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

Percentage Accurate: 88.6% → 98.3%

Time: 16.5s

Alternatives: 21

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 0.0× speedup

Math

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

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (* (/ (sqrt x_m) (- y z)) (/ (sqrt x_m) (- 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) {
	return x_s * ((sqrt(x_m) / (y - z)) * (sqrt(x_m) / (t - z)));
}

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 * ((sqrt(x_m) / (y - z)) * (sqrt(x_m) / (t - z)))
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 * ((Math.sqrt(x_m) / (y - z)) * (Math.sqrt(x_m) / (t - z)));
}

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 * ((math.sqrt(x_m) / (y - z)) * (math.sqrt(x_m) / (t - z)))

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(Float64(sqrt(x_m) / Float64(y - z)) * Float64(sqrt(x_m) / Float64(t - z))))
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 * ((sqrt(x_m) / (y - z)) * (sqrt(x_m) / (t - z)));
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[(N[(N[Sqrt[x$95$m], $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[x$95$m], $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 88.6%

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

   1. add-sqr-sqrt 45.8%

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

   2. times-frac 51.5%

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

4. Applied egg-rr 51.5%

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

5. Final simplification 51.5%

   \[\leadsto \frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z} \]
6. Add Preprocessing

Alternative 2: 72.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{\frac{-x_m}{z}}{t - z}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+196}:\\ \;\;\;\;\frac{\frac{x_m}{t - z}}{y}\\ \mathbf{elif}\;y \leq -7200000:\\ \;\;\;\;\frac{x_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-205}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x_m}{t}}{y}\\ \end{array} \end{array} \end{array} \]

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 (/ (/ (- x_m) z) (- t z))))
   (*
    x_s
    (if (<= y -7.2e+196)
      (/ (/ x_m (- t z)) y)
      (if (<= y -7200000.0)
        (/ x_m (* y (- t z)))
        (if (<= y 1.45e-251)
          t_1
          (if (<= y 8e-205)
            (/ x_m (* (- y z) t))
            (if (<= y 1.1e+28) t_1 (/ (/ 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 t_1 = (-x_m / z) / (t - z);
	double tmp;
	if (y <= -7.2e+196) {
		tmp = (x_m / (t - z)) / y;
	} else if (y <= -7200000.0) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 1.45e-251) {
		tmp = t_1;
	} else if (y <= 8e-205) {
		tmp = x_m / ((y - z) * t);
	} else if (y <= 1.1e+28) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (-x_m / z) / (t - z)
    if (y <= (-7.2d+196)) then
        tmp = (x_m / (t - z)) / y
    else if (y <= (-7200000.0d0)) then
        tmp = x_m / (y * (t - z))
    else if (y <= 1.45d-251) then
        tmp = t_1
    else if (y <= 8d-205) then
        tmp = x_m / ((y - z) * t)
    else if (y <= 1.1d+28) then
        tmp = t_1
    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 t_1 = (-x_m / z) / (t - z);
	double tmp;
	if (y <= -7.2e+196) {
		tmp = (x_m / (t - z)) / y;
	} else if (y <= -7200000.0) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 1.45e-251) {
		tmp = t_1;
	} else if (y <= 8e-205) {
		tmp = x_m / ((y - z) * t);
	} else if (y <= 1.1e+28) {
		tmp = t_1;
	} 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):
	t_1 = (-x_m / z) / (t - z)
	tmp = 0
	if y <= -7.2e+196:
		tmp = (x_m / (t - z)) / y
	elif y <= -7200000.0:
		tmp = x_m / (y * (t - z))
	elif y <= 1.45e-251:
		tmp = t_1
	elif y <= 8e-205:
		tmp = x_m / ((y - z) * t)
	elif y <= 1.1e+28:
		tmp = t_1
	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)
	t_1 = Float64(Float64(Float64(-x_m) / z) / Float64(t - z))
	tmp = 0.0
	if (y <= -7.2e+196)
		tmp = Float64(Float64(x_m / Float64(t - z)) / y);
	elseif (y <= -7200000.0)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (y <= 1.45e-251)
		tmp = t_1;
	elseif (y <= 8e-205)
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	elseif (y <= 1.1e+28)
		tmp = t_1;
	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)
	t_1 = (-x_m / z) / (t - z);
	tmp = 0.0;
	if (y <= -7.2e+196)
		tmp = (x_m / (t - z)) / y;
	elseif (y <= -7200000.0)
		tmp = x_m / (y * (t - z));
	elseif (y <= 1.45e-251)
		tmp = t_1;
	elseif (y <= 8e-205)
		tmp = x_m / ((y - z) * t);
	elseif (y <= 1.1e+28)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(N[((-x$95$m) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -7.2e+196], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -7200000.0], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e-251], t$95$1, If[LessEqual[y, 8e-205], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+28], t$95$1, N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]]]]]), $MachinePrecision]]

Derivation

1. Split input into 5 regimes

2. if y < -7.20000000000000015e196

   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 84.1%

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

      1. *-commutative 84.1%

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

      2. associate-/r* 100.0%

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

   5. Simplified 100.0%

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

   if -7.20000000000000015e196 < y < -7.2e6

   1. Initial program 84.8%

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

   3. Taylor expanded in y around inf 75.3%

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

      1. *-commutative 75.3%

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

   5. Simplified 75.3%

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

   if -7.2e6 < y < 1.45e-251 or 8e-205 < y < 1.09999999999999993e28

   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. add-sqr-sqrt 49.3%

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

      2. times-frac 56.4%

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

   4. Applied egg-rr 56.4%

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

      1. associate-*r/ 54.9%

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

      2. associate-*l/ 54.8%

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

      3. add-sqr-sqrt 98.3%

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

   6. Applied egg-rr 98.3%

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

   7. Taylor expanded in y around 0 81.3%

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

      1. associate-*r/ 81.3%

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

      2. neg-mul-1 81.3%

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

   9. Simplified 81.3%

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

   if 1.45e-251 < y < 8e-205

   1. Initial program 99.4%

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

   3. Taylor expanded in t around inf 79.4%

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

   if 1.09999999999999993e28 < y

   1. Initial program 89.6%

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

   3. Taylor expanded in y around inf 86.7%

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

      1. *-commutative 86.7%

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

      2. associate-/r* 87.1%

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

   5. Simplified 87.1%

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

   6. Taylor expanded in t around inf 54.3%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+196}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -7200000:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-251}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-205}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 47.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+184}:\\ \;\;\;\;\frac{\frac{-x_m}{y}}{z}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+65}:\\ \;\;\;\;\frac{x_m}{y \cdot t}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-24}:\\ \;\;\;\;\frac{-x_m}{y \cdot z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{-x_m}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x_m}{t}}{y}\\ \end{array} \end{array} \]

