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

Percentage Accurate: 88.5% → 98.0%

Time: 16.4s

Alternatives: 20

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: 88.5% 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: 98.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m}{\left(y - z\right) \cdot \left(t - z\right)}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{y - z}}{t - z}\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ x_m (* (- y z) (- t z)))))
   (* x_s (if (<= t_1 -1e-306) t_1 (/ (/ x_m (- y z)) (- t z))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
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 <= -1e-306) {
		tmp = t_1;
	} else {
		tmp = (x_m / (y - z)) / (t - z);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
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 <= (-1d-306)) then
        tmp = t_1
    else
        tmp = (x_m / (y - z)) / (t - z)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
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 <= -1e-306) {
		tmp = t_1;
	} else {
		tmp = (x_m / (y - z)) / (t - z);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= -1e-306:
		tmp = t_1
	else:
		tmp = (x_m / (y - z)) / (t - z)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
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 <= -1e-306)
		tmp = t_1;
	else
		tmp = Float64(Float64(x_m / Float64(y - z)) / Float64(t - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
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 <= -1e-306)
		tmp = t_1;
	else
		tmp = (x_m / (y - z)) / (t - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
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, -1e-306], t$95$1, N[(N[(x$95$m / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -1.00000000000000003e-306

   1. Initial program 96.6%

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

   if -1.00000000000000003e-306 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 81.8%

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

   3. Taylor expanded in x around 0 81.8%

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

      1. associate-/l/ 98.5%

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

   5. Simplified 98.5%

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

4. Final simplification 98.1%

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

Alternative 2: 49.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+291}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x\_m}{y}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+68}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+24}:\\ \;\;\;\;\frac{x\_m}{-y \cdot z}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{x\_m}{t} \cdot \frac{1}{y}\\ \mathbf{elif}\;y \leq 14500:\\ \;\;\;\;\frac{\frac{x\_m}{-t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y \cdot \frac{t}{x\_m}}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -1.5e+291)
    (* (/ -1.0 z) (/ x_m y))
    (if (<= y -4.6e+68)
      (/ (/ x_m y) t)
      (if (<= y -1.3e+24)
        (/ x_m (- (* y z)))
        (if (<= y -8.2e-66)
          (* (/ x_m t) (/ 1.0 y))
          (if (<= y 14500.0) (/ (/ x_m (- t)) z) (/ 1.0 (* y (/ t x_m))))))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e+291) {
		tmp = (-1.0 / z) * (x_m / y);
	} else if (y <= -4.6e+68) {
		tmp = (x_m / y) / t;
	} else if (y <= -1.3e+24) {
		tmp = x_m / -(y * z);
	} else if (y <= -8.2e-66) {
		tmp = (x_m / t) * (1.0 / y);
	} else if (y <= 14500.0) {
		tmp = (x_m / -t) / z;
	} else {
		tmp = 1.0 / (y * (t / x_m));
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
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 <= (-1.5d+291)) then
        tmp = ((-1.0d0) / z) * (x_m / y)
    else if (y <= (-4.6d+68)) then
        tmp = (x_m / y) / t
    else if (y <= (-1.3d+24)) then
        tmp = x_m / -(y * z)
    else if (y <= (-8.2d-66)) then
        tmp = (x_m / t) * (1.0d0 / y)
    else if (y <= 14500.0d0) then
        tmp = (x_m / -t) / z
    else
        tmp = 1.0d0 / (y * (t / x_m))
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e+291) {
		tmp = (-1.0 / z) * (x_m / y);
	} else if (y <= -4.6e+68) {
		tmp = (x_m / y) / t;
	} else if (y <= -1.3e+24) {
		tmp = x_m / -(y * z);
	} else if (y <= -8.2e-66) {
		tmp = (x_m / t) * (1.0 / y);
	} else if (y <= 14500.0) {
		tmp = (x_m / -t) / z;
	} else {
		tmp = 1.0 / (y * (t / x_m));
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -1.5e+291:
		tmp = (-1.0 / z) * (x_m / y)
	elif y <= -4.6e+68:
		tmp = (x_m / y) / t
	elif y <= -1.3e+24:
		tmp = x_m / -(y * z)
	elif y <= -8.2e-66:
		tmp = (x_m / t) * (1.0 / y)
	elif y <= 14500.0:
		tmp = (x_m / -t) / z
	else:
		tmp = 1.0 / (y * (t / x_m))
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -1.5e+291)
		tmp = Float64(Float64(-1.0 / z) * Float64(x_m / y));
	elseif (y <= -4.6e+68)
		tmp = Float64(Float64(x_m / y) / t);
	elseif (y <= -1.3e+24)
		tmp = Float64(x_m / Float64(-Float64(y * z)));
	elseif (y <= -8.2e-66)
		tmp = Float64(Float64(x_m / t) * Float64(1.0 / y));
	elseif (y <= 14500.0)
		tmp = Float64(Float64(x_m / Float64(-t)) / z);
	else
		tmp = Float64(1.0 / Float64(y * Float64(t / x_m)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -1.5e+291)
		tmp = (-1.0 / z) * (x_m / y);
	elseif (y <= -4.6e+68)
		tmp = (x_m / y) / t;
	elseif (y <= -1.3e+24)
		tmp = x_m / -(y * z);
	elseif (y <= -8.2e-66)
		tmp = (x_m / t) * (1.0 / y);
	elseif (y <= 14500.0)
		tmp = (x_m / -t) / z;
	else
		tmp = 1.0 / (y * (t / 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]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -1.5e+291], N[(N[(-1.0 / z), $MachinePrecision] * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.6e+68], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, -1.3e+24], N[(x$95$m / (-N[(y * z), $MachinePrecision])), $MachinePrecision], If[LessEqual[y, -8.2e-66], N[(N[(x$95$m / t), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 14500.0], N[(N[(x$95$m / (-t)), $MachinePrecision] / z), $MachinePrecision], N[(1.0 / N[(y * N[(t / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]), $MachinePrecision]

Derivation

1. Split input into 6 regimes

2. if y < -1.50000000000000008e291

   1. Initial program 76.5%

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

      1. associate-/l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

   7. Simplified 100.0%

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

      1. div-inv 100.0%

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

      2. associate-/l* 76.5%

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

      3. add-sqr-sqrt 49.6%

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

      4. sqrt-unprod 52.2%

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

      5. sqr-neg 52.2%

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

      6. sqrt-unprod 26.5%

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

      7. add-sqr-sqrt 28.6%

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

   9. Applied egg-rr 28.6%

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

       1. associate-/r* 28.6%

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

       2. associate-*r/ 28.6%

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

       3. *-rgt-identity 28.6%

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

   11. Simplified 28.6%

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

   12. Taylor expanded in z around 0 28.6%

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

       1. *-commutative 28.6%

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

   14. Simplified 28.6%

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

       1. frac-2neg 28.6%

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

       2. neg-mul-1 28.6%

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

       3. distribute-rgt-neg-out 28.6%

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

       4. times-frac 27.9%

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

       5. add-sqr-sqrt 27.9%

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

       6. sqrt-unprod 29.4%

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

       7. sqr-neg 29.4%

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

       8. sqrt-unprod 0.0%

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

       9. add-sqr-sqrt 81.9%

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

   16. Applied egg-rr 81.9%

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

   if -1.50000000000000008e291 < y < -4.6e68

   1. Initial program 81.7%

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

      1. associate-/r* 99.7%

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

      2. div-inv 99.6%

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

   4. Applied egg-rr 99.6%

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

      1. *-commutative 99.6%

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

      2. clear-num 99.6%

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

      3. un-div-inv 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in z around 0 61.8%

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

      1. associate-/l/ 71.9%

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

   9. Simplified 71.9%

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

   if -4.6e68 < y < -1.2999999999999999e24

   1. Initial program 99.6%

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

      1. associate-/l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 76.2%

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

      1. associate-*r/ 76.2%

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

      2. neg-mul-1 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in z around 0 76.2%

