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

Percentage Accurate: 89.5% → 97.8%

Time: 10.5s

Alternatives: 22

Speedup: 0.4×

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: 89.5% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (/ x (* (- y z) (- t z))))

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / ((y - z) * (t - z))
end function

Java

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

Python

def code(x, y, z, t):
	return x / ((y - z) * (t - z))

Julia

function code(x, y, z, t)
	return Float64(x / Float64(Float64(y - z) * Float64(t - z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x / ((y - z) * (t - z));
end

Wolfram

code[x_, y_, z_, t_] := N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x\_m}{\left(y - z\right) \cdot \left(t - z\right)}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{x\_m}{t - z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 (* (- y z) (- t z)))))
   (* x_s (if (<= t_1 0.0) (/ (/ x_m (- t z)) (- 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 / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= 0.0) {
		tmp = (x_m / (t - z)) / (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 / ((y - z) * (t - z))
    if (t_1 <= 0.0d0) then
        tmp = (x_m / (t - z)) / (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 / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= 0.0) {
		tmp = (x_m / (t - z)) / (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 / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= 0.0:
		tmp = (x_m / (t - z)) / (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(x_m / Float64(Float64(y - z) * Float64(t - z)))
	tmp = 0.0
	if (t_1 <= 0.0)
		tmp = Float64(Float64(x_m / Float64(t - z)) / Float64(y - 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 / ((y - z) * (t - z));
	tmp = 0.0;
	if (t_1 <= 0.0)
		tmp = (x_m / (t - z)) / (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[(x$95$m / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$1, 0.0], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], t$95$1]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 79.4%

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

      1. associate-/l/ 97.2%

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

   3. Simplified 97.2%

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

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

   1. Initial program 98.4%

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

4. Final simplification 97.6%

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

Alternative 2: 49.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{y}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-42}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= z -4.5e+106)
    (/ (/ x_m z) y)
    (if (<= z -2.5e-42)
      (/ x_m (* y (- z)))
      (if (<= z 2.2e+18) (/ (/ x_m t) y) (/ 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 tmp;
	if (z <= -4.5e+106) {
		tmp = (x_m / z) / y;
	} else if (z <= -2.5e-42) {
		tmp = x_m / (y * -z);
	} else if (z <= 2.2e+18) {
		tmp = (x_m / t) / y;
	} 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) :: tmp
    if (z <= (-4.5d+106)) then
        tmp = (x_m / z) / y
    else if (z <= (-2.5d-42)) then
        tmp = x_m / (y * -z)
    else if (z <= 2.2d+18) then
        tmp = (x_m / t) / y
    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 tmp;
	if (z <= -4.5e+106) {
		tmp = (x_m / z) / y;
	} else if (z <= -2.5e-42) {
		tmp = x_m / (y * -z);
	} else if (z <= 2.2e+18) {
		tmp = (x_m / t) / y;
	} 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):
	tmp = 0
	if z <= -4.5e+106:
		tmp = (x_m / z) / y
	elif z <= -2.5e-42:
		tmp = x_m / (y * -z)
	elif z <= 2.2e+18:
		tmp = (x_m / t) / y
	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)
	tmp = 0.0
	if (z <= -4.5e+106)
		tmp = Float64(Float64(x_m / z) / y);
	elseif (z <= -2.5e-42)
		tmp = Float64(x_m / Float64(y * Float64(-z)));
	elseif (z <= 2.2e+18)
		tmp = Float64(Float64(x_m / t) / y);
	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)
	tmp = 0.0;
	if (z <= -4.5e+106)
		tmp = (x_m / z) / y;
	elseif (z <= -2.5e-42)
		tmp = x_m / (y * -z);
	elseif (z <= 2.2e+18)
		tmp = (x_m / t) / y;
	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_] := N[(x$95$s * If[LessEqual[z, -4.5e+106], N[(N[(x$95$m / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, -2.5e-42], N[(x$95$m / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+18], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision], N[(x$95$m / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if z < -4.4999999999999997e106