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 (<= y -1.85e+184)
    (/ (/ (- x_m) y) z)
    (if (<= y -5.6e+65)
      (/ x_m (* y t))
      (if (<= y -2.8e-24)
        (/ (- x_m) (* y z))
        (if (<= y 2.2e+16) (/ (- x_m) (* z t)) (/ (/ 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 (y <= -1.85e+184) {
		tmp = (-x_m / y) / z;
	} else if (y <= -5.6e+65) {
		tmp = x_m / (y * t);
	} else if (y <= -2.8e-24) {
		tmp = -x_m / (y * z);
	} else if (y <= 2.2e+16) {
		tmp = -x_m / (z * t);
	} 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 (y <= (-1.85d+184)) then
        tmp = (-x_m / y) / z
    else if (y <= (-5.6d+65)) then
        tmp = x_m / (y * t)
    else if (y <= (-2.8d-24)) then
        tmp = -x_m / (y * z)
    else if (y <= 2.2d+16) then
        tmp = -x_m / (z * t)
    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 (y <= -1.85e+184) {
		tmp = (-x_m / y) / z;
	} else if (y <= -5.6e+65) {
		tmp = x_m / (y * t);
	} else if (y <= -2.8e-24) {
		tmp = -x_m / (y * z);
	} else if (y <= 2.2e+16) {
		tmp = -x_m / (z * t);
	} 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 y <= -1.85e+184:
		tmp = (-x_m / y) / z
	elif y <= -5.6e+65:
		tmp = x_m / (y * t)
	elif y <= -2.8e-24:
		tmp = -x_m / (y * z)
	elif y <= 2.2e+16:
		tmp = -x_m / (z * t)
	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 (y <= -1.85e+184)
		tmp = Float64(Float64(Float64(-x_m) / y) / z);
	elseif (y <= -5.6e+65)
		tmp = Float64(x_m / Float64(y * t));
	elseif (y <= -2.8e-24)
		tmp = Float64(Float64(-x_m) / Float64(y * z));
	elseif (y <= 2.2e+16)
		tmp = Float64(Float64(-x_m) / Float64(z * t));
	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 (y <= -1.85e+184)
		tmp = (-x_m / y) / z;
	elseif (y <= -5.6e+65)
		tmp = x_m / (y * t);
	elseif (y <= -2.8e-24)
		tmp = -x_m / (y * z);
	elseif (y <= 2.2e+16)
		tmp = -x_m / (z * t);
	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[LessEqual[y, -1.85e+184], N[(N[((-x$95$m) / y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -5.6e+65], N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.8e-24], N[((-x$95$m) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+16], N[((-x$95$m) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if y < -1.8499999999999999e184

   1. Initial program 85.7%

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

   3. Taylor expanded in y around inf 85.7%

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

      1. *-commutative 85.7%

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

      2. associate-/r* 99.9%

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

   5. Simplified 99.9%

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

      1. clear-num 99.5%

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

      2. inv-pow 99.5%

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

   7. Applied egg-rr 99.5%

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

      1. unpow-1 99.5%

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

   9. Simplified 99.5%

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

   10. Taylor expanded in t around 0 60.3%

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

       1. mul-1-neg 60.3%

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

       2. associate-/r* 79.1%

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

       3. distribute-neg-frac 79.1%

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

       4. distribute-frac-neg 79.1%

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

   12. Simplified 79.1%

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

   if -1.8499999999999999e184 < y < -5.5999999999999998e65

   1. Initial program 75.7%

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

   3. Taylor expanded in z around 0 37.3%

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

   if -5.5999999999999998e65 < y < -2.8000000000000002e-24

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf 75.1%

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

      1. *-commutative 75.1%

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

      2. associate-/r* 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in t around 0 44.4%

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

      1. associate-*r/ 44.4%

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

      2. neg-mul-1 44.4%

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

      3. *-commutative 44.4%

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

   8. Simplified 44.4%

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

   if -2.8000000000000002e-24 < y < 2.2e16

   1. Initial program 89.1%

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

   3. Taylor expanded in y around 0 74.7%

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

      1. associate-*r/ 74.7%

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

      2. neg-mul-1 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in z around 0 33.4%

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

      1. associate-*r/ 33.4%

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

      2. neg-mul-1 33.4%

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

   8. Simplified 33.4%

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

   if 2.2e16 < y

   1. Initial program 90.1%

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

   3. Taylor expanded in y around inf 86.6%

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

      1. *-commutative 86.6%

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

      2. associate-/r* 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in t around inf 52.9%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+184}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-24}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 46.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+190}:\\ \;\;\;\;\frac{\frac{-x_m}{z}}{y}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+66}:\\ \;\;\;\;\frac{x_m}{y \cdot t}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-24}:\\ \;\;\;\;\frac{-x_m}{y \cdot z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{-x_m}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x_m}{t}}{y}\\ \end{array} \end{array} \]

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 (<= y -9.8e+190)
    (/ (/ (- x_m) z) y)
    (if (<= y -1.05e+66)
      (/ x_m (* y t))
      (if (<= y -3.3e-24)
        (/ (- x_m) (* y z))
        (if (<= y 2.2e+16) (/ (- x_m) (* z t)) (/ (/ 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 (y <= -9.8e+190) {
		tmp = (-x_m / z) / y;
	} else if (y <= -1.05e+66) {
		tmp = x_m / (y * t);
	} else if (y <= -3.3e-24) {
		tmp = -x_m / (y * z);
	} else if (y <= 2.2e+16) {
		tmp = -x_m / (z * t);
	} 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 (y <= (-9.8d+190)) then
        tmp = (-x_m / z) / y
    else if (y <= (-1.05d+66)) then
        tmp = x_m / (y * t)
    else if (y <= (-3.3d-24)) then
        tmp = -x_m / (y * z)
    else if (y <= 2.2d+16) then
        tmp = -x_m / (z * t)
    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 (y <= -9.8e+190) {
		tmp = (-x_m / z) / y;
	} else if (y <= -1.05e+66) {
		tmp = x_m / (y * t);
	} else if (y <= -3.3e-24) {
		tmp = -x_m / (y * z);
	} else if (y <= 2.2e+16) {
		tmp = -x_m / (z * t);
	} 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 y <= -9.8e+190:
		tmp = (-x_m / z) / y
	elif y <= -1.05e+66:
		tmp = x_m / (y * t)
	elif y <= -3.3e-24:
		tmp = -x_m / (y * z)
	elif y <= 2.2e+16:
		tmp = -x_m / (z * t)
	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 (y <= -9.8e+190)
		tmp = Float64(Float64(Float64(-x_m) / z) / y);
	elseif (y <= -1.05e+66)
		tmp = Float64(x_m / Float64(y * t));
	elseif (y <= -3.3e-24)
		tmp = Float64(Float64(-x_m) / Float64(y * z));
	elseif (y <= 2.2e+16)
		tmp = Float64(Float64(-x_m) / Float64(z * t));
	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 (y <= -9.8e+190)
		tmp = (-x_m / z) / y;
	elseif (y <= -1.05e+66)
		tmp = x_m / (y * t);
	elseif (y <= -3.3e-24)
		tmp = -x_m / (y * z);
	elseif (y <= 2.2e+16)
		tmp = -x_m / (z * t);
	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[LessEqual[y, -9.8e+190], N[(N[((-x$95$m) / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -1.05e+66], N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.3e-24], N[((-x$95$m) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+16], N[((-x$95$m) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if y < -9.7999999999999993e190

   1. Initial program 85.7%

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

   3. Taylor expanded in y around inf 85.7%

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

      1. *-commutative 85.7%

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

      2. associate-/r* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in t around 0 74.5%