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

      1. mul-1-neg 76.2%

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

      2. distribute-neg-frac2 76.2%

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

      3. *-commutative 76.2%

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

      4. distribute-rgt-neg-out 76.2%

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

   10. Simplified 76.2%

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

   if -1.2999999999999999e24 < y < -8.19999999999999996e-66

   1. Initial program 78.3%

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

   3. Taylor expanded in z around 0 53.7%

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

      1. associate-/r* 53.6%

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

      2. div-inv 53.4%

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

   5. Applied egg-rr 53.4%

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

   if -8.19999999999999996e-66 < y < 14500

   1. Initial program 92.7%

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

   3. Taylor expanded in t around inf 67.4%

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

      1. associate-/r* 63.5%

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

   5. Simplified 63.5%

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

   6. Taylor expanded in y around 0 48.7%

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

      1. mul-1-neg 48.7%

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

      2. associate-/r* 47.8%

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

      3. distribute-neg-frac2 47.8%

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

   8. Simplified 47.8%

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

   if 14500 < y

   1. Initial program 74.5%

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

   3. Taylor expanded in z around 0 44.2%

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

      1. clear-num 45.6%

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

      2. inv-pow 45.6%

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

      3. *-commutative 45.6%

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

      4. associate-/l* 55.1%

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

   5. Applied egg-rr 55.1%

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

      1. unpow-1 55.1%

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

   7. Simplified 55.1%

      \[\leadsto \color{blue}{\frac{1}{y \cdot \frac{t}{x}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+291}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+68}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{-y \cdot z}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \mathbf{elif}\;y \leq 14500:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y \cdot \frac{t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{1}{\left(y - z\right) \cdot \frac{t}{x\_m}}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\frac{x\_m}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z - y}\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (*
    x_s
    (if (<= t_1 (- INFINITY))
      (/ 1.0 (* (- y z) (/ t x_m)))
      (if (<= t_1 2e+307) (/ x_m t_1) (/ (/ x_m z) (- z y)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
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 <= -((double) INFINITY)) {
		tmp = 1.0 / ((y - z) * (t / x_m));
	} else if (t_1 <= 2e+307) {
		tmp = x_m / t_1;
	} else {
		tmp = (x_m / z) / (z - y);
	}
	return x_s * tmp;
}

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
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 <= -Double.POSITIVE_INFINITY) {
		tmp = 1.0 / ((y - z) * (t / x_m));
	} else if (t_1 <= 2e+307) {
		tmp = x_m / t_1;
	} else {
		tmp = (x_m / z) / (z - y);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = 1.0 / ((y - z) * (t / x_m))
	elif t_1 <= 2e+307:
		tmp = x_m / t_1
	else:
		tmp = (x_m / z) / (z - y)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(1.0 / Float64(Float64(y - z) * Float64(t / x_m)));
	elseif (t_1 <= 2e+307)
		tmp = Float64(x_m / t_1);
	else
		tmp = Float64(Float64(x_m / z) / Float64(z - y));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = 1.0 / ((y - z) * (t / x_m));
	elseif (t_1 <= 2e+307)
		tmp = x_m / t_1;
	else
		tmp = (x_m / z) / (z - y);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
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, (-Infinity)], N[(1.0 / N[(N[(y - z), $MachinePrecision] * N[(t / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+307], N[(x$95$m / t$95$1), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 52.8%

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

   3. Taylor expanded in t around inf 45.9%

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

      1. associate-/r* 77.3%

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

   5. Simplified 77.3%

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

      1. clear-num 77.2%

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

      2. inv-pow 77.2%

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

      3. div-inv 77.1%

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

      4. clear-num 77.2%

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

   7. Applied egg-rr 77.2%

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

      1. unpow-1 77.2%

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

   9. Simplified 77.2%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 1.99999999999999997e307

   1. Initial program 97.8%

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

   if 1.99999999999999997e307 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 73.7%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 87.8%

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

      1. associate-*r/ 87.8%

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

      2. neg-mul-1 87.8%

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

   7. Simplified 87.8%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -\infty:\\ \;\;\;\;\frac{1}{\left(y - z\right) \cdot \frac{t}{x}}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{1}{\left(y - z\right) \cdot \frac{t}{x\_m}}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\frac{x\_m}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{y - z}{x\_m}}\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (*
    x_s
    (if (<= t_1 (- INFINITY))
      (/ 1.0 (* (- y z) (/ t x_m)))
      (if (<= t_1 2e+307) (/ x_m t_1) (/ (/ -1.0 z) (/ (- y z) x_m)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
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 <= -((double) INFINITY)) {
		tmp = 1.0 / ((y - z) * (t / x_m));
	} else if (t_1 <= 2e+307) {
		tmp = x_m / t_1;
	} else {
		tmp = (-1.0 / z) / ((y - z) / x_m);
	}
	return x_s * tmp;
}

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
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 <= -Double.POSITIVE_INFINITY) {
		tmp = 1.0 / ((y - z) * (t / x_m));
	} else if (t_1 <= 2e+307) {
		tmp = x_m / t_1;
	} else {
		tmp = (-1.0 / z) / ((y - z) / x_m);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = 1.0 / ((y - z) * (t / x_m))
	elif t_1 <= 2e+307:
		tmp = x_m / t_1
	else:
		tmp = (-1.0 / z) / ((y - z) / x_m)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(1.0 / Float64(Float64(y - z) * Float64(t / x_m)));
	elseif (t_1 <= 2e+307)
		tmp = Float64(x_m / t_1);
	else
		tmp = Float64(Float64(-1.0 / z) / Float64(Float64(y - z) / x_m));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = 1.0 / ((y - z) * (t / x_m));
	elseif (t_1 <= 2e+307)
		tmp = x_m / t_1;
	else
		tmp = (-1.0 / z) / ((y - 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]
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, (-Infinity)], N[(1.0 / N[(N[(y - z), $MachinePrecision] * N[(t / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+307], N[(x$95$m / t$95$1), $MachinePrecision], N[(N[(-1.0 / z), $MachinePrecision] / N[(N[(y - z), $MachinePrecision] / x$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 52.8%

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

   3. Taylor expanded in t around inf 45.9%

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

      1. associate-/r* 77.3%

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

   5. Simplified 77.3%

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

      1. clear-num 77.2%

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

      2. inv-pow 77.2%

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

      3. div-inv 77.1%

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

      4. clear-num 77.2%

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

   7. Applied egg-rr 77.2%

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

      1. unpow-1 77.2%

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

   9. Simplified 77.2%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 1.99999999999999997e307

   1. Initial program 97.8%

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

   if 1.99999999999999997e307 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 73.7%

