egg-rr 79.8%

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

       1. associate-*r/ 79.8%

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

       2. *-rgt-identity 79.8%

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

       3. neg-mul-1 79.8%

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

       4. +-commutative 79.8%

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

       5. neg-mul-1 79.8%

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

       6. sub-neg 79.8%

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

   11. Simplified 79.8%

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

   12. Taylor expanded in x around 0 73.9%

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

   if 8.7999999999999997e-109 < t < 3.30000000000000003e123

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf 66.9%

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

   if 3.30000000000000003e123 < t

   1. Initial program 86.4%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 95.5%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-211}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-109}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-291}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-110}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+123}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

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 (<= t -6e-291)
    (/ (/ x_m y) (- t z))
    (if (<= t 4.3e-110)
      (/ x_m (* z (- z y)))
      (if (<= t 5.1e+123) (/ x_m (* (- y 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 (t <= -6e-291) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 4.3e-110) {
		tmp = x_m / (z * (z - y));
	} else if (t <= 5.1e+123) {
		tmp = x_m / ((y - 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 (t <= (-6d-291)) then
        tmp = (x_m / y) / (t - z)
    else if (t <= 4.3d-110) then
        tmp = x_m / (z * (z - y))
    else if (t <= 5.1d+123) then
        tmp = x_m / ((y - 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 (t <= -6e-291) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 4.3e-110) {
		tmp = x_m / (z * (z - y));
	} else if (t <= 5.1e+123) {
		tmp = x_m / ((y - 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 t <= -6e-291:
		tmp = (x_m / y) / (t - z)
	elif t <= 4.3e-110:
		tmp = x_m / (z * (z - y))
	elif t <= 5.1e+123:
		tmp = x_m / ((y - 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 (t <= -6e-291)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (t <= 4.3e-110)
		tmp = Float64(x_m / Float64(z * Float64(z - y)));
	elseif (t <= 5.1e+123)
		tmp = Float64(x_m / Float64(Float64(y - 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 (t <= -6e-291)
		tmp = (x_m / y) / (t - z);
	elseif (t <= 4.3e-110)
		tmp = x_m / (z * (z - y));
	elseif (t <= 5.1e+123)
		tmp = x_m / ((y - 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[t, -6e-291], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.3e-110], N[(x$95$m / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.1e+123], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if t < -6.0000000000000001e-291

   1. Initial program 86.7%

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

   3. Taylor expanded in x around 0 86.7%

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

      1. associate-/l/ 96.7%

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

   5. Simplified 96.7%

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

   6. Taylor expanded in y around inf 64.3%

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

   if -6.0000000000000001e-291 < t < 4.30000000000000025e-110

   1. Initial program 95.6%

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

      1. associate-/l/ 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t around 0 80.8%

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

      1. associate-*r/ 80.8%

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

      2. neg-mul-1 80.8%

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

   7. Simplified 80.8%

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

      1. frac-2neg 80.8%

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

      2. div-inv 80.7%

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

      3. distribute-frac-neg 80.7%

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

      4. remove-double-neg 80.7%

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

      5. sub-neg 80.7%

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

      6. distribute-neg-in 80.7%

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

      7. add-sqr-sqrt 45.5%

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

      8. sqrt-unprod 61.9%

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

      9. sqr-neg 61.9%

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

      10. sqrt-unprod 16.4%

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

      11. add-sqr-sqrt 47.5%

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

      12. add-sqr-sqrt 31.0%

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

      13. sqrt-unprod 62.2%

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

      14. sqr-neg 62.2%

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

      15. sqrt-unprod 35.2%

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

      16. add-sqr-sqrt 80.7%

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

   9. Applied egg-rr 80.7%

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

       1. associate-*r/ 80.8%

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

       2. *-rgt-identity 80.8%

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

       3. neg-mul-1 80.8%

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

       4. +-commutative 80.8%

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

       5. neg-mul-1 80.8%

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

       6. sub-neg 80.8%

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

   11. Simplified 80.8%

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

   12. Taylor expanded in x around 0 79.0%

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

   if 4.30000000000000025e-110 < t < 5.09999999999999972e123

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf 66.9%

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

   if 5.09999999999999972e123 < t

   1. Initial program 86.4%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 95.5%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-291}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-110}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{-186}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-109}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z - y}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+123}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