   1. Initial program 65.0%

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

   3. Taylor expanded in y around inf 32.5%

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

      1. *-commutative 32.5%

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

   5. Simplified 32.5%

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

      1. *-un-lft-identity 32.5%

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

      2. times-frac 33.6%

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

   7. Applied egg-rr 33.6%

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

   8. Taylor expanded in t around 0 33.5%

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

      1. frac-times 32.3%

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

      2. neg-mul-1 32.3%

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

      3. add-sqr-sqrt 17.9%

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

      4. sqrt-unprod 39.5%

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

      5. sqr-neg 39.5%

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

      6. sqrt-unprod 13.5%

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

      7. add-sqr-sqrt 31.4%

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

      8. associate-/r* 40.2%

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

   10. Applied egg-rr 40.2%

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

   if -4.4999999999999997e106 < z < -2.50000000000000001e-42

   1. Initial program 93.1%

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

   3. Taylor expanded in y around inf 44.1%

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

      1. *-commutative 44.1%

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

   5. Simplified 44.1%

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

   6. Taylor expanded in t around 0 43.4%

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

      1. associate-*r/ 43.4%

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

      2. mul-1-neg 43.4%

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

      3. *-commutative 43.4%

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

   8. Simplified 43.4%

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

   if -2.50000000000000001e-42 < z < 2.2e18

   1. Initial program 93.6%

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

      1. associate-/l/ 92.5%

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

      2. div-inv 92.5%

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

   4. Applied egg-rr 92.5%

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

      1. *-commutative 92.5%

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

      2. clear-num 92.3%

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

      3. un-div-inv 92.5%

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

   6. Applied egg-rr 92.5%

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

   7. Taylor expanded in y around inf 71.5%

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

      1. associate-/l/ 71.7%

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

   9. Simplified 71.7%

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

   10. Taylor expanded in t around inf 57.4%

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

   if 2.2e18 < z

   1. Initial program 75.8%

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

   3. Taylor expanded in y around 0 57.7%

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

      1. associate-*r/ 57.7%

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

      2. neg-mul-1 57.7%

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

   5. Simplified 57.7%

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

   6. Taylor expanded in z around 0 39.5%

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

      1. associate-*r/ 39.5%

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

      2. mul-1-neg 39.5%

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

   8. Simplified 39.5%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+106}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{y}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-45}:\\ \;\;\;\;\frac{\frac{x\_m}{-y}}{z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= z -2.6e+106)
    (/ (/ x_m z) y)
    (if (<= z -1.1e-45)
      (/ (/ x_m (- y)) z)
      (if (<= z 1.55e+18) (/ (/ x_m t) y) (/ 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 tmp;
	if (z <= -2.6e+106) {
		tmp = (x_m / z) / y;
	} else if (z <= -1.1e-45) {
		tmp = (x_m / -y) / z;
	} else if (z <= 1.55e+18) {
		tmp = (x_m / t) / y;
	} 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) :: tmp
    if (z <= (-2.6d+106)) then
        tmp = (x_m / z) / y
    else if (z <= (-1.1d-45)) then
        tmp = (x_m / -y) / z
    else if (z <= 1.55d+18) then
        tmp = (x_m / t) / y
    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 tmp;
	if (z <= -2.6e+106) {
		tmp = (x_m / z) / y;
	} else if (z <= -1.1e-45) {
		tmp = (x_m / -y) / z;
	} else if (z <= 1.55e+18) {
		tmp = (x_m / t) / y;
	} 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):
	tmp = 0
	if z <= -2.6e+106:
		tmp = (x_m / z) / y
	elif z <= -1.1e-45:
		tmp = (x_m / -y) / z
	elif z <= 1.55e+18:
		tmp = (x_m / t) / y
	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)
	tmp = 0.0
	if (z <= -2.6e+106)
		tmp = Float64(Float64(x_m / z) / y);
	elseif (z <= -1.1e-45)
		tmp = Float64(Float64(x_m / Float64(-y)) / z);
	elseif (z <= 1.55e+18)
		tmp = Float64(Float64(x_m / t) / y);
	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)
	tmp = 0.0;
	if (z <= -2.6e+106)
		tmp = (x_m / z) / y;
	elseif (z <= -1.1e-45)
		tmp = (x_m / -y) / z;
	elseif (z <= 1.55e+18)
		tmp = (x_m / t) / y;
	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_] := N[(x$95$s * If[LessEqual[z, -2.6e+106], N[(N[(x$95$m / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, -1.1e-45], N[(N[(x$95$m / (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.55e+18], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision], N[(x$95$m / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if z < -2.6000000000000002e106

   1. Initial program 65.0%

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

   3. Taylor expanded in y around inf 32.5%

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

      1. *-commutative 32.5%

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

   5. Simplified 32.5%

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

      1. *-un-lft-identity 32.5%

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

      2. times-frac 33.6%

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

   7. Applied egg-rr 33.6%

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

   8. Taylor expanded in t around 0 33.5%

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

      1. frac-times 32.3%

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

      2. neg-mul-1 32.3%

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

      3. add-sqr-sqrt 17.9%

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

      4. sqrt-unprod 39.5%

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

      5. sqr-neg 39.5%

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

      6. sqrt-unprod 13.5%

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

      7. add-sqr-sqrt 31.4%

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

      8. associate-/r* 40.2%

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

   10. Applied egg-rr 40.2%

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

   if -2.6000000000000002e106 < z < -1.09999999999999997e-45

   1. Initial program 93.1%

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

   3. Taylor expanded in y around inf 44.1%

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

      1. *-commutative 44.1%

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

   5. Simplified 44.1%

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

      1. *-un-lft-identity 44.1%

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

      2. times-frac 50.3%

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

   7. Applied egg-rr 50.3%

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

   8. Taylor expanded in t around 0 43.4%

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

      1. mul-1-neg 43.4%

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

      2. associate-/r* 46.6%

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

      3. distribute-neg-frac2 46.6%

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

   10. Simplified 46.6%

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

   if -1.09999999999999997e-45 < z < 1.55e18

   1. Initial program 93.6%

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

      1. associate-/l/ 92.5%

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

      2. div-inv 92.5%

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

   4. Applied egg-rr 92.5%

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

      1. *-commutative 92.5%

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

      2. clear-num 92.3%

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

      3. un-div-inv 92.5%

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

   6. Applied egg-rr 92.5%

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

   7. Taylor expanded in y around inf 71.5%

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

      1. associate-/l/ 71.7%

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

   9. Simplified 71.7%

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

   10. Taylor expanded in t around inf 57.4%

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

   if 1.55e18 < z

   1. Initial program 75.8%

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

   3. Taylor expanded in y around 0 57.7%

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

      1. associate-*r/ 57.7%

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

      2. neg-mul-1 57.7%

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

   5. Simplified 57.7%

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

   6. Taylor expanded in z around 0 39.5%

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

      1. associate-*r/ 39.5%

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

      2. mul-1-neg 39.5%

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

   8. Simplified 39.5%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+106}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-45}:\\ \;\;\;\;\frac{\frac{x}{-y}}{z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x\_m}{z}}{-z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{x\_m}{-y}}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x_m z) (- z))))
   (*
    x_s
    (if (<= z -6.8e+102)
      t_1
      (if (<= z -2.7e-44)
        (/ (/ x_m (- y)) z)
        (if (<= z 3e+66) (/ (/ x_m t) y) t_1))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / z) / -z;
	double tmp;
	if (z <= -6.8e+102) {
		tmp = t_1;
	} else if (z <= -2.7e-44) {
		tmp = (x_m / -y) / z;
	} else if (z <= 3e+66) {
		tmp = (x_m / t) / y;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x_m / z) / -z
    if (z <= (-6.8d+102)) then
        tmp = t_1
    else if (z <= (-2.7d-44)) then
        tmp = (x_m / -y) / z
    else if (z <= 3d+66) then
        tmp = (x_m / t) / y
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / z) / -z;
	double tmp;
	if (z <= -6.8e+102) {
		tmp = t_1;
	} else if (z <= -2.7e-44) {
		tmp = (x_m / -y) / z;
	} else if (z <= 3e+66) {
		tmp = (x_m / t) / y;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	t_1 = (x_m / z) / -z
	tmp = 0
	if z <= -6.8e+102:
		tmp = t_1
	elif z <= -2.7e-44:
		tmp = (x_m / -y) / z
	elif z <= 3e+66:
		tmp = (x_m / t) / y
	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(-z))
	tmp = 0.0
	if (z <= -6.8e+102)
		tmp = t_1;
	elseif (z <= -2.7e-44)
		tmp = Float64(Float64(x_m / Float64(-y)) / z);
	elseif (z <= 3e+66)
		tmp = Float64(Float64(x_m / t) / y);
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m / z) / -z;
	tmp = 0.0;
	if (z <= -6.8e+102)
		tmp = t_1;
	elseif (z <= -2.7e-44)
		tmp = (x_m / -y) / z;
	elseif (z <= 3e+66)
		tmp = (x_m / t) / y;
	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] / (-z)), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -6.8e+102], t$95$1, If[LessEqual[z, -2.7e-44], N[(N[(x$95$m / (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3e+66], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8000000000000001e102 or 3.00000000000000002e66 < z