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

      1. associate-/r* 99.9%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 91.3%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -\infty:\\ \;\;\;\;\frac{1}{\left(y - z\right) \cdot \frac{t}{x}}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{y - z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-275}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-141}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z - y}\\ \mathbf{elif}\;t \leq 0.006:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z - t}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+175}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\left(y - z\right) \cdot \frac{t}{x\_m}}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -3.2e-275)
    (/ (/ x_m y) (- t z))
    (if (<= t 8.6e-141)
      (/ (/ x_m z) (- z y))
      (if (<= t 0.006)
        (/ (/ x_m z) (- z t))
        (if (<= t 2.95e+175)
          (/ x_m (* (- y z) t))
          (/ 1.0 (* (- y z) (/ t x_m)))))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -3.2e-275) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 8.6e-141) {
		tmp = (x_m / z) / (z - y);
	} else if (t <= 0.006) {
		tmp = (x_m / z) / (z - t);
	} else if (t <= 2.95e+175) {
		tmp = x_m / ((y - z) * t);
	} else {
		tmp = 1.0 / ((y - z) * (t / x_m));
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
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 <= (-3.2d-275)) then
        tmp = (x_m / y) / (t - z)
    else if (t <= 8.6d-141) then
        tmp = (x_m / z) / (z - y)
    else if (t <= 0.006d0) then
        tmp = (x_m / z) / (z - t)
    else if (t <= 2.95d+175) then
        tmp = x_m / ((y - z) * t)
    else
        tmp = 1.0d0 / ((y - z) * (t / x_m))
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -3.2e-275) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 8.6e-141) {
		tmp = (x_m / z) / (z - y);
	} else if (t <= 0.006) {
		tmp = (x_m / z) / (z - t);
	} else if (t <= 2.95e+175) {
		tmp = x_m / ((y - z) * t);
	} else {
		tmp = 1.0 / ((y - z) * (t / x_m));
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= -3.2e-275:
		tmp = (x_m / y) / (t - z)
	elif t <= 8.6e-141:
		tmp = (x_m / z) / (z - y)
	elif t <= 0.006:
		tmp = (x_m / z) / (z - t)
	elif t <= 2.95e+175:
		tmp = x_m / ((y - z) * t)
	else:
		tmp = 1.0 / ((y - z) * (t / x_m))
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= -3.2e-275)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (t <= 8.6e-141)
		tmp = Float64(Float64(x_m / z) / Float64(z - y));
	elseif (t <= 0.006)
		tmp = Float64(Float64(x_m / z) / Float64(z - t));
	elseif (t <= 2.95e+175)
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	else
		tmp = Float64(1.0 / Float64(Float64(y - z) * Float64(t / x_m)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -3.2e-275)
		tmp = (x_m / y) / (t - z);
	elseif (t <= 8.6e-141)
		tmp = (x_m / z) / (z - y);
	elseif (t <= 0.006)
		tmp = (x_m / z) / (z - t);
	elseif (t <= 2.95e+175)
		tmp = x_m / ((y - z) * t);
	else
		tmp = 1.0 / ((y - z) * (t / 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]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -3.2e-275], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.6e-141], N[(N[(x$95$m / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.006], N[(N[(x$95$m / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.95e+175], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(y - z), $MachinePrecision] * N[(t / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if t < -3.2e-275

   1. Initial program 84.7%

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

   3. Taylor expanded in y around inf 61.5%

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

      1. associate-/r* 69.4%

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

   5. Simplified 69.4%

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

   if -3.2e-275 < t < 8.59999999999999948e-141

   1. Initial program 79.5%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 89.5%

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

      1. associate-*r/ 89.5%

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

      2. neg-mul-1 89.5%

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

   7. Simplified 89.5%

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

   if 8.59999999999999948e-141 < t < 0.0060000000000000001

   1. Initial program 96.3%

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

   3. Taylor expanded in x around 0 96.3%

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

      1. associate-/l/ 97.1%

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

   5. Simplified 97.1%

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

   6. Taylor expanded in y around 0 64.3%

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

      1. mul-1-neg 64.3%

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

      2. associate-/r* 67.9%

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

      3. distribute-neg-frac2 67.9%

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

      4. neg-sub0 67.9%

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

      5. associate--r- 67.9%

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

      6. neg-sub0 67.9%

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

   8. Simplified 67.9%

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

   if 0.0060000000000000001 < t < 2.95000000000000015e175

   1. Initial program 86.5%

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

   3. Taylor expanded in t around inf 79.5%

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

   if 2.95000000000000015e175 < t

   1. Initial program 83.5%

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

   3. Taylor expanded in t around inf 83.5%

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

      1. associate-/r* 99.7%

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

   5. Simplified 99.7%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

      3. div-inv 99.7%

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

      4. clear-num 99.7%

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

   7. Applied egg-rr 99.7%

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

      1. unpow-1 99.7%

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

   9. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{1}{\left(y - z\right) \cdot \frac{t}{x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-275}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-141}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;t \leq 0.006:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+175}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\left(y - z\right) \cdot \frac{t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-275}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-139}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z - y}\\ \mathbf{elif}\;t \leq 0.0048:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z - t}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+174}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -3.2e-275)
    (/ (/ x_m y) (- t z))
    (if (<= t 3e-139)
      (/ (/ x_m z) (- z y))
      (if (<= t 0.0048)
        (/ (/ x_m z) (- z t))
        (if (<= t 5.8e+174) (/ x_m (* (- y z) t)) (/ (/ x_m t) (- y z))))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -3.2e-275) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 3e-139) {
		tmp = (x_m / z) / (z - y);
	} else if (t <= 0.0048) {
		tmp = (x_m / z) / (z - t);
	} else if (t <= 5.8e+174) {
		tmp = x_m / ((y - z) * t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
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 <= (-3.2d-275)) then
        tmp = (x_m / y) / (t - z)
    else if (t <= 3d-139) then
        tmp = (x_m / z) / (z - y)
    else if (t <= 0.0048d0) then
        tmp = (x_m / z) / (z - t)
    else if (t <= 5.8d+174) then
        tmp = x_m / ((y - z) * t)
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -3.2e-275) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 3e-139) {
		tmp = (x_m / z) / (z - y);
	} else if (t <= 0.0048) {
		tmp = (x_m / z) / (z - t);
	} else if (t <= 5.8e+174) {
		tmp = x_m / ((y - z) * t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= -3.2e-275:
		tmp = (x_m / y) / (t - z)
	elif t <= 3e-139:
		tmp = (x_m / z) / (z - y)
	elif t <= 0.0048:
		tmp = (x_m / z) / (z - t)
	elif t <= 5.8e+174:
		tmp = x_m / ((y - z) * t)
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= -3.2e-275)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (t <= 3e-139)
		tmp = Float64(Float64(x_m / z) / Float64(z - y));
	elseif (t <= 0.0048)
		tmp = Float64(Float64(x_m / z) / Float64(z - t));
	elseif (t <= 5.8e+174)
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -3.2e-275)
		tmp = (x_m / y) / (t - z);
	elseif (t <= 3e-139)
		tmp = (x_m / z) / (z - y);
	elseif (t <= 0.0048)
		tmp = (x_m / z) / (z - t);
	elseif (t <= 5.8e+174)
		tmp = x_m / ((y - z) * t);
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -3.2e-275], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-139], N[(N[(x$95$m / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.0048], N[(N[(x$95$m / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+174], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if t < -3.2e-275