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

      1. associate-*r/ 74.5%

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

      2. neg-mul-1 74.5%

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

   8. Simplified 74.5%

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

   if -9.7999999999999993e190 < y < -1.05000000000000003e66

   1. Initial program 75.7%

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

   3. Taylor expanded in z around 0 37.3%

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

   if -1.05000000000000003e66 < y < -3.29999999999999984e-24

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf 75.1%

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

      1. *-commutative 75.1%

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

      2. associate-/r* 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in t around 0 44.4%

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

      1. associate-*r/ 44.4%

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

      2. neg-mul-1 44.4%

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

      3. *-commutative 44.4%

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

   8. Simplified 44.4%

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

   if -3.29999999999999984e-24 < y < 2.2e16

   1. Initial program 89.1%

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

   3. Taylor expanded in y around 0 74.7%

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

      1. associate-*r/ 74.7%

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

      2. neg-mul-1 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in z around 0 33.4%

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

      1. associate-*r/ 33.4%

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

      2. neg-mul-1 33.4%

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

   8. Simplified 33.4%

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

   if 2.2e16 < y

   1. Initial program 90.1%

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

   3. Taylor expanded in y around inf 86.6%

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

      1. *-commutative 86.6%

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

      2. associate-/r* 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in t around inf 52.9%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+190}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-24}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 47.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+194}:\\ \;\;\;\;\frac{\frac{-x_m}{z}}{y}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+66}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x_m}}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-24}:\\ \;\;\;\;\frac{-x_m}{y \cdot z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+16}:\\ \;\;\;\;\frac{-x_m}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x_m}{t}}{y}\\ \end{array} \end{array} \]

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 (<= y -6.4e+194)
    (/ (/ (- x_m) z) y)
    (if (<= y -1.3e+66)
      (/ 1.0 (* t (/ y x_m)))
      (if (<= y -3.3e-24)
        (/ (- x_m) (* y z))
        (if (<= y 6.4e+16) (/ (- x_m) (* z t)) (/ (/ 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 (y <= -6.4e+194) {
		tmp = (-x_m / z) / y;
	} else if (y <= -1.3e+66) {
		tmp = 1.0 / (t * (y / x_m));
	} else if (y <= -3.3e-24) {
		tmp = -x_m / (y * z);
	} else if (y <= 6.4e+16) {
		tmp = -x_m / (z * t);
	} 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 (y <= (-6.4d+194)) then
        tmp = (-x_m / z) / y
    else if (y <= (-1.3d+66)) then
        tmp = 1.0d0 / (t * (y / x_m))
    else if (y <= (-3.3d-24)) then
        tmp = -x_m / (y * z)
    else if (y <= 6.4d+16) then
        tmp = -x_m / (z * t)
    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 (y <= -6.4e+194) {
		tmp = (-x_m / z) / y;
	} else if (y <= -1.3e+66) {
		tmp = 1.0 / (t * (y / x_m));
	} else if (y <= -3.3e-24) {
		tmp = -x_m / (y * z);
	} else if (y <= 6.4e+16) {
		tmp = -x_m / (z * t);
	} 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 y <= -6.4e+194:
		tmp = (-x_m / z) / y
	elif y <= -1.3e+66:
		tmp = 1.0 / (t * (y / x_m))
	elif y <= -3.3e-24:
		tmp = -x_m / (y * z)
	elif y <= 6.4e+16:
		tmp = -x_m / (z * t)
	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 (y <= -6.4e+194)
		tmp = Float64(Float64(Float64(-x_m) / z) / y);
	elseif (y <= -1.3e+66)
		tmp = Float64(1.0 / Float64(t * Float64(y / x_m)));
	elseif (y <= -3.3e-24)
		tmp = Float64(Float64(-x_m) / Float64(y * z));
	elseif (y <= 6.4e+16)
		tmp = Float64(Float64(-x_m) / Float64(z * t));
	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 (y <= -6.4e+194)
		tmp = (-x_m / z) / y;
	elseif (y <= -1.3e+66)
		tmp = 1.0 / (t * (y / x_m));
	elseif (y <= -3.3e-24)
		tmp = -x_m / (y * z);
	elseif (y <= 6.4e+16)
		tmp = -x_m / (z * t);
	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[LessEqual[y, -6.4e+194], N[(N[((-x$95$m) / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -1.3e+66], N[(1.0 / N[(t * N[(y / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.3e-24], N[((-x$95$m) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e+16], N[((-x$95$m) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if y < -6.40000000000000042e194

   1. Initial program 85.0%

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

   3. Taylor expanded in y around inf 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-/r* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in t around 0 73.2%

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

      1. associate-*r/ 73.2%

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

      2. neg-mul-1 73.2%

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

   8. Simplified 73.2%

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

   if -6.40000000000000042e194 < y < -1.30000000000000006e66

   1. Initial program 76.7%

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

   3. Taylor expanded in z around 0 35.9%

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

      1. clear-num 35.9%

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

      2. inv-pow 35.9%

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

      3. *-commutative 35.9%

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

      4. associate-/l* 43.9%

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

   5. Applied egg-rr 43.9%

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

      1. unpow-1 43.9%

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

      2. associate-/r/ 55.8%

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

   7. Simplified 55.8%

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

   if -1.30000000000000006e66 < y < -3.29999999999999984e-24

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf 75.1%

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

      1. *-commutative 75.1%

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

      2. associate-/r* 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in t around 0 44.4%

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

      1. associate-*r/ 44.4%

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

      2. neg-mul-1 44.4%

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

      3. *-commutative 44.4%

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

   8. Simplified 44.4%

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

   if -3.29999999999999984e-24 < y < 6.4e16

   1. Initial program 89.1%

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

   3. Taylor expanded in y around 0 74.7%

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

      1. associate-*r/ 74.7%

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

      2. neg-mul-1 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in z around 0 33.4%

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

      1. associate-*r/ 33.4%

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

      2. neg-mul-1 33.4%

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

   8. Simplified 33.4%

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

   if 6.4e16 < y

   1. Initial program 90.1%

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

   3. Taylor expanded in y around inf 86.6%

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

      1. *-commutative 86.6%

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

      2. associate-/r* 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in t around inf 52.9%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+194}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+66}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-24}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+16}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x_m}{t - z}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+197}:\\ \;\;\;\;\frac{t_1}{y}\\ \mathbf{elif}\;y \leq -8200000:\\ \;\;\;\;\frac{x_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+32}:\\ \;\;\;\;\frac{-1}{z} \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x_m}{t}}{y}\\ \end{array} \end{array} \end{array} \]