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 (<= t -9.2e-186)
    (/ (/ x_m y) (- t z))
    (if (<= t 9.2e-109)
      (/ (/ x_m z) (- z y))
      (if (<= t 3.8e+123) (/ x_m (* (- y 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 (t <= -9.2e-186) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 9.2e-109) {
		tmp = (x_m / z) / (z - y);
	} else if (t <= 3.8e+123) {
		tmp = x_m / ((y - 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 (t <= (-9.2d-186)) then
        tmp = (x_m / y) / (t - z)
    else if (t <= 9.2d-109) then
        tmp = (x_m / z) / (z - y)
    else if (t <= 3.8d+123) then
        tmp = x_m / ((y - 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 (t <= -9.2e-186) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 9.2e-109) {
		tmp = (x_m / z) / (z - y);
	} else if (t <= 3.8e+123) {
		tmp = x_m / ((y - 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 t <= -9.2e-186:
		tmp = (x_m / y) / (t - z)
	elif t <= 9.2e-109:
		tmp = (x_m / z) / (z - y)
	elif t <= 3.8e+123:
		tmp = x_m / ((y - 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 (t <= -9.2e-186)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (t <= 9.2e-109)
		tmp = Float64(Float64(x_m / z) / Float64(z - y));
	elseif (t <= 3.8e+123)
		tmp = Float64(x_m / Float64(Float64(y - 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 (t <= -9.2e-186)
		tmp = (x_m / y) / (t - z);
	elseif (t <= 9.2e-109)
		tmp = (x_m / z) / (z - y);
	elseif (t <= 3.8e+123)
		tmp = x_m / ((y - 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[t, -9.2e-186], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-109], N[(N[(x$95$m / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+123], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if t < -9.2000000000000003e-186

   1. Initial program 87.5%

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

   3. Taylor expanded in x around 0 87.5%

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

      1. associate-/l/ 96.1%

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

   5. Simplified 96.1%

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

   6. Taylor expanded in y around inf 62.3%

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

   if -9.2000000000000003e-186 < t < 9.2000000000000006e-109

   1. Initial program 91.2%

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

      1. associate-/l/ 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in t around 0 78.2%

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

      1. associate-*r/ 78.2%

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

      2. neg-mul-1 78.2%

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

   7. Simplified 78.2%

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

      1. frac-2neg 78.2%

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

      2. div-inv 78.2%

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

      3. distribute-frac-neg 78.2%

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

      4. remove-double-neg 78.2%

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

      5. sub-neg 78.2%

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

      6. distribute-neg-in 78.2%

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

      7. add-sqr-sqrt 42.2%

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

      8. sqrt-unprod 59.9%

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

      9. sqr-neg 59.9%

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

      10. sqrt-unprod 20.6%

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

      11. add-sqr-sqrt 51.4%

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

      12. add-sqr-sqrt 30.9%

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

      13. sqrt-unprod 61.2%

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

      14. sqr-neg 61.2%

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

      15. sqrt-unprod 35.9%

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

      16. add-sqr-sqrt 78.2%

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

   9. Applied egg-rr 78.2%

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

       1. associate-*r/ 78.2%

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

       2. *-rgt-identity 78.2%

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

       3. neg-mul-1 78.2%

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

       4. +-commutative 78.2%

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

       5. neg-mul-1 78.2%

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

       6. sub-neg 78.2%

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

   11. Simplified 78.2%

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

   if 9.2000000000000006e-109 < t < 3.79999999999999994e123

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf 66.9%

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

   if 3.79999999999999994e123 < t

   1. Initial program 86.4%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 95.5%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{-186}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-109}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 91.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+152}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

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 -2.05e+21)
    (/ (/ x_m y) (- t z))
    (if (<= t 6e+152) (/ x_m (* (- y z) (- t z))) (/ (/ 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 <= -2.05e+21) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 6e+152) {
		tmp = x_m / ((y - z) * (t - z));
	} 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 <= (-2.05d+21)) then
        tmp = (x_m / y) / (t - z)
    else if (t <= 6d+152) then
        tmp = x_m / ((y - z) * (t - z))
    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 <= -2.05e+21) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 6e+152) {
		tmp = x_m / ((y - z) * (t - z));
	} 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 <= -2.05e+21:
		tmp = (x_m / y) / (t - z)
	elif t <= 6e+152:
		tmp = x_m / ((y - z) * (t - z))
	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 <= -2.05e+21)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (t <= 6e+152)
		tmp = Float64(x_m / Float64(Float64(y - z) * Float64(t - z)));
	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 <= -2.05e+21)
		tmp = (x_m / y) / (t - z);
	elseif (t <= 6e+152)
		tmp = x_m / ((y - z) * (t - z));
	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, -2.05e+21], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+152], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * N[(t - z), $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 < -2.05e21