   1. Initial program 84.7%

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

   3. Taylor expanded in y around inf 61.5%

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

      1. associate-/r* 69.4%

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

   5. Simplified 69.4%

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

   if -3.2e-275 < t < 2.9999999999999999e-139

   1. Initial program 79.5%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 89.5%

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

      1. associate-*r/ 89.5%

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

      2. neg-mul-1 89.5%

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

   7. Simplified 89.5%

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

   if 2.9999999999999999e-139 < t < 0.00479999999999999958

   1. Initial program 96.3%

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

   3. Taylor expanded in x around 0 96.3%

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

      1. associate-/l/ 97.1%

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

   5. Simplified 97.1%

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

   6. Taylor expanded in y around 0 64.3%

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

      1. mul-1-neg 64.3%

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

      2. associate-/r* 67.9%

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

      3. distribute-neg-frac2 67.9%

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

      4. neg-sub0 67.9%

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

      5. associate--r- 67.9%

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

      6. neg-sub0 67.9%

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

   8. Simplified 67.9%

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

   if 0.00479999999999999958 < t < 5.7999999999999999e174

   1. Initial program 86.5%

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

   3. Taylor expanded in t around inf 79.5%

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

   if 5.7999999999999999e174 < t

   1. Initial program 83.5%

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

   3. Taylor expanded in t around inf 83.5%

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

      1. associate-/r* 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-275}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-139}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;t \leq 0.0048:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+174}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{\frac{x\_m}{-t}}{z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+104}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+247}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(-t\right)}\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x_m (- t)) z)))
   (*
    x_s
    (if (<= z -6.8e-106)
      t_1
      (if (<= z 4.6e+104)
        (/ (/ x_m y) t)
        (if (<= z 8.5e+173)
          t_1
          (if (<= z 1.85e+247) (/ (/ x_m z) y) (/ x_m (* z (- t))))))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / -t) / z;
	double tmp;
	if (z <= -6.8e-106) {
		tmp = t_1;
	} else if (z <= 4.6e+104) {
		tmp = (x_m / y) / t;
	} else if (z <= 8.5e+173) {
		tmp = t_1;
	} else if (z <= 1.85e+247) {
		tmp = (x_m / z) / y;
	} else {
		tmp = x_m / (z * -t);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x_m / -t) / z
    if (z <= (-6.8d-106)) then
        tmp = t_1
    else if (z <= 4.6d+104) then
        tmp = (x_m / y) / t
    else if (z <= 8.5d+173) then
        tmp = t_1
    else if (z <= 1.85d+247) then
        tmp = (x_m / z) / 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);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / -t) / z;
	double tmp;
	if (z <= -6.8e-106) {
		tmp = t_1;
	} else if (z <= 4.6e+104) {
		tmp = (x_m / y) / t;
	} else if (z <= 8.5e+173) {
		tmp = t_1;
	} else if (z <= 1.85e+247) {
		tmp = (x_m / z) / y;
	} else {
		tmp = x_m / (z * -t);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (x_m / -t) / z
	tmp = 0
	if z <= -6.8e-106:
		tmp = t_1
	elif z <= 4.6e+104:
		tmp = (x_m / y) / t
	elif z <= 8.5e+173:
		tmp = t_1
	elif z <= 1.85e+247:
		tmp = (x_m / z) / y
	else:
		tmp = x_m / (z * -t)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m / Float64(-t)) / z)
	tmp = 0.0
	if (z <= -6.8e-106)
		tmp = t_1;
	elseif (z <= 4.6e+104)
		tmp = Float64(Float64(x_m / y) / t);
	elseif (z <= 8.5e+173)
		tmp = t_1;
	elseif (z <= 1.85e+247)
		tmp = Float64(Float64(x_m / z) / 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);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m / -t) / z;
	tmp = 0.0;
	if (z <= -6.8e-106)
		tmp = t_1;
	elseif (z <= 4.6e+104)
		tmp = (x_m / y) / t;
	elseif (z <= 8.5e+173)
		tmp = t_1;
	elseif (z <= 1.85e+247)
		tmp = (x_m / z) / 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]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m / (-t)), $MachinePrecision] / z), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -6.8e-106], t$95$1, If[LessEqual[z, 4.6e+104], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 8.5e+173], t$95$1, If[LessEqual[z, 1.85e+247], N[(N[(x$95$m / z), $MachinePrecision] / y), $MachinePrecision], N[(x$95$m / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if z < -6.79999999999999965e-106 or 4.59999999999999969e104 < z < 8.5000000000000003e173

   1. Initial program 80.5%

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

   3. Taylor expanded in t around inf 49.1%

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

      1. associate-/r* 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in y around 0 43.0%

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

      1. mul-1-neg 43.0%

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

      2. associate-/r* 41.9%

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

      3. distribute-neg-frac2 41.9%

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

   8. Simplified 41.9%

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

   if -6.79999999999999965e-106 < z < 4.59999999999999969e104

   1. Initial program 89.4%

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

      1. associate-/r* 96.7%

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

      2. div-inv 96.6%

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

   4. Applied egg-rr 96.6%

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

      1. *-commutative 96.6%

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

      2. clear-num 96.6%

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

      3. un-div-inv 96.6%

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

   6. Applied egg-rr 96.6%

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

   7. Taylor expanded in z around 0 60.0%

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

      1. associate-/l/ 67.4%

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

   9. Simplified 67.4%

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

   if 8.5000000000000003e173 < z < 1.8499999999999999e247

   1. Initial program 78.1%

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

      1. associate-/l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

   7. Simplified 100.0%

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

      1. div-inv 99.9%

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

      2. associate-/l* 78.1%

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

      3. add-sqr-sqrt 46.6%

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

      4. sqrt-unprod 76.9%

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

      5. sqr-neg 76.9%

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

      6. sqrt-unprod 31.6%

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

      7. add-sqr-sqrt 78.1%

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

   9. Applied egg-rr 78.1%

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

       1. associate-/r* 78.1%

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

       2. associate-*r/ 78.1%

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

       3. *-rgt-identity 78.1%

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

   11. Simplified 78.1%

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

   12. Taylor expanded in z around 0 43.5%

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

       1. *-commutative 43.5%

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

   14. Simplified 43.5%

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

   15. Taylor expanded in x around 0 43.5%

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

       1. *-commutative 43.5%

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

       2. associate-/r* 65.0%

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

   17. Simplified 65.0%

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

   if 1.8499999999999999e247 < z

   1. Initial program 85.6%

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

   3. Taylor expanded in t around inf 53.9%

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

      1. associate-/r* 47.5%

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

   5. Simplified 47.5%

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

      1. div-inv 47.5%

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

      2. associate-/l* 48.3%

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

   7. Applied egg-rr 48.3%

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

   8. Taylor expanded in y around 0 53.9%

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

      1. mul-1-neg 53.9%

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

      2. distribute-frac-neg 53.9%

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

      3. *-commutative 53.9%

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

   10. Simplified 53.9%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-106}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+104}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+173}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+247}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-186}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-112}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+174}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -2.1e-186)
    (/ x_m (* y (- t z)))
    (if (<= t 3.25e-112)
      (/ x_m (* z (- z y)))
      (if (<= t 5.8e+174) (/ x_m (* (- y z) t)) (/ (/ x_m t) (- y z)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -2.1e-186) {
		tmp = x_m / (y * (t - z));
	} else if (t <= 3.25e-112) {
		tmp = x_m / (z * (z - y));
	} else if (t <= 5.8e+174) {
		tmp = x_m / ((y - z) * t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.1d-186)) then
        tmp = x_m / (y * (t - z))
    else if (t <= 3.25d-112) then
        tmp = x_m / (z * (z - y))
    else if (t <= 5.8d+174) then
        tmp = x_m / ((y - z) * t)
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -2.1e-186) {
		tmp = x_m / (y * (t - z));
	} else if (t <= 3.25e-112) {
		tmp = x_m / (z * (z - y));
	} else if (t <= 5.8e+174) {
		tmp = x_m / ((y - z) * t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= -2.1e-186:
		tmp = x_m / (y * (t - z))
	elif t <= 3.25e-112:
		tmp = x_m / (z * (z - y))
	elif t <= 5.8e+174:
		tmp = x_m / ((y - z) * t)
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= -2.1e-186)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (t <= 3.25e-112)
		tmp = Float64(x_m / Float64(z * Float64(z - y)));
	elseif (t <= 5.8e+174)
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -2.1e-186)
		tmp = x_m / (y * (t - z));
	elseif (t <= 3.25e-112)
		tmp = x_m / (z * (z - y));
	elseif (t <= 5.8e+174)
		tmp = x_m / ((y - z) * t);
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -2.1e-186], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.25e-112], N[(x$95$m / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+174], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if t < -2.1000000000000002e-186

   1. Initial program 83.4%

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

   3. Taylor expanded in y around inf 61.9%

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

      1. *-commutative 61.9%

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

   5. Simplified 61.9%

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

   if -2.1000000000000002e-186 < t < 3.24999999999999978e-112

   1. Initial program 83.2%

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

      1. *-commutative 83.2%

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

      2. sub-neg 83.2%

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

      3. distribute-lft-in 76.6%

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

   4. Applied egg-rr 76.6%

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

   5. Taylor expanded in t around 0 65.7%

      \[\leadsto \color{blue}{\frac{x}{-1 \cdot \left(y \cdot z\right) + {z}^{2}}} \]
   6. Step-by-step derivation