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 (/ x_m (- t z))))
   (*
    x_s
    (if (<= y -2.6e+197)
      (/ t_1 y)
      (if (<= y -8200000.0)
        (/ x_m (* y (- t z)))
        (if (<= y 3.9e+32) (* (/ -1.0 z) t_1) (/ (/ 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 t_1 = x_m / (t - z);
	double tmp;
	if (y <= -2.6e+197) {
		tmp = t_1 / y;
	} else if (y <= -8200000.0) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 3.9e+32) {
		tmp = (-1.0 / z) * t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x_m / (t - z)
    if (y <= (-2.6d+197)) then
        tmp = t_1 / y
    else if (y <= (-8200000.0d0)) then
        tmp = x_m / (y * (t - z))
    else if (y <= 3.9d+32) then
        tmp = ((-1.0d0) / z) * t_1
    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 t_1 = x_m / (t - z);
	double tmp;
	if (y <= -2.6e+197) {
		tmp = t_1 / y;
	} else if (y <= -8200000.0) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 3.9e+32) {
		tmp = (-1.0 / z) * t_1;
	} 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):
	t_1 = x_m / (t - z)
	tmp = 0
	if y <= -2.6e+197:
		tmp = t_1 / y
	elif y <= -8200000.0:
		tmp = x_m / (y * (t - z))
	elif y <= 3.9e+32:
		tmp = (-1.0 / z) * t_1
	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)
	t_1 = Float64(x_m / Float64(t - z))
	tmp = 0.0
	if (y <= -2.6e+197)
		tmp = Float64(t_1 / y);
	elseif (y <= -8200000.0)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (y <= 3.9e+32)
		tmp = Float64(Float64(-1.0 / z) * t_1);
	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)
	t_1 = x_m / (t - z);
	tmp = 0.0;
	if (y <= -2.6e+197)
		tmp = t_1 / y;
	elseif (y <= -8200000.0)
		tmp = x_m / (y * (t - z));
	elseif (y <= 3.9e+32)
		tmp = (-1.0 / z) * t_1;
	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_] := Block[{t$95$1 = N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -2.6e+197], N[(t$95$1 / y), $MachinePrecision], If[LessEqual[y, -8200000.0], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e+32], N[(N[(-1.0 / z), $MachinePrecision] * t$95$1), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if y < -2.59999999999999987e197

   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 84.1%

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

      1. *-commutative 84.1%

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

      2. associate-/r* 100.0%

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

   5. Simplified 100.0%

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

   if -2.59999999999999987e197 < y < -8.2e6

   1. Initial program 84.8%

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

   3. Taylor expanded in y around inf 75.3%

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

      1. *-commutative 75.3%

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

   5. Simplified 75.3%

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

   if -8.2e6 < y < 3.8999999999999999e32

   1. Initial program 89.9%

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

   3. Taylor expanded in y around 0 73.0%

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

      1. associate-*r/ 73.0%

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

      2. neg-mul-1 73.0%

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

   5. Simplified 73.0%

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

      1. neg-mul-1 73.0%

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

      2. times-frac 82.5%

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

   7. Applied egg-rr 82.5%

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

   if 3.8999999999999999e32 < y

   1. Initial program 89.5%

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

   3. Taylor expanded in y around inf 86.5%

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

      1. *-commutative 86.5%

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

      2. associate-/r* 86.9%

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

   5. Simplified 86.9%

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

   6. Taylor expanded in t around inf 55.1%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+197}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -8200000:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+32}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+200}:\\ \;\;\;\;\frac{\frac{x_m}{t - z}}{y}\\ \mathbf{elif}\;y \leq -10000000:\\ \;\;\;\;\frac{x_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{-59}:\\ \;\;\;\;\frac{-x_m}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -3e+200)
    (/ (/ x_m (- t z)) y)
    (if (<= y -10000000.0)
      (/ x_m (* y (- t z)))
      (if (<= y 1.62e-59) (/ (- x_m) (* z (- t z))) (/ 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 (y <= -3e+200) {
		tmp = (x_m / (t - z)) / y;
	} else if (y <= -10000000.0) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 1.62e-59) {
		tmp = -x_m / (z * (t - z));
	} 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 (y <= (-3d+200)) then
        tmp = (x_m / (t - z)) / y
    else if (y <= (-10000000.0d0)) then
        tmp = x_m / (y * (t - z))
    else if (y <= 1.62d-59) then
        tmp = -x_m / (z * (t - z))
    else
        tmp = x_m / ((y - z) * t)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -3e+200) {
		tmp = (x_m / (t - z)) / y;
	} else if (y <= -10000000.0) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 1.62e-59) {
		tmp = -x_m / (z * (t - z));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -3e+200:
		tmp = (x_m / (t - z)) / y
	elif y <= -10000000.0:
		tmp = x_m / (y * (t - z))
	elif y <= 1.62e-59:
		tmp = -x_m / (z * (t - z))
	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 (y <= -3e+200)
		tmp = Float64(Float64(x_m / Float64(t - z)) / y);
	elseif (y <= -10000000.0)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (y <= 1.62e-59)
		tmp = Float64(Float64(-x_m) / Float64(z * Float64(t - z)));
	else
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -3e+200)
		tmp = (x_m / (t - z)) / y;
	elseif (y <= -10000000.0)
		tmp = x_m / (y * (t - z));
	elseif (y <= 1.62e-59)
		tmp = -x_m / (z * (t - z));
	else
		tmp = x_m / ((y - z) * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -3e+200], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -10000000.0], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.62e-59], N[((-x$95$m) / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if y < -2.99999999999999991e200

   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 84.1%

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

      1. *-commutative 84.1%

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

      2. associate-/r* 100.0%

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

   5. Simplified 100.0%

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

   if -2.99999999999999991e200 < y < -1e7

   1. Initial program 84.8%

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

   3. Taylor expanded in y around inf 75.3%

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

      1. *-commutative 75.3%

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

   5. Simplified 75.3%

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

   if -1e7 < y < 1.61999999999999989e-59

   1. Initial program 90.9%

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

   3. Taylor expanded in y around 0 75.7%

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

      1. associate-*r/ 75.7%

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

      2. neg-mul-1 75.7%

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

   5. Simplified 75.7%

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

   if 1.61999999999999989e-59 < y

   1. Initial program 88.2%

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

   3. Taylor expanded in t around inf 52.7%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+200}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -10000000:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{-59}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{x_m}{y}}{t}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-24}:\\ \;\;\;\;\frac{-x_m}{y \cdot z}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+16}:\\ \;\;\;\;\frac{-x_m}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x_m}{t}}{y}\\ \end{array} \end{array} \]

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 (<= y -1.4e+66)
    (/ (/ x_m y) t)
    (if (<= y -2.6e-24)
      (/ (- x_m) (* y z))
      (if (<= y 3.6e+16) (/ (- x_m) (* z t)) (/ (/ 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 (y <= -1.4e+66) {
		tmp = (x_m / y) / t;
	} else if (y <= -2.6e-24) {
		tmp = -x_m / (y * z);
	} else if (y <= 3.6e+16) {
		tmp = -x_m / (z * t);
	} 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 (y <= (-1.4d+66)) then
        tmp = (x_m / y) / t
    else if (y <= (-2.6d-24)) then
        tmp = -x_m / (y * z)
    else if (y <= 3.6d+16) then
        tmp = -x_m / (z * t)
    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 (y <= -1.4e+66) {
		tmp = (x_m / y) / t;
	} else if (y <= -2.6e-24) {
		tmp = -x_m / (y * z);
	} else if (y <= 3.6e+16) {
		tmp = -x_m / (z * t);
	} 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 y <= -1.4e+66:
		tmp = (x_m / y) / t
	elif y <= -2.6e-24:
		tmp = -x_m / (y * z)
	elif y <= 3.6e+16:
		tmp = -x_m / (z * t)
	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 (y <= -1.4e+66)
		tmp = Float64(Float64(x_m / y) / t);
	elseif (y <= -2.6e-24)
		tmp = Float64(Float64(-x_m) / Float64(y * z));
	elseif (y <= 3.6e+16)
		tmp = Float64(Float64(-x_m) / Float64(z * t));
	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 (y <= -1.4e+66)
		tmp = (x_m / y) / t;
	elseif (y <= -2.6e-24)
		tmp = -x_m / (y * z);
	elseif (y <= 3.6e+16)
		tmp = -x_m / (z * t);
	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[LessEqual[y, -1.4e+66], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, -2.6e-24], N[((-x$95$m) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+16], N[((-x$95$m) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if y < -1.4e66