   1. Initial program 85.0%

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

   3. Taylor expanded in x around 0 85.0%

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

      1. associate-/l/ 94.5%

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

   5. Simplified 94.5%

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

   6. Taylor expanded in y around inf 62.0%

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

   if -2.05e21 < t < 5.99999999999999981e152

   1. Initial program 91.0%

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

   if 5.99999999999999981e152 < t

   1. Initial program 83.5%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 96.8%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1500000000000 \lor \neg \left(z \leq 8 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x\_m}{z} \cdot \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \end{array} \end{array} \]

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 -1500000000000.0) (not (<= z 8e-37)))
    (* (/ x_m z) (/ -1.0 y))
    (/ (/ x_m t) y))))

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 <= -1500000000000.0) || !(z <= 8e-37)) {
		tmp = (x_m / z) * (-1.0 / y);
	} else {
		tmp = (x_m / t) / y;
	}
	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 <= (-1500000000000.0d0)) .or. (.not. (z <= 8d-37))) then
        tmp = (x_m / z) * ((-1.0d0) / y)
    else
        tmp = (x_m / t) / y
    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 <= -1500000000000.0) || !(z <= 8e-37)) {
		tmp = (x_m / z) * (-1.0 / y);
	} else {
		tmp = (x_m / t) / y;
	}
	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 <= -1500000000000.0) or not (z <= 8e-37):
		tmp = (x_m / z) * (-1.0 / y)
	else:
		tmp = (x_m / t) / y
	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 <= -1500000000000.0) || !(z <= 8e-37))
		tmp = Float64(Float64(x_m / z) * Float64(-1.0 / y));
	else
		tmp = Float64(Float64(x_m / t) / y);
	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 <= -1500000000000.0) || ~((z <= 8e-37)))
		tmp = (x_m / z) * (-1.0 / y);
	else
		tmp = (x_m / t) / y;
	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, -1500000000000.0], N[Not[LessEqual[z, 8e-37]], $MachinePrecision]], N[(N[(x$95$m / z), $MachinePrecision] * N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e12 or 8.00000000000000053e-37 < z