   1. Initial program 68.4%

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

   3. Taylor expanded in y around 0 64.9%

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

      1. associate-*r/ 64.9%

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

      2. neg-mul-1 64.9%

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

   5. Simplified 64.9%

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

      1. div-inv 64.9%

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

      2. add-sqr-sqrt 29.7%

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

      3. sqrt-unprod 57.5%

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

      4. sqr-neg 57.5%

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

      5. sqrt-unprod 33.1%

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

      6. add-sqr-sqrt 59.5%

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

   7. Applied egg-rr 59.5%

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

      1. *-commutative 59.5%

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

      2. associate-*l/ 59.5%

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

      3. times-frac 59.0%

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

      4. associate-*l/ 59.0%

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

      5. *-lft-identity 59.0%

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

   9. Simplified 59.0%

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

   10. Taylor expanded in t around 0 55.8%

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

       1. associate-*r/ 45.1%

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

       2. neg-mul-1 45.1%

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

   12. Simplified 55.8%

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

   if -6.8000000000000001e102 < z < -2.6999999999999999e-44

   1. Initial program 92.6%

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

   3. Taylor expanded in y around inf 43.4%

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

      1. *-commutative 43.4%

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

   5. Simplified 43.4%

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

      1. *-un-lft-identity 43.4%

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

      2. times-frac 50.1%

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

   7. Applied egg-rr 50.1%

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

   8. Taylor expanded in t around 0 42.6%

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

      1. mul-1-neg 42.6%

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

      2. associate-/r* 46.1%

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

      3. distribute-neg-frac2 46.1%

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

   10. Simplified 46.1%

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

   if -2.6999999999999999e-44 < z < 3.00000000000000002e66

   1. Initial program 93.4%

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

      1. associate-/l/ 93.0%

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

      2. div-inv 93.0%

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

   4. Applied egg-rr 93.0%

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

      1. *-commutative 93.0%

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

      2. clear-num 92.8%

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

      3. un-div-inv 93.0%

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

   6. Applied egg-rr 93.0%

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

   7. Taylor expanded in y around inf 72.1%

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

      1. associate-/l/ 72.9%

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

   9. Simplified 72.9%

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

   10. Taylor expanded in t around inf 56.0%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+102}:\\ \;\;\;\;\frac{\frac{x}{z}}{-z}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{x}{-y}}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x\_m}{z}}{-z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-43}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{y}{x\_m}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+69}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x_m z) (- z))))
   (*
    x_s
    (if (<= z -7.5e+102)
      t_1
      (if (<= z -4.2e-43)
        (/ -1.0 (* z (/ y x_m)))
        (if (<= z 1.3e+69) (/ (/ x_m t) y) t_1))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / z) / -z;
	double tmp;
	if (z <= -7.5e+102) {
		tmp = t_1;
	} else if (z <= -4.2e-43) {
		tmp = -1.0 / (z * (y / x_m));
	} else if (z <= 1.3e+69) {
		tmp = (x_m / t) / y;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x_m / z) / -z
    if (z <= (-7.5d+102)) then
        tmp = t_1
    else if (z <= (-4.2d-43)) then
        tmp = (-1.0d0) / (z * (y / x_m))
    else if (z <= 1.3d+69) then
        tmp = (x_m / t) / y
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / z) / -z;
	double tmp;
	if (z <= -7.5e+102) {
		tmp = t_1;
	} else if (z <= -4.2e-43) {
		tmp = -1.0 / (z * (y / x_m));
	} else if (z <= 1.3e+69) {
		tmp = (x_m / t) / y;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	t_1 = (x_m / z) / -z
	tmp = 0
	if z <= -7.5e+102:
		tmp = t_1
	elif z <= -4.2e-43:
		tmp = -1.0 / (z * (y / x_m))
	elif z <= 1.3e+69:
		tmp = (x_m / t) / y
	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(-z))
	tmp = 0.0
	if (z <= -7.5e+102)
		tmp = t_1;
	elseif (z <= -4.2e-43)
		tmp = Float64(-1.0 / Float64(z * Float64(y / x_m)));
	elseif (z <= 1.3e+69)
		tmp = Float64(Float64(x_m / t) / y);
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m / z) / -z;
	tmp = 0.0;
	if (z <= -7.5e+102)
		tmp = t_1;
	elseif (z <= -4.2e-43)
		tmp = -1.0 / (z * (y / x_m));
	elseif (z <= 1.3e+69)
		tmp = (x_m / t) / y;
	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] / (-z)), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -7.5e+102], t$95$1, If[LessEqual[z, -4.2e-43], N[(-1.0 / N[(z * N[(y / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+69], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5e102 or 1.3000000000000001e69 < z

   1. Initial program 68.4%

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

   3. Taylor expanded in y around 0 64.9%

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

      1. associate-*r/ 64.9%

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

      2. neg-mul-1 64.9%

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

   5. Simplified 64.9%

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

      1. div-inv 64.9%

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

      2. add-sqr-sqrt 29.7%

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

      3. sqrt-unprod 57.5%

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

      4. sqr-neg 57.5%

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

      5. sqrt-unprod 33.1%

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

      6. add-sqr-sqrt 59.5%

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

   7. Applied egg-rr 59.5%

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

      1. *-commutative 59.5%

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

      2. associate-*l/ 59.5%

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

      3. times-frac 59.0%

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

      4. associate-*l/ 59.0%

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

      5. *-lft-identity 59.0%

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

   9. Simplified 59.0%

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

   10. Taylor expanded in t around 0 55.8%

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

       1. associate-*r/ 45.1%

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

       2. neg-mul-1 45.1%

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

   12. Simplified 55.8%

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

   if -7.5e102 < z < -4.2000000000000001e-43

   1. Initial program 92.6%

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

   3. Taylor expanded in y around inf 43.4%

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

      1. *-commutative 43.4%

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

   5. Simplified 43.4%

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

      1. *-un-lft-identity 43.4%

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

      2. times-frac 50.1%

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

   7. Applied egg-rr 50.1%

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

   8. Taylor expanded in t around 0 46.0%

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

      1. *-commutative 46.0%

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

      2. clear-num 45.9%

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

      3. frac-times 46.1%

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

      4. metadata-eval 46.1%

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

   10. Applied egg-rr 46.1%

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

   if -4.2000000000000001e-43 < z < 1.3000000000000001e69

   1. Initial program 93.4%

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

      1. associate-/l/ 93.0%

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

      2. div-inv 93.0%

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

   4. Applied egg-rr 93.0%

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

      1. *-commutative 93.0%

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

      2. clear-num 92.8%

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

      3. un-div-inv 93.0%

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

   6. Applied egg-rr 93.0%

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

   7. Taylor expanded in y around inf 72.1%

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

      1. associate-/l/ 72.9%

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

   9. Simplified 72.9%

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

   10. Taylor expanded in t around inf 56.0%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+102}:\\ \;\;\;\;\frac{\frac{x}{z}}{-z}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-43}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{y}{x}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+69}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\frac{x\_m}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{t - z} \cdot \frac{-1}{z}\\ \end{array} \end{array} \end{array} \]