   1. Initial program 80.4%

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

   3. Taylor expanded in z around 0 42.1%

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

      1. associate-/r* 46.5%

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

      2. div-inv 46.3%

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

   5. Applied egg-rr 46.3%

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

      1. associate-*l/ 50.3%

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

      2. un-div-inv 50.4%

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

   7. Applied egg-rr 50.4%

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

   if -1.4e66 < y < -2.6e-24

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf 75.1%

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

      1. *-commutative 75.1%

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

      2. associate-/r* 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in t around 0 44.4%

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

      1. associate-*r/ 44.4%

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

      2. neg-mul-1 44.4%

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

      3. *-commutative 44.4%

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

   8. Simplified 44.4%

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

   if -2.6e-24 < y < 3.6e16

   1. Initial program 89.1%

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

   3. Taylor expanded in y around 0 74.7%

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

      1. associate-*r/ 74.7%

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

      2. neg-mul-1 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in z around 0 33.4%

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

      1. associate-*r/ 33.4%

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

      2. neg-mul-1 33.4%

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

   8. Simplified 33.4%

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

   if 3.6e16 < y

   1. Initial program 90.1%

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

   3. Taylor expanded in y around inf 86.6%

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

      1. *-commutative 86.6%

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

      2. associate-/r* 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in t around inf 52.9%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-24}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+16}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 92.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{-x_m}{z}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+81}:\\ \;\;\;\;\frac{t_1}{t - z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+65}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{y - z}\\ \end{array} \end{array} \end{array} \]

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) z)))
   (*
    x_s
    (if (<= z -2.45e+81)
      (/ t_1 (- t z))
      (if (<= z 6e+65) (/ x_m (* (- y z) (- t z))) (/ t_1 (- 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 / z;
	double tmp;
	if (z <= -2.45e+81) {
		tmp = t_1 / (t - z);
	} else if (z <= 6e+65) {
		tmp = x_m / ((y - z) * (t - z));
	} else {
		tmp = t_1 / (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 / z
    if (z <= (-2.45d+81)) then
        tmp = t_1 / (t - z)
    else if (z <= 6d+65) then
        tmp = x_m / ((y - z) * (t - z))
    else
        tmp = t_1 / (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 / z;
	double tmp;
	if (z <= -2.45e+81) {
		tmp = t_1 / (t - z);
	} else if (z <= 6e+65) {
		tmp = x_m / ((y - z) * (t - z));
	} else {
		tmp = t_1 / (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 / z
	tmp = 0
	if z <= -2.45e+81:
		tmp = t_1 / (t - z)
	elif z <= 6e+65:
		tmp = x_m / ((y - z) * (t - z))
	else:
		tmp = t_1 / (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(Float64(-x_m) / z)
	tmp = 0.0
	if (z <= -2.45e+81)
		tmp = Float64(t_1 / Float64(t - z));
	elseif (z <= 6e+65)
		tmp = Float64(x_m / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(t_1 / 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 / z;
	tmp = 0.0;
	if (z <= -2.45e+81)
		tmp = t_1 / (t - z);
	elseif (z <= 6e+65)
		tmp = x_m / ((y - z) * (t - z));
	else
		tmp = t_1 / (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) / z), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -2.45e+81], N[(t$95$1 / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+65], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(y - z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -2.45000000000000011e81

   1. Initial program 75.6%

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

      1. add-sqr-sqrt 35.4%

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

      2. times-frac 47.6%

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

   4. Applied egg-rr 47.6%

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

      1. associate-*r/ 47.6%

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

      2. associate-*l/ 47.5%

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

      3. add-sqr-sqrt 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around 0 89.4%

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

      1. associate-*r/ 89.4%

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

      2. neg-mul-1 89.4%

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

   9. Simplified 89.4%

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

   if -2.45000000000000011e81 < z < 6.0000000000000004e65

   1. Initial program 97.0%

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

   if 6.0000000000000004e65 < z

   1. Initial program 77.4%

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

      1. add-sqr-sqrt 42.0%

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

      2. times-frac 55.8%

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

   4. Applied egg-rr 55.8%

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

   5. Taylor expanded in t around 0 75.8%

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

      1. mul-1-neg 75.8%

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

      2. associate-/r* 89.9%

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

      3. distribute-neg-frac 89.9%

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

      4. distribute-frac-neg 89.9%

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

   7. Simplified 89.9%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+81}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 92.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+81}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{t - z}{x_m}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+65}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x_m}{z}}{y - z}\\ \end{array} \end{array} \]

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 (<= z -2.65e+81)
    (/ (/ -1.0 z) (/ (- t z) x_m))
    (if (<= z 6e+65) (/ x_m (* (- y z) (- t z))) (/ (/ (- x_m) 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 tmp;
	if (z <= -2.65e+81) {
		tmp = (-1.0 / z) / ((t - z) / x_m);
	} else if (z <= 6e+65) {
		tmp = x_m / ((y - z) * (t - z));
	} else {
		tmp = (-x_m / 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) :: tmp
    if (z <= (-2.65d+81)) then
        tmp = ((-1.0d0) / z) / ((t - z) / x_m)
    else if (z <= 6d+65) then
        tmp = x_m / ((y - z) * (t - z))
    else
        tmp = (-x_m / 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 tmp;
	if (z <= -2.65e+81) {
		tmp = (-1.0 / z) / ((t - z) / x_m);
	} else if (z <= 6e+65) {
		tmp = x_m / ((y - z) * (t - z));
	} else {
		tmp = (-x_m / 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):
	tmp = 0
	if z <= -2.65e+81:
		tmp = (-1.0 / z) / ((t - z) / x_m)
	elif z <= 6e+65:
		tmp = x_m / ((y - z) * (t - z))
	else:
		tmp = (-x_m / 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)
	tmp = 0.0
	if (z <= -2.65e+81)
		tmp = Float64(Float64(-1.0 / z) / Float64(Float64(t - z) / x_m));
	elseif (z <= 6e+65)
		tmp = Float64(x_m / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(Float64(Float64(-x_m) / 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)
	tmp = 0.0;
	if (z <= -2.65e+81)
		tmp = (-1.0 / z) / ((t - z) / x_m);
	elseif (z <= 6e+65)
		tmp = x_m / ((y - z) * (t - z));
	else
		tmp = (-x_m / 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_] := N[(x$95$s * If[LessEqual[z, -2.65e+81], N[(N[(-1.0 / z), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] / x$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+65], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-x$95$m) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -2.65000000000000014e81