   1. Initial program 83.9%

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

      1. associate-/l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 80.8%

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

      1. associate-*r/ 80.8%

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

      2. neg-mul-1 80.8%

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

   7. Simplified 80.8%

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

      1. div-inv 80.9%

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

      2. add-sqr-sqrt 37.1%

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

      3. sqrt-unprod 55.0%

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

      4. sqr-neg 55.0%

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

      5. sqrt-unprod 27.5%

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

      6. add-sqr-sqrt 52.4%

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

      7. sub-neg 52.4%

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

      8. add-sqr-sqrt 26.9%

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

      9. sqrt-unprod 60.1%

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

      10. sqr-neg 60.1%

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

      11. sqrt-unprod 37.6%

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

      12. add-sqr-sqrt 72.4%

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

   9. Applied egg-rr 72.4%

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

   10. Taylor expanded in z around 0 33.7%

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

       1. *-commutative 33.7%

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

   12. Simplified 33.7%

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

       1. add-sqr-sqrt 14.6%

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

       2. sqrt-unprod 37.4%

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

       3. sqr-neg 37.4%

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

       4. sqrt-unprod 21.1%

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

       5. add-sqr-sqrt 37.5%

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

       6. neg-mul-1 37.5%

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

       7. *-commutative 37.5%

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

       8. times-frac 46.1%

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

   14. Applied egg-rr 46.1%

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

   if -1.5e12 < z < 8.00000000000000053e-37

   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 62.3%

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

      1. associate-/r* 68.2%

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

      2. div-inv 68.2%

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

   5. Applied egg-rr 68.2%

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

      1. un-div-inv 68.2%

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

   7. Applied egg-rr 68.2%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1500000000000 \lor \neg \left(z \leq 8 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -0.00075:\\ \;\;\;\;\frac{x\_m}{t} \cdot \frac{1}{y}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-112}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 -0.00075)
    (* (/ x_m t) (/ 1.0 y))
    (if (<= t 1.8e-112) (/ x_m (* 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 <= -0.00075) {
		tmp = (x_m / t) * (1.0 / y);
	} else if (t <= 1.8e-112) {
		tmp = x_m / (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 <= (-0.00075d0)) then
        tmp = (x_m / t) * (1.0d0 / y)
    else if (t <= 1.8d-112) then
        tmp = x_m / (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 <= -0.00075) {
		tmp = (x_m / t) * (1.0 / y);
	} else if (t <= 1.8e-112) {
		tmp = x_m / (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 <= -0.00075:
		tmp = (x_m / t) * (1.0 / y)
	elif t <= 1.8e-112:
		tmp = x_m / (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 <= -0.00075)
		tmp = Float64(Float64(x_m / t) * Float64(1.0 / y));
	elseif (t <= 1.8e-112)
		tmp = Float64(x_m / Float64(z * Float64(-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 <= -0.00075)
		tmp = (x_m / t) * (1.0 / y);
	elseif (t <= 1.8e-112)
		tmp = x_m / (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, -0.00075], N[(N[(x$95$m / t), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e-112], N[(x$95$m / N[(z * (-y)), $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 < -7.5000000000000002e-4

   1. Initial program 85.1%

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

   3. Taylor expanded in z around 0 51.5%

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

      1. associate-/r* 62.1%

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

      2. div-inv 62.2%

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

   5. Applied egg-rr 62.2%

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

   if -7.5000000000000002e-4 < t < 1.8e-112

   1. Initial program 92.2%

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

      1. associate-/l/ 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in t around 0 76.3%

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

      1. associate-*r/ 76.3%

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

      2. neg-mul-1 76.3%

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

   7. Simplified 76.3%

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

   8. Taylor expanded in z around 0 46.8%

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

      1. associate-*r/ 46.8%

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

      2. mul-1-neg 46.8%

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

      3. *-commutative 46.8%

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

   10. Simplified 46.8%

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

   if 1.8e-112 < t

   1. Initial program 87.3%

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

   3. Taylor expanded in t around inf 75.1%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.00075:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-112}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.7:\\ \;\;\;\;\frac{x\_m}{t} \cdot \frac{1}{y}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-109}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 -2.7)
    (* (/ x_m t) (/ 1.0 y))
    (if (<= t 9.2e-109) (/ 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 <= -2.7) {
		tmp = (x_m / t) * (1.0 / y);
	} else if (t <= 9.2e-109) {
		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 <= (-2.7d0)) then
        tmp = (x_m / t) * (1.0d0 / y)
    else if (t <= 9.2d-109) 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 <= -2.7) {
		tmp = (x_m / t) * (1.0 / y);
	} else if (t <= 9.2e-109) {
		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 <= -2.7:
		tmp = (x_m / t) * (1.0 / y)
	elif t <= 9.2e-109:
		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 <= -2.7)
		tmp = Float64(Float64(x_m / t) * Float64(1.0 / y));
	elseif (t <= 9.2e-109)
		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 <= -2.7)
		tmp = (x_m / t) * (1.0 / y);
	elseif (t <= 9.2e-109)
		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, -2.7], N[(N[(x$95$m / t), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-109], 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 < -2.7000000000000002

   1. Initial program 85.1%

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

   3. Taylor expanded in z around 0 51.5%

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

      1. associate-/r* 62.1%

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

      2. div-inv 62.2%

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

   5. Applied egg-rr 62.2%

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

   if -2.7000000000000002 < t < 9.2000000000000006e-109

   1. Initial program 92.2%

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

      1. associate-/l/ 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in t around 0 76.3%