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 (* (- y z) (- t z))))
   (* x_s (if (<= t_1 5e+304) (/ x_m t_1) (* (/ x_m (- t 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 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= 5e+304) {
		tmp = x_m / t_1;
	} else {
		tmp = (x_m / (t - 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 = (y - z) * (t - z)
    if (t_1 <= 5d+304) then
        tmp = x_m / t_1
    else
        tmp = (x_m / (t - 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 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= 5e+304) {
		tmp = x_m / t_1;
	} else {
		tmp = (x_m / (t - 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 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= 5e+304:
		tmp = x_m / t_1
	else:
		tmp = (x_m / (t - 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(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= 5e+304)
		tmp = Float64(x_m / t_1);
	else
		tmp = Float64(Float64(x_m / Float64(t - 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 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= 5e+304)
		tmp = x_m / t_1;
	else
		tmp = (x_m / (t - 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[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$1, 5e+304], N[(x$95$m / t$95$1), $MachinePrecision], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < 4.9999999999999997e304

   1. Initial program 95.1%

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

   if 4.9999999999999997e304 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 58.5%

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

      1. associate-/l/ 100.0%

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

      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 86.2%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{-1}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\frac{x\_m}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{t - z}{x\_m}}\\ \end{array} \end{array} \end{array} \]

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 (<= t_1 5e+304) (/ x_m t_1) (/ (/ -1.0 z) (/ (- t z) x_m))))))

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 <= 5e+304) {
		tmp = x_m / t_1;
	} else {
		tmp = (-1.0 / z) / ((t - z) / x_m);
	}
	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 <= 5d+304) then
        tmp = x_m / t_1
    else
        tmp = ((-1.0d0) / z) / ((t - z) / x_m)
    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 <= 5e+304) {
		tmp = x_m / t_1;
	} else {
		tmp = (-1.0 / z) / ((t - z) / x_m);
	}
	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 <= 5e+304:
		tmp = x_m / t_1
	else:
		tmp = (-1.0 / z) / ((t - z) / x_m)
	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 <= 5e+304)
		tmp = Float64(x_m / t_1);
	else
		tmp = Float64(Float64(-1.0 / z) / Float64(Float64(t - z) / x_m));
	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 <= 5e+304)
		tmp = x_m / t_1;
	else
		tmp = (-1.0 / z) / ((t - z) / x_m);
	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[LessEqual[t$95$1, 5e+304], N[(x$95$m / t$95$1), $MachinePrecision], N[(N[(-1.0 / z), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] / x$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < 4.9999999999999997e304

   1. Initial program 95.1%

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

   if 4.9999999999999997e304 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 58.5%

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

      1. associate-/l/ 100.0%

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

      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. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 86.2%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{t - z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-81}:\\ \;\;\;\;\frac{x\_m}{t - z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

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 -1.55e-44)
    (/ (/ x_m y) (- t z))
    (if (<= y 1.52e-81)
      (* (/ x_m (- t z)) (/ -1.0 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 (y <= -1.55e-44) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 1.52e-81) {
		tmp = (x_m / (t - z)) * (-1.0 / 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 (y <= (-1.55d-44)) then
        tmp = (x_m / y) / (t - z)
    else if (y <= 1.52d-81) then
        tmp = (x_m / (t - z)) * ((-1.0d0) / 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 (y <= -1.55e-44) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 1.52e-81) {
		tmp = (x_m / (t - z)) * (-1.0 / 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 y <= -1.55e-44:
		tmp = (x_m / y) / (t - z)
	elif y <= 1.52e-81:
		tmp = (x_m / (t - z)) * (-1.0 / 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 (y <= -1.55e-44)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (y <= 1.52e-81)
		tmp = Float64(Float64(x_m / Float64(t - z)) * Float64(-1.0 / 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 (y <= -1.55e-44)
		tmp = (x_m / y) / (t - z);
	elseif (y <= 1.52e-81)
		tmp = (x_m / (t - z)) * (-1.0 / 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[y, -1.55e-44], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.52e-81], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -1.54999999999999992e-44

   1. Initial program 88.9%

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

      1. associate-/l/ 95.4%

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

      2. div-inv 95.4%

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

   4. Applied egg-rr 95.4%

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

   5. Taylor expanded in y around inf 88.1%

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

      1. associate-/r* 93.1%

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

   7. Simplified 93.1%

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

   if -1.54999999999999992e-44 < y < 1.52000000000000008e-81

   1. Initial program 83.0%

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

      1. associate-/l/ 96.1%

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

      2. div-inv 96.0%

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

   4. Applied egg-rr 96.0%

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

   5. Taylor expanded in y around 0 82.9%

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

   if 1.52000000000000008e-81 < y

   1. Initial program 84.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 inf 59.0%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{-67}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-161}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 -4.9e-67)
    (/ (/ x_m t) y)
    (if (<= t 4.3e-161) (/ (/ 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 <= -4.9e-67) {
		tmp = (x_m / t) / y;
	} else if (t <= 4.3e-161) {
		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 <= (-4.9d-67)) then
        tmp = (x_m / t) / y
    else if (t <= 4.3d-161) 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 <= -4.9e-67) {
		tmp = (x_m / t) / y;
	} else if (t <= 4.3e-161) {
		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 <= -4.9e-67:
		tmp = (x_m / t) / y
	elif t <= 4.3e-161:
		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 <= -4.9e-67)
		tmp = Float64(Float64(x_m / t) / y);
	elseif (t <= 4.3e-161)
		tmp = Float64(Float64(x_m / 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 <= -4.9e-67)
		tmp = (x_m / t) / y;
	elseif (t <= 4.3e-161)
		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, -4.9e-67], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 4.3e-161], N[(N[(x$95$m / z), $MachinePrecision] / (-y)), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -4.89999999999999993e-67

   1. Initial program 88.6%

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

      1. associate-/l/ 96.0%

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

      2. div-inv 96.0%

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

   4. Applied egg-rr 96.0%

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

      1. *-commutative 96.0%

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

      2. clear-num 95.8%

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

      3. un-div-inv 96.0%

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

   6. Applied egg-rr 96.0%

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

   7. Taylor expanded in y around inf 52.9%

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

      1. associate-/l/ 55.4%

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

   9. Simplified 55.4%

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

   10. Taylor expanded in t around inf 49.8%

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

   if -4.89999999999999993e-67 < t < 4.29999999999999967e-161

   1. Initial program 90.1%

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

      1. associate-/l/ 93.3%

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

      2. div-inv 93.2%

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

   4. Applied egg-rr 93.2%

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

      1. *-commutative 93.2%

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

      2. clear-num 93.0%

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

      3. un-div-inv 93.1%

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

   6. Applied egg-rr 93.1%

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

   7. Taylor expanded in y around inf 61.2%

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

      1. associate-/l/ 62.2%

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

   9. Simplified 62.2%

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

   10. Taylor expanded in t around 0 52.7%

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

       1. associate-*r/ 52.7%

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

       2. neg-mul-1 52.7%

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

   12. Simplified 52.7%

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

   if 4.29999999999999967e-161 < t

   1. Initial program 77.2%

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

   3. Taylor expanded in t around inf 63.0%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{-67}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-161}:\\ \;\;\;\;\frac{\frac{x}{z}}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-45}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-220}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