   1. Initial program 75.6%

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

      1. add-sqr-sqrt 35.4%

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

      2. times-frac 47.6%

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

   4. Applied egg-rr 47.6%

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

      1. frac-times 35.4%

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

      2. add-sqr-sqrt 75.6%

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

      3. associate-/l/ 99.7%

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

      4. clear-num 99.6%

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

      5. associate-/l/ 99.8%

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

      6. associate-/r* 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 89.5%

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

   if -2.65000000000000014e81 < z < 6.0000000000000004e65

   1. Initial program 97.0%

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

   if 6.0000000000000004e65 < z

   1. Initial program 77.4%

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

      1. add-sqr-sqrt 42.0%

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

      2. times-frac 55.8%

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

   4. Applied egg-rr 55.8%

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

   5. Taylor expanded in t around 0 75.8%

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

      1. mul-1-neg 75.8%

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

      2. associate-/r* 89.9%

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

      3. distribute-neg-frac 89.9%

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

      4. distribute-frac-neg 89.9%

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

   7. Simplified 89.9%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+81}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{t - z}{x}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-116}:\\ \;\;\;\;\frac{x_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+48}:\\ \;\;\;\;\frac{\frac{-x_m}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 -8.5e-116)
    (/ x_m (* y (- t z)))
    (if (<= t 1.85e+48) (/ (/ (- x_m) z) (- y z)) (/ 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 <= -8.5e-116) {
		tmp = x_m / (y * (t - z));
	} else if (t <= 1.85e+48) {
		tmp = (-x_m / z) / (y - z);
	} 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 <= (-8.5d-116)) then
        tmp = x_m / (y * (t - z))
    else if (t <= 1.85d+48) then
        tmp = (-x_m / z) / (y - z)
    else
        tmp = x_m / ((y - z) * t)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -8.5e-116) {
		tmp = x_m / (y * (t - z));
	} else if (t <= 1.85e+48) {
		tmp = (-x_m / z) / (y - z);
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= -8.5e-116:
		tmp = x_m / (y * (t - z))
	elif t <= 1.85e+48:
		tmp = (-x_m / z) / (y - z)
	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 <= -8.5e-116)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (t <= 1.85e+48)
		tmp = Float64(Float64(Float64(-x_m) / z) / Float64(y - z));
	else
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -8.5e-116)
		tmp = x_m / (y * (t - z));
	elseif (t <= 1.85e+48)
		tmp = (-x_m / z) / (y - z);
	else
		tmp = x_m / ((y - z) * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -8.5e-116], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e+48], N[(N[((-x$95$m) / z), $MachinePrecision] / N[(y - z), $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 < -8.4999999999999995e-116

   1. Initial program 88.0%

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

   3. Taylor expanded in y around inf 57.4%

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

      1. *-commutative 57.4%

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

   5. Simplified 57.4%

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

   if -8.4999999999999995e-116 < t < 1.85e48

   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. add-sqr-sqrt 44.2%

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

      2. times-frac 49.4%

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

   4. Applied egg-rr 49.4%

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

   5. Taylor expanded in t around 0 73.0%

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

      1. mul-1-neg 73.0%

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

      2. associate-/r* 79.9%

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

      3. distribute-neg-frac 79.9%

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

      4. distribute-frac-neg 79.9%

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

   7. Simplified 79.9%

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

   if 1.85e48 < t

   1. Initial program 87.7%

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

   3. Taylor expanded in t around inf 86.6%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+48}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-117} \lor \neg \left(t \leq 3 \cdot 10^{-130}\right):\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x_m}{z}}{y}\\ \end{array} \end{array} \]

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 (or (<= t -1.55e-117) (not (<= t 3e-130)))
    (/ x_m (* (- y z) 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 ((t <= -1.55e-117) || !(t <= 3e-130)) {
		tmp = x_m / ((y - z) * 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 ((t <= (-1.55d-117)) .or. (.not. (t <= 3d-130))) then
        tmp = x_m / ((y - z) * 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 ((t <= -1.55e-117) || !(t <= 3e-130)) {
		tmp = x_m / ((y - z) * 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 (t <= -1.55e-117) or not (t <= 3e-130):
		tmp = x_m / ((y - z) * 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 ((t <= -1.55e-117) || !(t <= 3e-130))
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	else
		tmp = Float64(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 ((t <= -1.55e-117) || ~((t <= 3e-130)))
		tmp = x_m / ((y - z) * 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[Or[LessEqual[t, -1.55e-117], N[Not[LessEqual[t, 3e-130]], $MachinePrecision]], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[((-x$95$m) / z), $MachinePrecision] / y), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < -1.55000000000000005e-117 or 2.99999999999999986e-130 < t

   1. Initial program 88.8%

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

   3. Taylor expanded in t around inf 68.5%

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

   if -1.55000000000000005e-117 < t < 2.99999999999999986e-130

   1. Initial program 88.3%

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

   3. Taylor expanded in y around inf 54.4%

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

      1. *-commutative 54.4%

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

      2. associate-/r* 52.7%

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

   5. Simplified 52.7%

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

   6. Taylor expanded in t around 0 41.8%

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

      1. associate-*r/ 41.8%

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

      2. neg-mul-1 41.8%

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

   8. Simplified 41.8%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-117} \lor \neg \left(t \leq 3 \cdot 10^{-130}\right):\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+130} \lor \neg \left(z \leq 1.5 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{x_m}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -2.75e+130) (not (<= z 1.5e+71)))
    (/ x_m (* z (- t z)))
    (/ 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 ((z <= -2.75e+130) || !(z <= 1.5e+71)) {
		tmp = x_m / (z * (t - z));
	} 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 ((z <= (-2.75d+130)) .or. (.not. (z <= 1.5d+71))) then
        tmp = x_m / (z * (t - z))
    else
        tmp = x_m / ((y - z) * t)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -2.75e+130) || !(z <= 1.5e+71)) {
		tmp = x_m / (z * (t - z));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -2.75e+130) or not (z <= 1.5e+71):
		tmp = x_m / (z * (t - z))
	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 ((z <= -2.75e+130) || !(z <= 1.5e+71))
		tmp = Float64(x_m / Float64(z * Float64(t - z)));
	else
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -2.75e+130) || ~((z <= 1.5e+71)))
		tmp = x_m / (z * (t - z));
	else
		tmp = x_m / ((y - z) * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -2.75e+130], N[Not[LessEqual[z, 1.5e+71]], $MachinePrecision]], N[(x$95$m / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -2.7499999999999999e130 or 1.50000000000000006e71 < z

   1. Initial program 76.8%

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

   3. Taylor expanded in y around 0 74.6%

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

      1. associate-*r/ 74.6%

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

      2. neg-mul-1 74.6%

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

   5. Simplified 74.6%

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

      1. expm1-log1p-u 74.5%

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

      2. expm1-udef 72.5%

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

      3. add-sqr-sqrt 34.0%

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

      4. sqrt-unprod 57.4%

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

      5. sqr-neg 57.4%

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

      6. sqrt-unprod 37.3%

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

      7. add-sqr-sqrt 71.4%

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

      8. associate-/r* 71.4%

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

   7. Applied egg-rr 71.4%

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

      1. expm1-def 68.9%

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

      2. expm1-log1p 68.9%

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

      3. associate-/r* 70.4%

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

   9. Simplified 70.4%

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

   if -2.7499999999999999e130 < z < 1.50000000000000006e71

   1. Initial program 94.9%

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

   3. Taylor expanded in t around inf 56.8%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+130} \lor \neg \left(z \leq 1.5 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 66.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+130}:\\ \;\;\;\;\frac{x_m}{z \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+65}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{z \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