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

      1. associate-*r/ 76.3%

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

      2. neg-mul-1 76.3%

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

   7. Simplified 76.3%

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

      1. frac-2neg 76.3%

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

      2. div-inv 76.3%

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

      3. distribute-frac-neg 76.3%

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

      4. remove-double-neg 76.3%

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

      5. sub-neg 76.3%

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

      6. distribute-neg-in 76.3%

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

      7. add-sqr-sqrt 41.3%

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

      8. sqrt-unprod 59.9%

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

      9. sqr-neg 59.9%

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

      10. sqrt-unprod 20.6%

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

      11. add-sqr-sqrt 51.7%

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

      12. add-sqr-sqrt 31.1%

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

      13. sqrt-unprod 61.1%

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

      14. sqr-neg 61.1%

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

      15. sqrt-unprod 35.0%

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

      16. add-sqr-sqrt 76.3%

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

   9. Applied egg-rr 76.3%

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

       1. associate-*r/ 76.3%

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

       2. *-rgt-identity 76.3%

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

       3. neg-mul-1 76.3%

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

       4. +-commutative 76.3%

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

       5. neg-mul-1 76.3%

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

       6. sub-neg 76.3%

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

   11. Simplified 76.3%

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

   12. Taylor expanded in x around 0 71.3%

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

   if 9.2000000000000006e-109 < t

   1. Initial program 87.3%

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

   3. Taylor expanded in t around inf 75.1%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-109}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 77.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-210}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-109}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 -1.15e-210)
    (/ x_m (* y (- t z)))
    (if (<= t 6e-109) (/ 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 <= -1.15e-210) {
		tmp = x_m / (y * (t - z));
	} else if (t <= 6e-109) {
		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 <= (-1.15d-210)) then
        tmp = x_m / (y * (t - z))
    else if (t <= 6d-109) 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 <= -1.15e-210) {
		tmp = x_m / (y * (t - z));
	} else if (t <= 6e-109) {
		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 <= -1.15e-210:
		tmp = x_m / (y * (t - z))
	elif t <= 6e-109:
		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 <= -1.15e-210)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (t <= 6e-109)
		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 <= -1.15e-210)
		tmp = x_m / (y * (t - z));
	elseif (t <= 6e-109)
		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, -1.15e-210], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-109], 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 < -1.15e-210

   1. Initial program 88.0%

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

   3. Taylor expanded in y around inf 59.9%

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

      1. *-commutative 59.9%

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

   5. Simplified 59.9%

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

   if -1.15e-210 < t < 6.00000000000000043e-109

   1. Initial program 90.4%

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

      1. associate-/l/ 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in t around 0 79.8%

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

      1. associate-*r/ 79.8%

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

      2. neg-mul-1 79.8%

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

   7. Simplified 79.8%

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

      1. frac-2neg 79.8%

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

      2. div-inv 79.8%

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

      3. distribute-frac-neg 79.8%

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

      4. remove-double-neg 79.8%

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

      5. sub-neg 79.8%

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

      6. distribute-neg-in 79.8%

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

      7. add-sqr-sqrt 40.7%

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

      8. sqrt-unprod 59.9%

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

      9. sqr-neg 59.9%

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

      10. sqrt-unprod 22.4%

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

      11. add-sqr-sqrt 50.7%

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

      12. add-sqr-sqrt 28.3%

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

      13. sqrt-unprod 61.3%

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

      14. sqr-neg 61.3%

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

      15. sqrt-unprod 39.1%

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

      16. add-sqr-sqrt 79.8%

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

   9. Applied egg-rr 79.8%

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

       1. associate-*r/ 79.8%

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

       2. *-rgt-identity 79.8%

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

       3. neg-mul-1 79.8%

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

       4. +-commutative 79.8%

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

       5. neg-mul-1 79.8%

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

       6. sub-neg 79.8%

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

   11. Simplified 79.8%

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

   12. Taylor expanded in x around 0 73.9%

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

   if 6.00000000000000043e-109 < t

   1. Initial program 87.3%

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

   3. Taylor expanded in t around inf 75.1%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-210}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-109}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 80.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-179}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{y - z}}{t}\\ \end{array} \end{array} \]

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 -1.35e-44)
    (/ (/ x_m y) (- t z))
    (if (<= y 9.5e-179) (/ 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 <= -1.35e-44) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 9.5e-179) {
		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 <= (-1.35d-44)) then
        tmp = (x_m / y) / (t - z)
    else if (y <= 9.5d-179) 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 <= -1.35e-44) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 9.5e-179) {
		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 <= -1.35e-44:
		tmp = (x_m / y) / (t - z)
	elif y <= 9.5e-179:
		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 <= -1.35e-44)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (y <= 9.5e-179)
		tmp = Float64(x_m / Float64(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 <= -1.35e-44)
		tmp = (x_m / y) / (t - z);
	elseif (y <= 9.5e-179)
		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, -1.35e-44], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e-179], N[(x$95$m / N[(z * N[(z - t), $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 < -1.35e-44