      1. associate-*r* 65.7%

         \[\leadsto \frac{x}{\color{blue}{\left(-1 \cdot y\right) \cdot z} + {z}^{2}} \]

      2. unpow2 65.7%

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

      3. distribute-rgt-out 70.6%

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

      4. +-commutative 70.6%

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

      5. mul-1-neg 70.6%

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

      6. unsub-neg 70.6%

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

   7. Simplified 70.6%

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

   if 3.24999999999999978e-112 < t < 5.7999999999999999e174

   1. Initial program 90.5%

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

   3. Taylor expanded in t around inf 70.2%

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

   if 5.7999999999999999e174 < t

   1. Initial program 83.5%

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

   3. Taylor expanded in t around inf 83.5%

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

      1. associate-/r* 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-112}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+174}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-290}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-111}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+174}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -1.7e-290)
    (/ (/ x_m y) (- t z))
    (if (<= t 9.2e-111)
      (/ x_m (* z (- z y)))
      (if (<= t 5.5e+174) (/ x_m (* (- y z) t)) (/ (/ x_m t) (- y z)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.7e-290) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 9.2e-111) {
		tmp = x_m / (z * (z - y));
	} else if (t <= 5.5e+174) {
		tmp = x_m / ((y - z) * t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.7d-290)) then
        tmp = (x_m / y) / (t - z)
    else if (t <= 9.2d-111) then
        tmp = x_m / (z * (z - y))
    else if (t <= 5.5d+174) then
        tmp = x_m / ((y - z) * t)
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.7e-290) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 9.2e-111) {
		tmp = x_m / (z * (z - y));
	} else if (t <= 5.5e+174) {
		tmp = x_m / ((y - z) * t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= -1.7e-290:
		tmp = (x_m / y) / (t - z)
	elif t <= 9.2e-111:
		tmp = x_m / (z * (z - y))
	elif t <= 5.5e+174:
		tmp = x_m / ((y - z) * t)
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= -1.7e-290)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (t <= 9.2e-111)
		tmp = Float64(x_m / Float64(z * Float64(z - y)));
	elseif (t <= 5.5e+174)
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -1.7e-290)
		tmp = (x_m / y) / (t - z);
	elseif (t <= 9.2e-111)
		tmp = x_m / (z * (z - y));
	elseif (t <= 5.5e+174)
		tmp = x_m / ((y - z) * t);
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -1.7e-290], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-111], N[(x$95$m / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+174], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if t < -1.69999999999999992e-290

   1. Initial program 84.1%

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

   3. Taylor expanded in y around inf 61.4%

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

      1. associate-/r* 69.7%

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

   5. Simplified 69.7%

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

   if -1.69999999999999992e-290 < t < 9.2e-111

   1. Initial program 82.2%

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

      1. *-commutative 82.2%

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

      2. sub-neg 82.2%

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

      3. distribute-lft-in 75.8%

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

   4. Applied egg-rr 75.8%

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

   5. Taylor expanded in t around 0 61.6%

      \[\leadsto \color{blue}{\frac{x}{-1 \cdot \left(y \cdot z\right) + {z}^{2}}} \]
   6. Step-by-step derivation

      1. associate-*r* 61.6%

         \[\leadsto \frac{x}{\color{blue}{\left(-1 \cdot y\right) \cdot z} + {z}^{2}} \]

      2. unpow2 61.6%

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

      3. distribute-rgt-out 65.9%

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

      4. +-commutative 65.9%

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

      5. mul-1-neg 65.9%

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

      6. unsub-neg 65.9%

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

   7. Simplified 65.9%

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

   if 9.2e-111 < t < 5.4999999999999998e174

   1. Initial program 90.2%

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

   3. Taylor expanded in t around inf 72.1%

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

   if 5.4999999999999998e174 < t

   1. Initial program 83.5%

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

   3. Taylor expanded in t around inf 83.5%

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

      1. associate-/r* 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-290}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-111}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+174}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m}{\left(y - z\right) \cdot \left(t - z\right)}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-254}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t - z}}{y - z}\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ x_m (* (- y z) (- t z)))))
   (* x_s (if (<= t_1 -5e-254) t_1 (/ (/ x_m (- t z)) (- y z))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
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 <= -5e-254) {
		tmp = t_1;
	} else {
		tmp = (x_m / (t - z)) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
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 <= (-5d-254)) then
        tmp = t_1
    else
        tmp = (x_m / (t - z)) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
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 <= -5e-254) {
		tmp = t_1;
	} else {
		tmp = (x_m / (t - z)) / (y - z);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= -5e-254:
		tmp = t_1
	else:
		tmp = (x_m / (t - z)) / (y - z)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
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 <= -5e-254)
		tmp = t_1;
	else
		tmp = Float64(Float64(x_m / Float64(t - z)) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
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 <= -5e-254)
		tmp = t_1;
	else
		tmp = (x_m / (t - z)) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
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, -5e-254], t$95$1, N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -5.0000000000000003e-254

   1. Initial program 96.5%

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

   if -5.0000000000000003e-254 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 82.0%

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

      1. associate-/l/ 97.5%

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

   3. Simplified 97.5%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \leq -5 \cdot 10^{-254}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-151}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t}\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{-146}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x\_m}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -1.75e-151)
    (/ (/ x_m y) t)
    (if (<= t 6.9e-146) (* (/ -1.0 z) (/ x_m y)) (/ x_m (* (- y z) t))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.75e-151) {
		tmp = (x_m / y) / t;
	} else if (t <= 6.9e-146) {
		tmp = (-1.0 / z) * (x_m / y);
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.75d-151)) then
        tmp = (x_m / y) / t
    else if (t <= 6.9d-146) then
        tmp = ((-1.0d0) / z) * (x_m / 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);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.75e-151) {
		tmp = (x_m / y) / t;
	} else if (t <= 6.9e-146) {
		tmp = (-1.0 / z) * (x_m / 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)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= -1.75e-151:
		tmp = (x_m / y) / t
	elif t <= 6.9e-146:
		tmp = (-1.0 / z) * (x_m / y)
	else:
		tmp = x_m / ((y - z) * t)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= -1.75e-151)
		tmp = Float64(Float64(x_m / y) / t);
	elseif (t <= 6.9e-146)
		tmp = Float64(Float64(-1.0 / z) * Float64(x_m / 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);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -1.75e-151)
		tmp = (x_m / y) / t;
	elseif (t <= 6.9e-146)
		tmp = (-1.0 / z) * (x_m / 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]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -1.75e-151], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 6.9e-146], N[(N[(-1.0 / z), $MachinePrecision] * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -1.74999999999999998e-151

   1. Initial program 81.3%

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

      1. associate-/r* 98.7%

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

      2. div-inv 98.6%

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

   4. Applied egg-rr 98.6%

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

      1. *-commutative 98.6%

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

      2. clear-num 98.5%

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

      3. un-div-inv 98.5%

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

   6. Applied egg-rr 98.5%

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

   7. Taylor expanded in z around 0 52.3%

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

      1. associate-/l/ 60.0%

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

   9. Simplified 60.0%

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

   if -1.74999999999999998e-151 < t < 6.9000000000000002e-146

   1. Initial program 85.4%

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

      1. associate-/l/ 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in t around 0 86.6%