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 (<= y -1.22e-45)
    (/ (/ x_m y) (- t z))
    (if (<= y 1.95e-220) (/ x_m (* z (- z t))) (/ (/ x_m t) (- y z))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -1.22e-45) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 1.95e-220) {
		tmp = x_m / (z * (z - t));
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.22d-45)) then
        tmp = (x_m / y) / (t - z)
    else if (y <= 1.95d-220) then
        tmp = x_m / (z * (z - t))
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -1.22e-45) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 1.95e-220) {
		tmp = x_m / (z * (z - t));
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -1.22e-45:
		tmp = (x_m / y) / (t - z)
	elif y <= 1.95e-220:
		tmp = x_m / (z * (z - t))
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -1.22e-45)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (y <= 1.95e-220)
		tmp = Float64(x_m / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -1.22e-45)
		tmp = (x_m / y) / (t - z);
	elseif (y <= 1.95e-220)
		tmp = x_m / (z * (z - t));
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -1.22e-45], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e-220], N[(x$95$m / N[(z * N[(z - t), $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 y < -1.22000000000000007e-45

   1. Initial program 89.0%

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

      1. associate-/l/ 95.5%

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

      2. div-inv 95.4%

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

   4. Applied egg-rr 95.4%

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

   5. Taylor expanded in y around inf 88.3%

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

      1. associate-/r* 93.2%

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

   7. Simplified 93.2%

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

   if -1.22000000000000007e-45 < y < 1.95000000000000001e-220

   1. Initial program 82.3%

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

   3. Taylor expanded in y around 0 70.7%

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

      1. associate-*r/ 70.7%

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

      2. neg-mul-1 70.7%

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

   5. Simplified 70.7%

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

   if 1.95000000000000001e-220 < y

   1. Initial program 84.2%

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

      1. associate-/l/ 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in t around inf 58.9%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-45}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-220}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-45}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-118}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -2.6e-45)
    (/ (/ x_m y) (- t z))
    (if (<= y 3.3e-118) (/ (/ x_m z) (- z t)) (/ (/ x_m t) (- y z))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e-45) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 3.3e-118) {
		tmp = (x_m / z) / (z - t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.6d-45)) then
        tmp = (x_m / y) / (t - z)
    else if (y <= 3.3d-118) then
        tmp = (x_m / z) / (z - t)
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e-45) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 3.3e-118) {
		tmp = (x_m / z) / (z - t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -2.6e-45:
		tmp = (x_m / y) / (t - z)
	elif y <= 3.3e-118:
		tmp = (x_m / z) / (z - t)
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -2.6e-45)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (y <= 3.3e-118)
		tmp = Float64(Float64(x_m / z) / Float64(z - t));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -2.6e-45)
		tmp = (x_m / y) / (t - z);
	elseif (y <= 3.3e-118)
		tmp = (x_m / z) / (z - t);
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -2.6e-45], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e-118], N[(N[(x$95$m / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -2.59999999999999987e-45

   1. Initial program 88.9%

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

      1. associate-/l/ 95.4%

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

      2. div-inv 95.4%

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

   4. Applied egg-rr 95.4%

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

   5. Taylor expanded in y around inf 88.1%

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

      1. associate-/r* 93.1%

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

   7. Simplified 93.1%

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

   if -2.59999999999999987e-45 < y < 3.3e-118

   1. Initial program 83.3%

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

   3. Taylor expanded in x around 0 83.3%

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

      1. associate-/l/ 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in y around 0 81.7%

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

      1. mul-1-neg 81.7%

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

   8. Simplified 81.7%

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

   if 3.3e-118 < y

   1. Initial program 83.9%

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

      1. associate-/l/ 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in t around inf 59.9%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-45}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-118}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-93} \lor \neg \left(y \leq 1.5 \cdot 10^{-81}\right):\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= y -1.55e-93) (not (<= y 1.5e-81)))
    (/ (/ x_m t) y)
    (/ 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 tmp;
	if ((y <= -1.55e-93) || !(y <= 1.5e-81)) {
		tmp = (x_m / t) / y;
	} 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) :: tmp
    if ((y <= (-1.55d-93)) .or. (.not. (y <= 1.5d-81))) then
        tmp = (x_m / t) / y
    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 tmp;
	if ((y <= -1.55e-93) || !(y <= 1.5e-81)) {
		tmp = (x_m / t) / y;
	} 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):
	tmp = 0
	if (y <= -1.55e-93) or not (y <= 1.5e-81):
		tmp = (x_m / t) / y
	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)
	tmp = 0.0
	if ((y <= -1.55e-93) || !(y <= 1.5e-81))
		tmp = Float64(Float64(x_m / t) / y);
	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)
	tmp = 0.0;
	if ((y <= -1.55e-93) || ~((y <= 1.5e-81)))
		tmp = (x_m / t) / y;
	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_] := N[(x$95$s * If[Or[LessEqual[y, -1.55e-93], N[Not[LessEqual[y, 1.5e-81]], $MachinePrecision]], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision], N[(x$95$m / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -1.55e-93 or 1.4999999999999999e-81 < y

   1. Initial program 85.8%

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

      1. associate-/l/ 96.2%

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

      2. div-inv 96.2%

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

   4. Applied egg-rr 96.2%

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

      1. *-commutative 96.2%

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

      2. clear-num 96.0%

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

      3. un-div-inv 96.1%

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

   6. Applied egg-rr 96.1%

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

   7. Taylor expanded in y around inf 76.6%

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

      1. associate-/l/ 80.4%

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

   9. Simplified 80.4%

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

   10. Taylor expanded in t around inf 52.3%

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

   if -1.55e-93 < y < 1.4999999999999999e-81

   1. Initial program 83.6%

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

   3. Taylor expanded in y around 0 68.6%

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

      1. associate-*r/ 68.6%

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

      2. neg-mul-1 68.6%

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

   5. Simplified 68.6%

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

   6. Taylor expanded in z around 0 41.8%

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

      1. associate-*r/ 41.8%

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

      2. mul-1-neg 41.8%

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

   8. Simplified 41.8%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-93} \lor \neg \left(y \leq 1.5 \cdot 10^{-81}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{-y}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= z -2.2e-42)
    (/ (/ x_m z) (- y))
    (if (<= z 2.5e+18) (/ (/ x_m t) y) (/ 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 tmp;
	if (z <= -2.2e-42) {
		tmp = (x_m / z) / -y;
	} else if (z <= 2.5e+18) {
		tmp = (x_m / t) / y;
	} 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) :: tmp
    if (z <= (-2.2d-42)) then
        tmp = (x_m / z) / -y
    else if (z <= 2.5d+18) then
        tmp = (x_m / t) / y
    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 tmp;
	if (z <= -2.2e-42) {
		tmp = (x_m / z) / -y;
	} else if (z <= 2.5e+18) {
		tmp = (x_m / t) / y;
	} 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):
	tmp = 0
	if z <= -2.2e-42:
		tmp = (x_m / z) / -y
	elif z <= 2.5e+18:
		tmp = (x_m / t) / y
	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)
	tmp = 0.0
	if (z <= -2.2e-42)
		tmp = Float64(Float64(x_m / z) / Float64(-y));
	elseif (z <= 2.5e+18)
		tmp = Float64(Float64(x_m / t) / y);
	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)
	tmp = 0.0;
	if (z <= -2.2e-42)
		tmp = (x_m / z) / -y;
	elseif (z <= 2.5e+18)
		tmp = (x_m / t) / y;
	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_] := N[(x$95$s * If[LessEqual[z, -2.2e-42], N[(N[(x$95$m / z), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[z, 2.5e+18], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision], N[(x$95$m / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -2.20000000000000005e-42