   1. Initial program 86.9%

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

   3. Taylor expanded in x around 0 86.9%

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

      1. associate-/l/ 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in y around inf 84.2%

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

   if -1.35e-44 < y < 9.50000000000000037e-179

   1. Initial program 91.3%

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

   3. Taylor expanded in y around 0 78.2%

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

      1. associate-*r/ 78.2%

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

      2. neg-mul-1 78.2%

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

   5. Simplified 78.2%

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

   if 9.50000000000000037e-179 < y

   1. Initial program 87.2%

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

      1. associate-/r* 98.8%

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

      2. div-inv 98.7%

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

   4. Applied egg-rr 98.7%

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

   5. Taylor expanded in t around inf 75.0%

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

      1. un-div-inv 75.1%

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

   7. Applied egg-rr 75.1%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-179}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 48.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+42} \lor \neg \left(z \leq 8.2 \cdot 10^{-84}\right):\\ \;\;\;\;\frac{\frac{x\_m}{y}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \end{array} \end{array} \]

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 -3e+42) (not (<= z 8.2e-84)))
    (/ (/ x_m y) (- z))
    (/ (/ x_m t) y))))

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 <= -3e+42) || !(z <= 8.2e-84)) {
		tmp = (x_m / y) / -z;
	} else {
		tmp = (x_m / t) / y;
	}
	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 <= (-3d+42)) .or. (.not. (z <= 8.2d-84))) then
        tmp = (x_m / y) / -z
    else
        tmp = (x_m / t) / y
    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 <= -3e+42) || !(z <= 8.2e-84)) {
		tmp = (x_m / y) / -z;
	} else {
		tmp = (x_m / t) / y;
	}
	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 <= -3e+42) or not (z <= 8.2e-84):
		tmp = (x_m / y) / -z
	else:
		tmp = (x_m / t) / y
	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 <= -3e+42) || !(z <= 8.2e-84))
		tmp = Float64(Float64(x_m / y) / Float64(-z));
	else
		tmp = Float64(Float64(x_m / t) / y);
	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 <= -3e+42) || ~((z <= 8.2e-84)))
		tmp = (x_m / y) / -z;
	else
		tmp = (x_m / t) / y;
	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, -3e+42], N[Not[LessEqual[z, 8.2e-84]], $MachinePrecision]], N[(N[(x$95$m / y), $MachinePrecision] / (-z)), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -3.00000000000000029e42 or 8.2000000000000001e-84 < z

   1. Initial program 86.5%

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

      1. associate-/l/ 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in t around 0 76.3%

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

      1. associate-*r/ 76.3%

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

      2. neg-mul-1 76.3%

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

   7. Simplified 76.3%

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

   8. Taylor expanded in z around 0 37.0%

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

      1. associate-*r/ 37.0%

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

      2. mul-1-neg 37.0%

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

      3. *-commutative 37.0%

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

   10. Simplified 37.0%

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

   11. Taylor expanded in x around 0 37.0%

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

       1. mul-1-neg 37.0%

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

       2. associate-/r* 37.2%

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

       3. distribute-neg-frac2 37.2%

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

   13. Simplified 37.2%

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

   if -3.00000000000000029e42 < z < 8.2000000000000001e-84

   1. Initial program 90.4%

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

   3. Taylor expanded in z around 0 62.9%

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

      1. associate-/r* 71.7%

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

      2. div-inv 71.7%

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

   5. Applied egg-rr 71.7%

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

      1. un-div-inv 71.7%

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

   7. Applied egg-rr 71.7%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+42} \lor \neg \left(z \leq 8.2 \cdot 10^{-84}\right):\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 45.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -550000000000 \lor \neg \left(z \leq 1.2 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{x\_m}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{y \cdot t}\\ \end{array} \end{array} \]

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 -550000000000.0) (not (<= z 1.2e-36)))
    (/ 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 <= -550000000000.0) || !(z <= 1.2e-36)) {
		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 <= (-550000000000.0d0)) .or. (.not. (z <= 1.2d-36))) 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 <= -550000000000.0) || !(z <= 1.2e-36)) {
		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 <= -550000000000.0) or not (z <= 1.2e-36):
		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 <= -550000000000.0) || !(z <= 1.2e-36))
		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 <= -550000000000.0) || ~((z <= 1.2e-36)))
		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, -550000000000.0], N[Not[LessEqual[z, 1.2e-36]], $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 < -5.5e11 or 1.2e-36 < z