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

      1. associate-*r/ 86.6%

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

      2. neg-mul-1 86.6%

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

   7. Simplified 86.6%

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

      1. div-inv 86.4%

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

      2. associate-/l* 77.1%

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

      3. add-sqr-sqrt 42.9%

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

      4. sqrt-unprod 46.8%

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

      5. sqr-neg 46.8%

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

      6. sqrt-unprod 11.6%

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

      7. add-sqr-sqrt 28.0%

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

   9. Applied egg-rr 28.0%

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

       1. associate-/r* 28.0%

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

       2. associate-*r/ 28.0%

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

       3. *-rgt-identity 28.0%

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

   11. Simplified 28.0%

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

   12. Taylor expanded in z around 0 21.8%

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

       1. *-commutative 21.8%

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

   14. Simplified 21.8%

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

       1. frac-2neg 21.8%

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

       2. neg-mul-1 21.8%

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

       3. distribute-rgt-neg-out 21.8%

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

       4. times-frac 18.6%

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

       5. add-sqr-sqrt 7.6%

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

       6. sqrt-unprod 26.7%

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

       7. sqr-neg 26.7%

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

       8. sqrt-unprod 26.6%

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

       9. add-sqr-sqrt 57.1%

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

   16. Applied egg-rr 57.1%

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

   if 6.9000000000000002e-146 < t

   1. Initial program 88.3%

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

   3. Taylor expanded in t around inf 72.4%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-151}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{-146}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-151}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-111}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -3e-151)
    (/ (/ x_m y) t)
    (if (<= t 8.5e-111) (/ x_m (* z (- z y))) (/ x_m (* (- y z) t))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -3e-151) {
		tmp = (x_m / y) / t;
	} else if (t <= 8.5e-111) {
		tmp = x_m / (z * (z - y));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
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 <= (-3d-151)) then
        tmp = (x_m / y) / t
    else if (t <= 8.5d-111) then
        tmp = x_m / (z * (z - y))
    else
        tmp = x_m / ((y - z) * t)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -3e-151) {
		tmp = (x_m / y) / t;
	} else if (t <= 8.5e-111) {
		tmp = x_m / (z * (z - y));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= -3e-151:
		tmp = (x_m / y) / t
	elif t <= 8.5e-111:
		tmp = x_m / (z * (z - y))
	else:
		tmp = x_m / ((y - z) * t)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= -3e-151)
		tmp = Float64(Float64(x_m / y) / t);
	elseif (t <= 8.5e-111)
		tmp = Float64(x_m / Float64(z * Float64(z - y)));
	else
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -3e-151)
		tmp = (x_m / y) / t;
	elseif (t <= 8.5e-111)
		tmp = x_m / (z * (z - y));
	else
		tmp = x_m / ((y - z) * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -3e-151], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 8.5e-111], N[(x$95$m / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -3e-151

   1. Initial program 81.3%

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

      1. associate-/r* 98.7%

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

      2. div-inv 98.6%

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

   4. Applied egg-rr 98.6%

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

      1. *-commutative 98.6%

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

      2. clear-num 98.5%

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

      3. un-div-inv 98.5%

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

   6. Applied egg-rr 98.5%

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

   7. Taylor expanded in z around 0 52.3%

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

      1. associate-/l/ 60.0%

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

   9. Simplified 60.0%

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

   if -3e-151 < t < 8.5000000000000003e-111

   1. Initial program 86.0%

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

      1. *-commutative 86.0%

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

      2. sub-neg 86.0%

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

      3. distribute-lft-in 79.3%

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

   4. Applied egg-rr 79.3%

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

   5. Taylor expanded in t around 0 67.6%

      \[\leadsto \color{blue}{\frac{x}{-1 \cdot \left(y \cdot z\right) + {z}^{2}}} \]
   6. Step-by-step derivation

      1. associate-*r* 67.6%

         \[\leadsto \frac{x}{\color{blue}{\left(-1 \cdot y\right) \cdot z} + {z}^{2}} \]

      2. unpow2 67.6%

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

      3. distribute-rgt-out 73.0%

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

      4. +-commutative 73.0%

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

      5. mul-1-neg 73.0%

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

      6. unsub-neg 73.0%

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

   7. Simplified 73.0%

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

   if 8.5000000000000003e-111 < t

   1. Initial program 88.1%

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

   3. Taylor expanded in t around inf 75.6%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-151}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-111}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-186}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-112}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -1.2e-186)
    (/ x_m (* y (- t z)))
    (if (<= t 4.5e-112) (/ x_m (* z (- z y))) (/ x_m (* (- y z) t))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.2e-186) {
		tmp = x_m / (y * (t - z));
	} else if (t <= 4.5e-112) {
		tmp = x_m / (z * (z - y));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.2d-186)) then
        tmp = x_m / (y * (t - z))
    else if (t <= 4.5d-112) then
        tmp = x_m / (z * (z - y))
    else
        tmp = x_m / ((y - z) * t)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.2e-186) {
		tmp = x_m / (y * (t - z));
	} else if (t <= 4.5e-112) {
		tmp = x_m / (z * (z - y));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= -1.2e-186:
		tmp = x_m / (y * (t - z))
	elif t <= 4.5e-112:
		tmp = x_m / (z * (z - y))
	else:
		tmp = x_m / ((y - z) * t)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= -1.2e-186)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (t <= 4.5e-112)
		tmp = Float64(x_m / Float64(z * Float64(z - y)));
	else
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -1.2e-186)
		tmp = x_m / (y * (t - z));
	elseif (t <= 4.5e-112)
		tmp = x_m / (z * (z - y));
	else
		tmp = x_m / ((y - z) * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -1.2e-186], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-112], N[(x$95$m / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -1.20000000000000002e-186

   1. Initial program 83.4%

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

   3. Taylor expanded in y around inf 61.9%

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

      1. *-commutative 61.9%

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

   5. Simplified 61.9%

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

   if -1.20000000000000002e-186 < t < 4.50000000000000012e-112

   1. Initial program 83.2%

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

      1. *-commutative 83.2%

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

      2. sub-neg 83.2%

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

      3. distribute-lft-in 76.6%

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

   4. Applied egg-rr 76.6%

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

   5. Taylor expanded in t around 0 65.7%

      \[\leadsto \color{blue}{\frac{x}{-1 \cdot \left(y \cdot z\right) + {z}^{2}}} \]
   6. Step-by-step derivation

      1. associate-*r* 65.7%

         \[\leadsto \frac{x}{\color{blue}{\left(-1 \cdot y\right) \cdot z} + {z}^{2}} \]

      2. unpow2 65.7%

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

      3. distribute-rgt-out 70.6%

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

      4. +-commutative 70.6%

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

      5. mul-1-neg 70.6%

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

      6. unsub-neg 70.6%

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

   7. Simplified 70.6%

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

   if 4.50000000000000012e-112 < t

   1. Initial program 88.4%

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

   3. Taylor expanded in t around inf 74.2%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-112}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 48.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-106} \lor \neg \left(z \leq 7.8 \cdot 10^{+94}\right):\\ \;\;\;\;\frac{x\_m}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -8e-106) (not (<= z 7.8e+94)))
    (/ x_m (* z (- t)))
    (/ (/ x_m y) t))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -8e-106) || !(z <= 7.8e+94)) {
		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)
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 <= (-8d-106)) .or. (.not. (z <= 7.8d+94))) 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);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -8e-106) || !(z <= 7.8e+94)) {
		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)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -8e-106) or not (z <= 7.8e+94):
		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)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -8e-106) || !(z <= 7.8e+94))
		tmp = Float64(x_m / Float64(z * Float64(-t)));
	else
		tmp = Float64(Float64(x_m / y) / t);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -8e-106) || ~((z <= 7.8e+94)))
		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]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -8e-106], N[Not[LessEqual[z, 7.8e+94]], $MachinePrecision]], N[(x$95$m / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -7.99999999999999953e-106 or 7.79999999999999971e94 < z