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 -1.35e+130)
    (/ x_m (* z (- t z)))
    (if (<= z 2.5e+65) (/ x_m (* (- y z) t)) (/ x_m (* 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 tmp;
	if (z <= -1.35e+130) {
		tmp = x_m / (z * (t - z));
	} else if (z <= 2.5e+65) {
		tmp = x_m / ((y - z) * t);
	} else {
		tmp = x_m / (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) :: tmp
    if (z <= (-1.35d+130)) then
        tmp = x_m / (z * (t - z))
    else if (z <= 2.5d+65) then
        tmp = x_m / ((y - z) * t)
    else
        tmp = x_m / (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 tmp;
	if (z <= -1.35e+130) {
		tmp = x_m / (z * (t - z));
	} else if (z <= 2.5e+65) {
		tmp = x_m / ((y - z) * t);
	} else {
		tmp = x_m / (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):
	tmp = 0
	if z <= -1.35e+130:
		tmp = x_m / (z * (t - z))
	elif z <= 2.5e+65:
		tmp = x_m / ((y - z) * t)
	else:
		tmp = x_m / (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)
	tmp = 0.0
	if (z <= -1.35e+130)
		tmp = Float64(x_m / Float64(z * Float64(t - z)));
	elseif (z <= 2.5e+65)
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	else
		tmp = Float64(x_m / Float64(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)
	tmp = 0.0;
	if (z <= -1.35e+130)
		tmp = x_m / (z * (t - z));
	elseif (z <= 2.5e+65)
		tmp = x_m / ((y - z) * t);
	else
		tmp = x_m / (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_] := N[(x$95$s * If[LessEqual[z, -1.35e+130], N[(x$95$m / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+65], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -1.3499999999999999e130

   1. Initial program 74.8%

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

   3. Taylor expanded in y around 0 74.7%

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

      1. associate-*r/ 74.7%

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

      2. neg-mul-1 74.7%

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

   5. Simplified 74.7%

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

      1. expm1-log1p-u 74.7%

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

      2. expm1-udef 74.8%

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

      3. add-sqr-sqrt 40.4%

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

      4. sqrt-unprod 52.3%

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

      5. sqr-neg 52.3%

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

      6. sqrt-unprod 34.4%

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

      7. add-sqr-sqrt 74.8%

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

      8. associate-/r* 74.8%

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

   7. Applied egg-rr 74.8%

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

      1. expm1-def 71.7%

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

      2. expm1-log1p 71.7%

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

      3. associate-/r* 74.8%

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

   9. Simplified 74.8%

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

   if -1.3499999999999999e130 < z < 2.49999999999999986e65

   1. Initial program 95.4%

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

   3. Taylor expanded in t around inf 57.8%

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

   if 2.49999999999999986e65 < z

   1. Initial program 77.4%

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

      1. add-sqr-sqrt 42.0%

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

      2. times-frac 55.8%

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

   4. Applied egg-rr 55.8%

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

   5. Taylor expanded in t around 0 75.8%

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

      1. mul-1-neg 75.8%

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

      2. associate-/r* 89.9%

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

      3. distribute-neg-frac 89.9%

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

      4. distribute-frac-neg 89.9%

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

   7. Simplified 89.9%

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

      1. expm1-log1p-u 88.0%

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

      2. expm1-udef 68.0%

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

      3. associate-/l/ 67.5%

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

      4. add-sqr-sqrt 28.8%

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

      5. sqrt-unprod 57.4%

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

      6. sqr-neg 57.4%

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

      7. sqrt-unprod 37.1%

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

      8. add-sqr-sqrt 66.0%

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

      9. *-commutative 66.0%

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

   9. Applied egg-rr 66.0%

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

       1. expm1-def 65.8%

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

       2. expm1-log1p 65.8%

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

   11. Simplified 65.8%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+130}:\\ \;\;\;\;\frac{x}{z \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+198}:\\ \;\;\;\;\frac{\frac{x_m}{t - z}}{y}\\ \mathbf{elif}\;y \leq -1.46 \cdot 10^{-30}:\\ \;\;\;\;\frac{x_m}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -1.7e+198)
    (/ (/ x_m (- t z)) y)
    (if (<= y -1.46e-30) (/ x_m (* y (- t z))) (/ 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 (y <= -1.7e+198) {
		tmp = (x_m / (t - z)) / y;
	} else if (y <= -1.46e-30) {
		tmp = x_m / (y * (t - z));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
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 <= (-1.7d+198)) then
        tmp = (x_m / (t - z)) / y
    else if (y <= (-1.46d-30)) then
        tmp = x_m / (y * (t - z))
    else
        tmp = x_m / ((y - z) * t)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e+198) {
		tmp = (x_m / (t - z)) / y;
	} else if (y <= -1.46e-30) {
		tmp = x_m / (y * (t - z));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -1.7e+198:
		tmp = (x_m / (t - z)) / y
	elif y <= -1.46e-30:
		tmp = x_m / (y * (t - z))
	else:
		tmp = x_m / ((y - z) * t)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -1.7e+198)
		tmp = Float64(Float64(x_m / Float64(t - z)) / y);
	elseif (y <= -1.46e-30)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	else
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e+198)
		tmp = (x_m / (t - z)) / y;
	elseif (y <= -1.46e-30)
		tmp = x_m / (y * (t - z));
	else
		tmp = x_m / ((y - z) * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -1.7e+198], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -1.46e-30], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e198

   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 84.1%

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

      1. *-commutative 84.1%

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

      2. associate-/r* 100.0%

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

   5. Simplified 100.0%

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

   if -1.7e198 < y < -1.4600000000000001e-30

   1. Initial program 87.2%

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

   3. Taylor expanded in y around inf 75.0%

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

      1. *-commutative 75.0%

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

   5. Simplified 75.0%

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

   if -1.4600000000000001e-30 < y

   1. Initial program 89.4%

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

   3. Taylor expanded in t around inf 49.2%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+198}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -1.46 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -22000 \lor \neg \left(z \leq 1.8 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{-x_m}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x_m}{t}}{y}\\ \end{array} \end{array} \]

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 -22000.0) (not (<= z 1.8e-51)))
    (/ (- x_m) (* z t))
    (/ (/ 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 <= -22000.0) || !(z <= 1.8e-51)) {
		tmp = -x_m / (z * t);
	} 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 <= (-22000.0d0)) .or. (.not. (z <= 1.8d-51))) then
        tmp = -x_m / (z * t)
    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 <= -22000.0) || !(z <= 1.8e-51)) {
		tmp = -x_m / (z * t);
	} 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 <= -22000.0) or not (z <= 1.8e-51):
		tmp = -x_m / (z * t)
	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 <= -22000.0) || !(z <= 1.8e-51))
		tmp = Float64(Float64(-x_m) / Float64(z * t));
	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 <= -22000.0) || ~((z <= 1.8e-51)))
		tmp = -x_m / (z * t);
	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, -22000.0], N[Not[LessEqual[z, 1.8e-51]], $MachinePrecision]], N[((-x$95$m) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -22000 or 1.8e-51 < z