   1. Initial program 75.3%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. *-commutative 99.7%

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

      2. clear-num 99.6%

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

      3. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 36.7%

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

      1. associate-/l/ 45.9%

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

   9. Simplified 45.9%

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

   10. Taylor expanded in t around 0 44.4%

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

       1. associate-*r/ 44.4%

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

       2. neg-mul-1 44.4%

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

   12. Simplified 44.4%

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

   if -2.20000000000000005e-42 < z < 2.5e18

   1. Initial program 93.6%

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

      1. associate-/l/ 92.5%

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

      2. div-inv 92.5%

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

   4. Applied egg-rr 92.5%

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

      1. *-commutative 92.5%

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

      2. clear-num 92.3%

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

      3. un-div-inv 92.5%

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

   6. Applied egg-rr 92.5%

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

   7. Taylor expanded in y around inf 71.5%

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

      1. associate-/l/ 71.7%

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

   9. Simplified 71.7%

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

   10. Taylor expanded in t around inf 57.4%

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

   if 2.5e18 < z

   1. Initial program 75.8%

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

   3. Taylor expanded in y around 0 57.7%

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

      1. associate-*r/ 57.7%

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

      2. neg-mul-1 57.7%

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

   5. Simplified 57.7%

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

   6. Taylor expanded in z around 0 39.5%

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

      1. associate-*r/ 39.5%

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

      2. mul-1-neg 39.5%

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

   8. Simplified 39.5%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{x}{z}}{-y}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 45.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+102} \lor \neg \left(z \leq 5.5 \cdot 10^{+70}\right):\\ \;\;\;\;\frac{x\_m}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{y \cdot t}\\ \end{array} \end{array} \]

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 -7.6e+102) (not (<= z 5.5e+70)))
    (/ x_m (* z t))
    (/ x_m (* y t)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -7.6e+102) || !(z <= 5.5e+70)) {
		tmp = x_m / (z * t);
	} else {
		tmp = x_m / (y * t);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-7.6d+102)) .or. (.not. (z <= 5.5d+70))) then
        tmp = x_m / (z * t)
    else
        tmp = x_m / (y * t)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -7.6e+102) || !(z <= 5.5e+70)) {
		tmp = x_m / (z * t);
	} else {
		tmp = x_m / (y * t);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -7.6e+102) or not (z <= 5.5e+70):
		tmp = x_m / (z * t)
	else:
		tmp = x_m / (y * t)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -7.6e+102) || !(z <= 5.5e+70))
		tmp = Float64(x_m / Float64(z * t));
	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 <= -7.6e+102) || ~((z <= 5.5e+70)))
		tmp = x_m / (z * t);
	else
		tmp = x_m / (y * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -7.6e+102], N[Not[LessEqual[z, 5.5e+70]], $MachinePrecision]], N[(x$95$m / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -7.59999999999999958e102 or 5.49999999999999986e70 < z

   1. Initial program 68.4%

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

   3. Taylor expanded in y around 0 64.9%

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

      1. associate-*r/ 64.9%

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

      2. neg-mul-1 64.9%

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

   5. Simplified 64.9%

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

      1. div-inv 64.9%

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

      2. add-sqr-sqrt 29.7%

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

      3. sqrt-unprod 57.5%

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

      4. sqr-neg 57.5%

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

      5. sqrt-unprod 33.1%

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

      6. add-sqr-sqrt 59.5%

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

   7. Applied egg-rr 59.5%

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

      1. *-commutative 59.5%

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

      2. associate-*l/ 59.5%

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

      3. times-frac 59.0%

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

      4. associate-*l/ 59.0%

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

      5. *-lft-identity 59.0%

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

   9. Simplified 59.0%

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

   10. Taylor expanded in t around inf 31.2%

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

       1. *-commutative 31.2%

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

   12. Simplified 31.2%

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

   if -7.59999999999999958e102 < z < 5.49999999999999986e70

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0 49.1%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+102} \lor \neg \left(z \leq 5.5 \cdot 10^{+70}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 45.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x\_m}{y \cdot z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{x\_m}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z \cdot t}\\ \end{array} \end{array} \]

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 (<= z -2.4e-11)
    (/ x_m (* y z))
    (if (<= z 5.5e+69) (/ x_m (* y t)) (/ 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 tmp;
	if (z <= -2.4e-11) {
		tmp = x_m / (y * z);
	} else if (z <= 5.5e+69) {
		tmp = x_m / (y * t);
	} 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) :: tmp
    if (z <= (-2.4d-11)) then
        tmp = x_m / (y * z)
    else if (z <= 5.5d+69) then
        tmp = x_m / (y * t)
    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 tmp;
	if (z <= -2.4e-11) {
		tmp = x_m / (y * z);
	} else if (z <= 5.5e+69) {
		tmp = x_m / (y * t);
	} 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):
	tmp = 0
	if z <= -2.4e-11:
		tmp = x_m / (y * z)
	elif z <= 5.5e+69:
		tmp = x_m / (y * t)
	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)
	tmp = 0.0
	if (z <= -2.4e-11)
		tmp = Float64(x_m / Float64(y * z));
	elseif (z <= 5.5e+69)
		tmp = Float64(x_m / Float64(y * t));
	else
		tmp = Float64(x_m / Float64(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 (z <= -2.4e-11)
		tmp = x_m / (y * z);
	elseif (z <= 5.5e+69)
		tmp = x_m / (y * t);
	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_] := N[(x$95$s * If[LessEqual[z, -2.4e-11], N[(x$95$m / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+69], N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(z * t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -2.4000000000000001e-11