   1. Initial program 81.2%

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

   3. Taylor expanded in t around inf 48.3%

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

      1. associate-/r* 47.4%

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

   5. Simplified 47.4%

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

      1. div-inv 47.4%

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

      2. associate-/l* 46.1%

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

   7. Applied egg-rr 46.1%

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

   8. Taylor expanded in y around 0 43.8%

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

      1. mul-1-neg 43.8%

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

      2. distribute-frac-neg 43.8%

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

      3. *-commutative 43.8%

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

   10. Simplified 43.8%

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

   if -7.99999999999999953e-106 < z < 7.79999999999999971e94

   1. Initial program 89.3%

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

      1. associate-/r* 96.7%

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

      2. div-inv 96.6%

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

   4. Applied egg-rr 96.6%

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

      1. *-commutative 96.6%

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

      2. clear-num 96.5%

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

      3. un-div-inv 96.6%

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

   6. Applied egg-rr 96.6%

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

   7. Taylor expanded in z around 0 60.9%

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

      1. associate-/l/ 68.5%

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

   9. Simplified 68.5%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-106} \lor \neg \left(z \leq 7.8 \cdot 10^{+94}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 45.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+88} \lor \neg \left(z \leq 7.8 \cdot 10^{+93}\right):\\ \;\;\;\;\frac{x\_m}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -3.4e+88) (not (<= z 7.8e+93)))
    (/ x_m (* y z))
    (/ x_m (* y t)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -3.4e+88) || !(z <= 7.8e+93)) {
		tmp = x_m / (y * z);
	} else {
		tmp = x_m / (y * t);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
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 <= (-3.4d+88)) .or. (.not. (z <= 7.8d+93))) then
        tmp = x_m / (y * z)
    else
        tmp = x_m / (y * t)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -3.4e+88) || !(z <= 7.8e+93)) {
		tmp = x_m / (y * z);
	} else {
		tmp = x_m / (y * t);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -3.4e+88) or not (z <= 7.8e+93):
		tmp = x_m / (y * z)
	else:
		tmp = x_m / (y * t)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -3.4e+88) || !(z <= 7.8e+93))
		tmp = Float64(x_m / Float64(y * z));
	else
		tmp = Float64(x_m / Float64(y * t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -3.4e+88) || ~((z <= 7.8e+93)))
		tmp = x_m / (y * z);
	else
		tmp = x_m / (y * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -3.4e+88], N[Not[LessEqual[z, 7.8e+93]], $MachinePrecision]], N[(x$95$m / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -3.40000000000000004e88 or 7.8000000000000005e93 < z

   1. Initial program 77.2%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 95.0%

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

      1. associate-*r/ 95.0%

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

      2. neg-mul-1 95.0%

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

   7. Simplified 95.0%

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

      1. div-inv 94.9%

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

      2. associate-/l* 74.8%

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

      3. add-sqr-sqrt 43.6%

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

      4. sqrt-unprod 69.4%

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

      5. sqr-neg 69.4%

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

      6. sqrt-unprod 28.2%

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

      7. add-sqr-sqrt 69.3%

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

   9. Applied egg-rr 69.3%

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

       1. associate-/r* 70.3%

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

       2. associate-*r/ 70.3%

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

       3. *-rgt-identity 70.3%

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

   11. Simplified 70.3%

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

   12. Taylor expanded in z around 0 42.8%

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

       1. *-commutative 42.8%

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

   14. Simplified 42.8%

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

   if -3.40000000000000004e88 < z < 7.8000000000000005e93

   1. Initial program 89.8%

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

   3. Taylor expanded in z around 0 53.2%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+88} \lor \neg \left(z \leq 7.8 \cdot 10^{+93}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 47.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+136} \lor \neg \left(z \leq 1.05 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{x\_m}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -1.7e+136) (not (<= z 1.05e+113)))
    (/ x_m (* y z))
    (/ (/ x_m t) y))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e+136) || !(z <= 1.05e+113)) {
		tmp = x_m / (y * z);
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.7d+136)) .or. (.not. (z <= 1.05d+113))) then
        tmp = x_m / (y * z)
    else
        tmp = (x_m / t) / y
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e+136) || !(z <= 1.05e+113)) {
		tmp = x_m / (y * z);
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -1.7e+136) or not (z <= 1.05e+113):
		tmp = x_m / (y * z)
	else:
		tmp = (x_m / t) / y
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -1.7e+136) || !(z <= 1.05e+113))
		tmp = Float64(x_m / Float64(y * z));
	else
		tmp = Float64(Float64(x_m / t) / y);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -1.7e+136) || ~((z <= 1.05e+113)))
		tmp = x_m / (y * z);
	else
		tmp = (x_m / t) / y;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -1.7e+136], N[Not[LessEqual[z, 1.05e+113]], $MachinePrecision]], N[(x$95$m / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.69999999999999998e136 or 1.0499999999999999e113 < z

   1. Initial program 76.3%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 96.6%

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

      1. associate-*r/ 96.6%

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

      2. neg-mul-1 96.6%

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

   7. Simplified 96.6%

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

      1. div-inv 96.4%

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

      2. associate-/l* 75.7%

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

      3. add-sqr-sqrt 44.9%

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

      4. sqrt-unprod 70.7%

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

      5. sqr-neg 70.7%

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

      6. sqrt-unprod 28.6%

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

      7. add-sqr-sqrt 71.8%

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

   9. Applied egg-rr 71.8%

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

       1. associate-/r* 71.8%

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

       2. associate-*r/ 71.8%

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

       3. *-rgt-identity 71.8%

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

   11. Simplified 71.8%

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

   12. Taylor expanded in z around 0 43.8%

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

       1. *-commutative 43.8%

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

   14. Simplified 43.8%

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

   if -1.69999999999999998e136 < z < 1.0499999999999999e113

   1. Initial program 89.4%

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

   3. Taylor expanded in x around 0 89.4%

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

      1. associate-/l/ 96.0%

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

   5. Simplified 96.0%

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

   6. Taylor expanded in z around 0 50.6%

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

      1. associate-/r* 56.1%

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

   8. Simplified 56.1%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+136} \lor \neg \left(z \leq 1.05 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+136}:\\ \;\;\;\;\frac{x\_m}{y \cdot z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+95}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{y}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= z -6.6e+136)
    (/ x_m (* y z))
    (if (<= z 6.8e+95) (/ (/ x_m t) y) (/ (/ x_m z) y)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -6.6e+136) {
		tmp = x_m / (y * z);
	} else if (z <= 6.8e+95) {
		tmp = (x_m / t) / y;
	} else {
		tmp = (x_m / z) / y;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6.6d+136)) then
        tmp = x_m / (y * z)
    else if (z <= 6.8d+95) then
        tmp = (x_m / t) / y
    else
        tmp = (x_m / z) / y
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -6.6e+136) {
		tmp = x_m / (y * z);
	} else if (z <= 6.8e+95) {
		tmp = (x_m / t) / y;
	} else {
		tmp = (x_m / z) / y;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if z <= -6.6e+136:
		tmp = x_m / (y * z)
	elif z <= 6.8e+95:
		tmp = (x_m / t) / y
	else:
		tmp = (x_m / z) / y
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (z <= -6.6e+136)
		tmp = Float64(x_m / Float64(y * z));
	elseif (z <= 6.8e+95)
		tmp = Float64(Float64(x_m / t) / y);
	else
		tmp = Float64(Float64(x_m / z) / y);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (z <= -6.6e+136)
		tmp = x_m / (y * z);
	elseif (z <= 6.8e+95)
		tmp = (x_m / t) / y;
	else
		tmp = (x_m / z) / y;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[z, -6.6e+136], N[(x$95$m / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+95], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] / y), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -6.59999999999999984e136