   1. Initial program 83.8%

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

   3. Taylor expanded in y around 0 68.4%

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

      1. associate-*r/ 68.4%

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

      2. neg-mul-1 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in z around 0 31.4%

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

      1. associate-*r/ 31.4%

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

      2. neg-mul-1 31.4%

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

   8. Simplified 31.4%

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

   if -22000 < z < 1.8e-51

   1. Initial program 96.1%

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

   3. Taylor expanded in y around inf 70.9%

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

      1. *-commutative 70.9%

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

      2. associate-/r* 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in t around inf 60.7%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -22000 \lor \neg \left(z \leq 1.8 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 46.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+61} \lor \neg \left(z \leq 1.7 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{x_m}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{y \cdot t}\\ \end{array} \end{array} \]

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 -1e+61) (not (<= z 1.7e+63)))
    (/ 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 <= -1e+61) || !(z <= 1.7e+63)) {
		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 <= (-1d+61)) .or. (.not. (z <= 1.7d+63))) 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 <= -1e+61) || !(z <= 1.7e+63)) {
		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 <= -1e+61) or not (z <= 1.7e+63):
		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 <= -1e+61) || !(z <= 1.7e+63))
		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 <= -1e+61) || ~((z <= 1.7e+63)))
		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, -1e+61], N[Not[LessEqual[z, 1.7e+63]], $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 < -9.99999999999999949e60 or 1.6999999999999999e63 < z

   1. Initial program 77.9%

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

   3. Taylor expanded in y around inf 41.0%

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

      1. *-commutative 41.0%

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

      2. associate-/r* 45.3%

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

   5. Simplified 45.3%

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

   6. Taylor expanded in t around 0 43.0%

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

      1. associate-*r/ 43.0%

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

      2. neg-mul-1 43.0%

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

   8. Simplified 43.0%

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

      1. expm1-log1p-u 42.6%

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

      2. expm1-udef 52.9%

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

      3. associate-/l/ 52.7%

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

      4. add-sqr-sqrt 26.8%

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

      5. sqrt-unprod 44.2%

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

      6. sqr-neg 44.2%

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

      7. sqrt-unprod 25.8%

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

      8. add-sqr-sqrt 52.6%

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

   10. Applied egg-rr 52.6%

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

       1. expm1-def 37.7%

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

       2. expm1-log1p 38.1%

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

       3. *-commutative 38.1%

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

   12. Simplified 38.1%

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

   if -9.99999999999999949e60 < z < 1.6999999999999999e63

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 47.4%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+61} \lor \neg \left(z \leq 1.7 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 48.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+105} \lor \neg \left(z \leq 2.2 \cdot 10^{+65}\right):\\ \;\;\;\;\frac{x_m}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x_m}{t}}{y}\\ \end{array} \end{array} \]

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 -5.4e+105) (not (<= z 2.2e+65)))
    (/ 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 <= -5.4e+105) || !(z <= 2.2e+65)) {
		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 <= (-5.4d+105)) .or. (.not. (z <= 2.2d+65))) 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 <= -5.4e+105) || !(z <= 2.2e+65)) {
		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 <= -5.4e+105) or not (z <= 2.2e+65):
		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 <= -5.4e+105) || !(z <= 2.2e+65))
		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 <= -5.4e+105) || ~((z <= 2.2e+65)))
		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, -5.4e+105], N[Not[LessEqual[z, 2.2e+65]], $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 < -5.40000000000000033e105 or 2.1999999999999998e65 < z

   1. Initial program 77.7%

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

   3. Taylor expanded in y around inf 43.3%

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

      1. *-commutative 43.3%

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

      2. associate-/r* 46.3%

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

   5. Simplified 46.3%

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

   6. Taylor expanded in t around 0 44.6%

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

      1. associate-*r/ 44.6%

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

      2. neg-mul-1 44.6%

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

   8. Simplified 44.6%

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

      1. expm1-log1p-u 44.4%

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

      2. expm1-udef 57.3%

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

      3. associate-/l/ 57.0%

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

      4. add-sqr-sqrt 28.5%

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

      5. sqrt-unprod 47.4%

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

      6. sqr-neg 47.4%

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

      7. sqrt-unprod 28.4%

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

      8. add-sqr-sqrt 56.9%

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

   10. Applied egg-rr 56.9%

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

       1. expm1-def 41.0%

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

       2. expm1-log1p 41.3%

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

       3. *-commutative 41.3%

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

   12. Simplified 41.3%

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

   if -5.40000000000000033e105 < z < 2.1999999999999998e65

   1. Initial program 95.3%

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

   3. Taylor expanded in y around inf 62.2%

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

      1. *-commutative 62.2%

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

      2. associate-/r* 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in t around inf 46.9%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+105} \lor \neg \left(z \leq 2.2 \cdot 10^{+65}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 64.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;t \leq 8.5 \cdot 10^{-101}:\\ \;\;\;\;\frac{x_m}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= t 8.5e-101) (/ x_m (* y (- t z))) (/ 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 <= 8.5e-101) {
		tmp = x_m / (y * (t - z));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
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 <= 8.5d-101) then
        tmp = x_m / (y * (t - z))
    else
        tmp = x_m / ((y - z) * t)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= 8.5e-101) {
		tmp = x_m / (y * (t - z));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= 8.5e-101:
		tmp = x_m / (y * (t - z))
	else:
		tmp = x_m / ((y - z) * t)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= 8.5e-101)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	else
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= 8.5e-101)
		tmp = x_m / (y * (t - z));
	else
		tmp = x_m / ((y - z) * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, 8.5e-101], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < 8.49999999999999941e-101

   1. Initial program 88.5%

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

   3. Taylor expanded in y around inf 54.9%

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

      1. *-commutative 54.9%

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

   5. Simplified 54.9%

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

   if 8.49999999999999941e-101 < t

   1. Initial program 88.9%

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

   3. Taylor expanded in t around inf 67.8%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 8.5 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 96.7% accurate, 1.0× speedup

Math

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

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 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) {
	return x_s * ((x_m / (y - z)) / (t - z));
}

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 - z)) / (t - z))
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 - z)) / (t - z));
}

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 - z)) / (t - z))

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(Float64(x_m / Float64(y - z)) / Float64(t - z)))
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 - z)) / (t - z));
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[(N[(x$95$m / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 88.6%

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

   1. add-sqr-sqrt 45.8%

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

   2. times-frac 51.5%

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

4. Applied egg-rr 51.5%

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

   1. associate-*r/ 49.9%

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

   2. associate-*l/ 49.8%

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

   3. add-sqr-sqrt 96.8%

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

6. Applied egg-rr 96.8%

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

7. Final simplification 96.8%

   \[\leadsto \frac{\frac{x}{y - z}}{t - z} \]
8. Add Preprocessing

Alternative 21: 39.4% 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 88.6%

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

3. Taylor expanded in z around 0 34.0%

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

4. Final simplification 34.0%

   \[\leadsto \frac{x}{y \cdot t} \]
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 2024019 
(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))))