   1. Initial program 74.0%

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

   3. Taylor expanded in y around inf 37.2%

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

      1. *-commutative 37.2%

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

   5. Simplified 37.2%

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

      1. *-un-lft-identity 37.2%

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

      2. times-frac 40.3%

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

   7. Applied egg-rr 40.3%

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

   8. Taylor expanded in t around 0 38.8%

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

      1. frac-times 36.8%

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

      2. neg-mul-1 36.8%

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

      3. add-sqr-sqrt 16.2%

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

      4. sqrt-unprod 38.0%

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

      5. sqr-neg 38.0%

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

      6. sqrt-unprod 16.1%

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

      7. add-sqr-sqrt 28.6%

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

   10. Applied egg-rr 28.6%

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

   if -2.4000000000000001e-11 < z < 5.50000000000000002e69

   1. Initial program 93.5%

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

   3. Taylor expanded in z around 0 54.2%

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

   if 5.50000000000000002e69 < z

   1. Initial program 71.5%

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

   3. Taylor expanded in y around 0 65.5%

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

      1. associate-*r/ 65.5%

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

      2. neg-mul-1 65.5%

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

   5. Simplified 65.5%

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

      1. div-inv 65.5%

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

      2. add-sqr-sqrt 27.9%

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

      3. sqrt-unprod 58.4%

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

      4. sqr-neg 58.4%

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

      5. sqrt-unprod 38.0%

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

      6. add-sqr-sqrt 60.1%

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

   7. Applied egg-rr 60.1%

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

      1. *-commutative 60.1%

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

      2. associate-*l/ 60.1%

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

      3. times-frac 59.8%

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

      4. associate-*l/ 59.8%

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

      5. *-lft-identity 59.8%

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

   9. Simplified 59.8%

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

   10. Taylor expanded in t around inf 41.8%

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

       1. *-commutative 41.8%

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

   12. Simplified 41.8%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 48.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+124}:\\ \;\;\;\;\frac{x\_m}{y \cdot z}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+116}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z \cdot t}\\ \end{array} \end{array} \]

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 (<= z -2.1e+124)
    (/ x_m (* y z))
    (if (<= z 5.3e+116) (/ (/ x_m t) y) (/ 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 tmp;
	if (z <= -2.1e+124) {
		tmp = x_m / (y * z);
	} else if (z <= 5.3e+116) {
		tmp = (x_m / t) / y;
	} 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) :: tmp
    if (z <= (-2.1d+124)) then
        tmp = x_m / (y * z)
    else if (z <= 5.3d+116) then
        tmp = (x_m / t) / y
    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 tmp;
	if (z <= -2.1e+124) {
		tmp = x_m / (y * z);
	} else if (z <= 5.3e+116) {
		tmp = (x_m / t) / y;
	} 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):
	tmp = 0
	if z <= -2.1e+124:
		tmp = x_m / (y * z)
	elif z <= 5.3e+116:
		tmp = (x_m / t) / y
	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)
	tmp = 0.0
	if (z <= -2.1e+124)
		tmp = Float64(x_m / Float64(y * z));
	elseif (z <= 5.3e+116)
		tmp = Float64(Float64(x_m / t) / y);
	else
		tmp = Float64(x_m / Float64(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 (z <= -2.1e+124)
		tmp = x_m / (y * z);
	elseif (z <= 5.3e+116)
		tmp = (x_m / t) / y;
	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_] := N[(x$95$s * If[LessEqual[z, -2.1e+124], N[(x$95$m / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.3e+116], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision], N[(x$95$m / N[(z * t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -2.10000000000000011e124

   1. Initial program 64.1%

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

   3. Taylor expanded in y around inf 34.9%

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

      1. *-commutative 34.9%

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

   5. Simplified 34.9%

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

      1. *-un-lft-identity 34.9%

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

      2. times-frac 34.1%

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

   7. Applied egg-rr 34.1%

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

   8. Taylor expanded in t around 0 34.0%

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

      1. frac-times 34.8%

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

      2. neg-mul-1 34.8%

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

      3. add-sqr-sqrt 19.4%

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

      4. sqrt-unprod 40.6%

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

      5. sqr-neg 40.6%

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

      6. sqrt-unprod 14.3%

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

      7. add-sqr-sqrt 33.8%

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

   10. Applied egg-rr 33.8%

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

   if -2.10000000000000011e124 < z < 5.3000000000000002e116

   1. Initial program 91.6%

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

      1. associate-/l/ 94.5%

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

      2. div-inv 94.4%

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

   4. Applied egg-rr 94.4%

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

      1. *-commutative 94.4%

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

      2. clear-num 94.3%

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

      3. un-div-inv 94.4%

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

   6. Applied egg-rr 94.4%

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

   7. Taylor expanded in y around inf 64.7%

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

      1. associate-/l/ 68.9%

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

   9. Simplified 68.9%

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

   10. Taylor expanded in t around inf 48.3%

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

   if 5.3000000000000002e116 < z

   1. Initial program 75.0%

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

   3. Taylor expanded in y around 0 75.0%

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

      1. associate-*r/ 75.0%

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

      2. neg-mul-1 75.0%

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

   5. Simplified 75.0%

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

      1. div-inv 74.9%

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

      2. add-sqr-sqrt 31.6%

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

      3. sqrt-unprod 66.0%

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

      4. sqr-neg 66.0%

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

      5. sqrt-unprod 43.3%

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

      6. add-sqr-sqrt 71.2%

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

   7. Applied egg-rr 71.2%

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

      1. *-commutative 71.2%

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

      2. associate-*l/ 71.2%

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

      3. times-frac 70.8%

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

      4. associate-*l/ 70.8%

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

      5. *-lft-identity 70.8%

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

   9. Simplified 70.8%

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

   10. Taylor expanded in t around inf 52.3%

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

       1. *-commutative 52.3%

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

   12. Simplified 52.3%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+124}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+116}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+45}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{y}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+116}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z \cdot t}\\ \end{array} \end{array} \]

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 (<= z -3.7e+45)
    (/ (/ x_m z) y)
    (if (<= z 4.5e+116) (/ (/ x_m t) y) (/ 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 tmp;
	if (z <= -3.7e+45) {
		tmp = (x_m / z) / y;
	} else if (z <= 4.5e+116) {
		tmp = (x_m / t) / y;
	} 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) :: tmp
    if (z <= (-3.7d+45)) then
        tmp = (x_m / z) / y
    else if (z <= 4.5d+116) then
        tmp = (x_m / t) / y
    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 tmp;
	if (z <= -3.7e+45) {
		tmp = (x_m / z) / y;
	} else if (z <= 4.5e+116) {
		tmp = (x_m / t) / y;
	} 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):
	tmp = 0
	if z <= -3.7e+45:
		tmp = (x_m / z) / y
	elif z <= 4.5e+116:
		tmp = (x_m / t) / y
	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)
	tmp = 0.0
	if (z <= -3.7e+45)
		tmp = Float64(Float64(x_m / z) / y);
	elseif (z <= 4.5e+116)
		tmp = Float64(Float64(x_m / t) / y);
	else
		tmp = Float64(x_m / Float64(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 (z <= -3.7e+45)
		tmp = (x_m / z) / y;
	elseif (z <= 4.5e+116)
		tmp = (x_m / t) / y;
	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_] := N[(x$95$s * If[LessEqual[z, -3.7e+45], N[(N[(x$95$m / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 4.5e+116], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision], N[(x$95$m / N[(z * t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -3.69999999999999977e45