   1. Initial program 77.9%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 99.9%

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

      1. associate-*r/ 99.9%

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

      2. neg-mul-1 99.9%

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

   7. Simplified 99.9%

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

      1. div-inv 99.8%

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

      2. associate-/l* 77.8%

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

      3. add-sqr-sqrt 45.1%

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

      4. sqrt-unprod 73.9%

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

      5. sqr-neg 73.9%

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

      6. sqrt-unprod 32.8%

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

      7. add-sqr-sqrt 75.1%

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

   9. Applied egg-rr 75.1%

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

       1. associate-/r* 75.1%

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

       2. associate-*r/ 75.1%

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

       3. *-rgt-identity 75.1%

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

   11. Simplified 75.1%

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

   12. Taylor expanded in z around 0 45.0%

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

       1. *-commutative 45.0%

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

   14. Simplified 45.0%

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

   if -6.59999999999999984e136 < z < 6.80000000000000043e95

   1. Initial program 89.1%

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

   3. Taylor expanded in x around 0 89.1%

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

      1. associate-/l/ 95.9%

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

   5. Simplified 95.9%

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

   6. Taylor expanded in z around 0 51.7%

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

      1. associate-/r* 57.4%

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

   8. Simplified 57.4%

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

   if 6.80000000000000043e95 < z

   1. Initial program 77.5%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 93.0%

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

      1. associate-*r/ 93.0%

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

      2. neg-mul-1 93.0%

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

   7. Simplified 93.0%

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

      1. div-inv 92.9%

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

      2. associate-/l* 74.9%

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

      3. add-sqr-sqrt 42.6%

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

      4. sqrt-unprod 69.7%

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

      5. sqr-neg 69.7%

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

      6. sqrt-unprod 28.8%

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

      7. add-sqr-sqrt 68.7%

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

   9. Applied egg-rr 68.7%

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

       1. associate-/r* 68.8%

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

       2. associate-*r/ 68.8%

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

       3. *-rgt-identity 68.8%

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

   11. Simplified 68.8%

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

   12. Taylor expanded in z around 0 44.7%

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

       1. *-commutative 44.7%

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

   14. Simplified 44.7%

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

   15. Taylor expanded in x around 0 44.7%

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

       1. *-commutative 44.7%

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

       2. associate-/r* 48.2%

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

   17. Simplified 48.2%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+136}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+95}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 48.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-51}:\\ \;\;\;\;\frac{x\_m}{-y \cdot z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+96}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{y}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= z -4.2e-51)
    (/ x_m (- (* y z)))
    (if (<= z 2.7e+96) (/ (/ x_m y) t) (/ (/ x_m z) y)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e-51) {
		tmp = x_m / -(y * z);
	} else if (z <= 2.7e+96) {
		tmp = (x_m / y) / t;
	} else {
		tmp = (x_m / z) / y;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
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 <= (-4.2d-51)) then
        tmp = x_m / -(y * z)
    else if (z <= 2.7d+96) then
        tmp = (x_m / y) / t
    else
        tmp = (x_m / z) / y
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e-51) {
		tmp = x_m / -(y * z);
	} else if (z <= 2.7e+96) {
		tmp = (x_m / y) / t;
	} else {
		tmp = (x_m / z) / y;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if z <= -4.2e-51:
		tmp = x_m / -(y * z)
	elif z <= 2.7e+96:
		tmp = (x_m / y) / t
	else:
		tmp = (x_m / z) / y
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (z <= -4.2e-51)
		tmp = Float64(x_m / Float64(-Float64(y * z)));
	elseif (z <= 2.7e+96)
		tmp = Float64(Float64(x_m / y) / t);
	else
		tmp = Float64(Float64(x_m / z) / y);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (z <= -4.2e-51)
		tmp = x_m / -(y * z);
	elseif (z <= 2.7e+96)
		tmp = (x_m / y) / t;
	else
		tmp = (x_m / z) / y;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[z, -4.2e-51], N[(x$95$m / (-N[(y * z), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 2.7e+96], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] / y), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -4.20000000000000003e-51

   1. Initial program 82.6%

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

      1. associate-/l/ 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in t around 0 85.4%

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

      1. associate-*r/ 85.4%

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

      2. neg-mul-1 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in z around 0 36.8%

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

      1. mul-1-neg 36.8%

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

      2. distribute-neg-frac2 36.8%

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

      3. *-commutative 36.8%

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

      4. distribute-rgt-neg-out 36.8%

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

   10. Simplified 36.8%

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

   if -4.20000000000000003e-51 < z < 2.70000000000000022e96

   1. Initial program 89.4%

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

      1. associate-/r* 96.2%

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

      2. div-inv 96.2%

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

   4. Applied egg-rr 96.2%

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

      1. *-commutative 96.2%

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

      2. clear-num 96.1%

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

      3. un-div-inv 96.2%

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

   6. Applied egg-rr 96.2%

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

   7. Taylor expanded in z around 0 57.6%

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

      1. associate-/l/ 64.7%

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

   9. Simplified 64.7%

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

   if 2.70000000000000022e96 < z

   1. Initial program 77.5%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 93.0%

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

      1. associate-*r/ 93.0%

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

      2. neg-mul-1 93.0%

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

   7. Simplified 93.0%

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

      1. div-inv 92.9%

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

      2. associate-/l* 74.9%

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

      3. add-sqr-sqrt 42.6%

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

      4. sqrt-unprod 69.7%

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

      5. sqr-neg 69.7%

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

      6. sqrt-unprod 28.8%

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

      7. add-sqr-sqrt 68.7%

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

   9. Applied egg-rr 68.7%

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

       1. associate-/r* 68.8%

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

       2. associate-*r/ 68.8%

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

       3. *-rgt-identity 68.8%

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

   11. Simplified 68.8%

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

   12. Taylor expanded in z around 0 44.7%

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

       1. *-commutative 44.7%

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

   14. Simplified 44.7%

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

   15. Taylor expanded in x around 0 44.7%

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

       1. *-commutative 44.7%

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

       2. associate-/r* 48.2%

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

   17. Simplified 48.2%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{-y \cdot z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+96}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 69.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z - t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= y -5.2e-63) (/ (/ x_m y) (- t z)) (/ (/ x_m z) (- z t)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e-63) {
		tmp = (x_m / y) / (t - z);
	} else {
		tmp = (x_m / z) / (z - t);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
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 <= (-5.2d-63)) then
        tmp = (x_m / y) / (t - z)
    else
        tmp = (x_m / z) / (z - t)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e-63) {
		tmp = (x_m / y) / (t - z);
	} else {
		tmp = (x_m / z) / (z - t);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -5.2e-63:
		tmp = (x_m / y) / (t - z)
	else:
		tmp = (x_m / z) / (z - t)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -5.2e-63)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	else
		tmp = Float64(Float64(x_m / z) / Float64(z - t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -5.2e-63)
		tmp = (x_m / y) / (t - z);
	else
		tmp = (x_m / z) / (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]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -5.2e-63], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -5.2000000000000003e-63

   1. Initial program 81.8%

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

   3. Taylor expanded in y around inf 77.1%

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

      1. associate-/r* 85.0%

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

   5. Simplified 85.0%

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

   if -5.2000000000000003e-63 < y

   1. Initial program 86.7%

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

   3. Taylor expanded in x around 0 86.7%

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

      1. associate-/l/ 97.1%

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

   5. Simplified 97.1%

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

   6. Taylor expanded in y around 0 60.5%

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

      1. mul-1-neg 60.5%

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

      2. associate-/r* 64.8%

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

      3. distribute-neg-frac2 64.8%

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

      4. neg-sub0 64.8%

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

      5. associate--r- 64.8%

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

      6. neg-sub0 64.8%

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

   8. Simplified 64.8%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 39.1% accurate, 1.8× speedup

Math

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

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(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);
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)
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);
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)
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)
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);
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]
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 85.2%

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

3. Taylor expanded in z around 0 40.8%

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

4. Final simplification 40.8%

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

Developer target: 87.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;\frac{x}{t\_1} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (< (/ x t_1) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if ((x / t_1) < 0.0d0) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = x * (1.0d0 / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if (x / t_1) < 0.0:
		tmp = (x / (y - z)) / (t - z)
	else:
		tmp = x * (1.0 / t_1)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (Float64(x / t_1) < 0.0)
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(x * Float64(1.0 / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if ((x / t_1) < 0.0)
		tmp = (x / (y - z)) / (t - z);
	else
		tmp = x * (1.0 / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Less[N[(x / t$95$1), $MachinePrecision], 0.0], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024039 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

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

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