   1. Initial program 83.9%

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

      1. associate-/l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 80.8%

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

      1. associate-*r/ 80.8%

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

      2. neg-mul-1 80.8%

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

   7. Simplified 80.8%

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

      1. div-inv 80.9%

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

      2. add-sqr-sqrt 37.1%

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

      3. sqrt-unprod 55.0%

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

      4. sqr-neg 55.0%

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

      5. sqrt-unprod 27.5%

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

      6. add-sqr-sqrt 52.4%

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

      7. sub-neg 52.4%

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

      8. add-sqr-sqrt 26.9%

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

      9. sqrt-unprod 60.1%

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

      10. sqr-neg 60.1%

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

      11. sqrt-unprod 37.6%

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

      12. add-sqr-sqrt 72.4%

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

   9. Applied egg-rr 72.4%

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

   10. Taylor expanded in z around 0 33.7%

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

       1. *-commutative 33.7%

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

   12. Simplified 33.7%

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

   if -5.5e11 < z < 1.2e-36

   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 62.3%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -550000000000 \lor \neg \left(z \leq 1.2 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 47.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+105} \lor \neg \left(z \leq 1.2 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{x\_m}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \end{array} \end{array} \]

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 -1.08e+105) (not (<= z 1.2e-36)))
    (/ x_m (* y z))
    (/ (/ x_m t) y))))

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 <= -1.08e+105) || !(z <= 1.2e-36)) {
		tmp = x_m / (y * z);
	} else {
		tmp = (x_m / t) / y;
	}
	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 <= (-1.08d+105)) .or. (.not. (z <= 1.2d-36))) then
        tmp = x_m / (y * z)
    else
        tmp = (x_m / t) / y
    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 <= -1.08e+105) || !(z <= 1.2e-36)) {
		tmp = x_m / (y * z);
	} else {
		tmp = (x_m / t) / y;
	}
	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 <= -1.08e+105) or not (z <= 1.2e-36):
		tmp = x_m / (y * z)
	else:
		tmp = (x_m / t) / y
	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 <= -1.08e+105) || !(z <= 1.2e-36))
		tmp = Float64(x_m / Float64(y * z));
	else
		tmp = Float64(Float64(x_m / t) / y);
	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 <= -1.08e+105) || ~((z <= 1.2e-36)))
		tmp = x_m / (y * z);
	else
		tmp = (x_m / t) / y;
	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, -1.08e+105], N[Not[LessEqual[z, 1.2e-36]], $MachinePrecision]], N[(x$95$m / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.07999999999999994e105 or 1.2e-36 < z

   1. Initial program 83.9%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 84.6%

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

      1. associate-*r/ 84.6%

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

      2. neg-mul-1 84.6%

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

   7. Simplified 84.6%

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

      1. div-inv 84.6%

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

      2. add-sqr-sqrt 36.8%

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

      3. sqrt-unprod 58.8%

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

      4. sqr-neg 58.8%

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

      5. sqrt-unprod 32.0%

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

      6. add-sqr-sqrt 59.5%

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

      7. sub-neg 59.5%

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

      8. add-sqr-sqrt 28.0%

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

      9. sqrt-unprod 68.9%

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

      10. sqr-neg 68.9%

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

      11. sqrt-unprod 46.1%

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

      12. add-sqr-sqrt 79.0%

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

   9. Applied egg-rr 79.0%

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

   10. Taylor expanded in z around 0 37.7%

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

       1. *-commutative 37.7%

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

   12. Simplified 37.7%

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

   if -1.07999999999999994e105 < z < 1.2e-36

   1. Initial program 91.3%

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

   3. Taylor expanded in z around 0 54.5%

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

      1. associate-/r* 61.9%

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

      2. div-inv 61.9%

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

   5. Applied egg-rr 61.9%

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

      1. un-div-inv 61.9%

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

   7. Applied egg-rr 61.9%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+105} \lor \neg \left(z \leq 1.2 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 39.7% 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 88.3%

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

3. Taylor expanded in z around 0 40.5%

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

4. Final simplification 40.5%

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

Developer target: 88.3% 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 2024078 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :alt
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

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