   1. Initial program 69.7%

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

   3. Taylor expanded in y around inf 36.9%

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

      1. *-commutative 36.9%

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

   5. Simplified 36.9%

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

      1. *-un-lft-identity 36.9%

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

      2. times-frac 39.3%

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

   7. Applied egg-rr 39.3%

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

   8. Taylor expanded in t around 0 39.2%

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

      1. frac-times 36.8%

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

      2. neg-mul-1 36.8%

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

      3. add-sqr-sqrt 14.8%

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

      4. sqrt-unprod 39.1%

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

      5. sqr-neg 39.1%

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

      6. sqrt-unprod 16.2%

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

      7. add-sqr-sqrt 31.1%

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

      8. associate-/r* 38.3%

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

   10. Applied egg-rr 38.3%

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

   if -3.69999999999999977e45 < z < 4.50000000000000016e116

   1. Initial program 92.0%

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

      1. associate-/l/ 94.0%

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

      2. div-inv 93.9%

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

   4. Applied egg-rr 93.9%

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

      1. *-commutative 93.9%

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

      2. clear-num 93.8%

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

      3. un-div-inv 93.9%

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

   6. Applied egg-rr 93.9%

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

   7. Taylor expanded in y around inf 66.6%

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

      1. associate-/l/ 69.6%

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

   9. Simplified 69.6%

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

   10. Taylor expanded in t around inf 49.9%

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

   if 4.50000000000000016e116 < z

   1. Initial program 75.0%

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

   3. Taylor expanded in y around 0 75.0%

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

      1. associate-*r/ 75.0%

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

      2. neg-mul-1 75.0%

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

   5. Simplified 75.0%

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

      1. div-inv 74.9%

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

      2. add-sqr-sqrt 31.6%

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

      3. sqrt-unprod 66.0%

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

      4. sqr-neg 66.0%

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

      5. sqrt-unprod 43.3%

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

      6. add-sqr-sqrt 71.2%

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

   7. Applied egg-rr 71.2%

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

      1. *-commutative 71.2%

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

      2. associate-*l/ 71.2%

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

      3. times-frac 70.8%

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

      4. associate-*l/ 70.8%

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

      5. *-lft-identity 70.8%

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

   9. Simplified 70.8%

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

   10. Taylor expanded in t around inf 52.3%

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

       1. *-commutative 52.3%

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

   12. Simplified 52.3%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+45}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+116}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 71.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.46 \cdot 10^{-76}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 (<= y -1.46e-76) (/ x_m (* y (- t z))) (/ 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 <= -1.46e-76) {
		tmp = x_m / (y * (t - z));
	} 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 <= (-1.46d-76)) then
        tmp = x_m / (y * (t - z))
    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 <= -1.46e-76) {
		tmp = x_m / (y * (t - z));
	} 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 <= -1.46e-76:
		tmp = x_m / (y * (t - z))
	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 <= -1.46e-76)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	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 (y <= -1.46e-76)
		tmp = x_m / (y * (t - z));
	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, -1.46e-76], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -1.45999999999999985e-76

   1. Initial program 88.4%

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

   3. Taylor expanded in y around inf 85.0%

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

      1. *-commutative 85.0%

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

   5. Simplified 85.0%

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

   if -1.45999999999999985e-76 < y

   1. Initial program 83.6%

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

   3. Taylor expanded in t around inf 54.1%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.46 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 71.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{-79}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

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 (<= y -5.1e-79) (/ x_m (* y (- 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 (y <= -5.1e-79) {
		tmp = x_m / (y * (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 (y <= (-5.1d-79)) then
        tmp = x_m / (y * (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 (y <= -5.1e-79) {
		tmp = x_m / (y * (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 y <= -5.1e-79:
		tmp = x_m / (y * (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 (y <= -5.1e-79)
		tmp = Float64(x_m / Float64(y * 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 (y <= -5.1e-79)
		tmp = x_m / (y * (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[y, -5.1e-79], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -5.0999999999999999e-79

   1. Initial program 88.4%

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

   3. Taylor expanded in y around inf 85.0%

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

      1. *-commutative 85.0%

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

   5. Simplified 85.0%

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

   if -5.0999999999999999e-79 < y

   1. Initial program 83.6%

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

      1. associate-/l/ 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in t around inf 55.7%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 72.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

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 -6e-79) (/ (/ x_m y) (- 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 (y <= -6e-79) {
		tmp = (x_m / y) / (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 (y <= (-6d-79)) then
        tmp = (x_m / y) / (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 (y <= -6e-79) {
		tmp = (x_m / y) / (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 y <= -6e-79:
		tmp = (x_m / y) / (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 (y <= -6e-79)
		tmp = Float64(Float64(x_m / y) / 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 (y <= -6e-79)
		tmp = (x_m / y) / (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[y, -6e-79], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -5.99999999999999999e-79

   1. Initial program 88.4%

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

      1. associate-/l/ 95.8%

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

      2. div-inv 95.7%

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

   4. Applied egg-rr 95.7%

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

   5. Taylor expanded in y around inf 85.0%

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

      1. associate-/r* 89.7%

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

   7. Simplified 89.7%

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

   if -5.99999999999999999e-79 < y

   1. Initial program 83.6%

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

      1. associate-/l/ 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in t around inf 55.7%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 73.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq 4.7 \cdot 10^{-30}:\\ \;\;\;\;\frac{\frac{x\_m}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

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 4.7e-30) (/ (/ x_m (- t z)) y) (/ (/ x_m t) (- y z)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= 4.7e-30) {
		tmp = (x_m / (t - z)) / y;
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 4.7d-30) then
        tmp = (x_m / (t - z)) / y
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= 4.7e-30) {
		tmp = (x_m / (t - z)) / y;
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= 4.7e-30:
		tmp = (x_m / (t - z)) / y
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= 4.7e-30)
		tmp = Float64(Float64(x_m / Float64(t - z)) / y);
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= 4.7e-30)
		tmp = (x_m / (t - z)) / y;
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, 4.7e-30], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < 4.69999999999999969e-30

   1. Initial program 88.1%

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

      1. associate-/l/ 95.2%

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

      2. div-inv 95.0%

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

   4. Applied egg-rr 95.0%

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

      1. *-commutative 95.0%

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

      2. clear-num 94.9%

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

      3. un-div-inv 95.1%

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

   6. Applied egg-rr 95.1%

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

   7. Taylor expanded in y around inf 56.9%

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

      1. associate-/l/ 59.2%

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

   9. Simplified 59.2%

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

   if 4.69999999999999969e-30 < t

   1. Initial program 76.6%

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

      1. associate-/l/ 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in t around inf 82.2%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4.7 \cdot 10^{-30}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 38.9% 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 85.0%

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

3. Taylor expanded in z around 0 38.8%

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

4. Final simplification 38.8%

   \[\leadsto \frac{x}{y \cdot t} \]
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 2024115 
(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))))