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

Percentage Accurate: 89.4% → 98.3%

Time: 14.0s

Alternatives: 20

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: 89.4% 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 49.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{-x_m}{z \cdot t}\\ t_2 := \frac{\frac{x_m}{y}}{t}\\ t_3 := \frac{-x_m}{y \cdot z}\\ t_4 := \frac{\frac{x_m}{t}}{y}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+190}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+82}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-95}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-188}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \end{array} \]

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)))
        (t_2 (/ (/ x_m y) t))
        (t_3 (/ (- x_m) (* y z)))
        (t_4 (/ (/ x_m t) y)))
   (*
    x_s
    (if (<= y -6e+190)
      t_3
      (if (<= y -3.5e+116)
        t_2
        (if (<= y -1.4e+82)
          t_3
          (if (<= y -3.7e-95)
            t_4
            (if (<= y -1.7e-153)
              t_1
              (if (<= y -7.6e-188) t_2 (if (<= y 1.95e-39) t_1 t_4))))))))))

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);
	double t_2 = (x_m / y) / t;
	double t_3 = -x_m / (y * z);
	double t_4 = (x_m / t) / y;
	double tmp;
	if (y <= -6e+190) {
		tmp = t_3;
	} else if (y <= -3.5e+116) {
		tmp = t_2;
	} else if (y <= -1.4e+82) {
		tmp = t_3;
	} else if (y <= -3.7e-95) {
		tmp = t_4;
	} else if (y <= -1.7e-153) {
		tmp = t_1;
	} else if (y <= -7.6e-188) {
		tmp = t_2;
	} else if (y <= 1.95e-39) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = -x_m / (z * t)
    t_2 = (x_m / y) / t
    t_3 = -x_m / (y * z)
    t_4 = (x_m / t) / y
    if (y <= (-6d+190)) then
        tmp = t_3
    else if (y <= (-3.5d+116)) then
        tmp = t_2
    else if (y <= (-1.4d+82)) then
        tmp = t_3
    else if (y <= (-3.7d-95)) then
        tmp = t_4
    else if (y <= (-1.7d-153)) then
        tmp = t_1
    else if (y <= (-7.6d-188)) then
        tmp = t_2
    else if (y <= 1.95d-39) then
        tmp = t_1
    else
        tmp = t_4
    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);
	double t_2 = (x_m / y) / t;
	double t_3 = -x_m / (y * z);
	double t_4 = (x_m / t) / y;
	double tmp;
	if (y <= -6e+190) {
		tmp = t_3;
	} else if (y <= -3.5e+116) {
		tmp = t_2;
	} else if (y <= -1.4e+82) {
		tmp = t_3;
	} else if (y <= -3.7e-95) {
		tmp = t_4;
	} else if (y <= -1.7e-153) {
		tmp = t_1;
	} else if (y <= -7.6e-188) {
		tmp = t_2;
	} else if (y <= 1.95e-39) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	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)
	t_2 = (x_m / y) / t
	t_3 = -x_m / (y * z)
	t_4 = (x_m / t) / y
	tmp = 0
	if y <= -6e+190:
		tmp = t_3
	elif y <= -3.5e+116:
		tmp = t_2
	elif y <= -1.4e+82:
		tmp = t_3
	elif y <= -3.7e-95:
		tmp = t_4
	elif y <= -1.7e-153:
		tmp = t_1
	elif y <= -7.6e-188:
		tmp = t_2
	elif y <= 1.95e-39:
		tmp = t_1
	else:
		tmp = t_4
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(-x_m) / Float64(z * t))
	t_2 = Float64(Float64(x_m / y) / t)
	t_3 = Float64(Float64(-x_m) / Float64(y * z))
	t_4 = Float64(Float64(x_m / t) / y)
	tmp = 0.0
	if (y <= -6e+190)
		tmp = t_3;
	elseif (y <= -3.5e+116)
		tmp = t_2;
	elseif (y <= -1.4e+82)
		tmp = t_3;
	elseif (y <= -3.7e-95)
		tmp = t_4;
	elseif (y <= -1.7e-153)
		tmp = t_1;
	elseif (y <= -7.6e-188)
		tmp = t_2;
	elseif (y <= 1.95e-39)
		tmp = t_1;
	else
		tmp = t_4;
	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);
	t_2 = (x_m / y) / t;
	t_3 = -x_m / (y * z);
	t_4 = (x_m / t) / y;
	tmp = 0.0;
	if (y <= -6e+190)
		tmp = t_3;
	elseif (y <= -3.5e+116)
		tmp = t_2;
	elseif (y <= -1.4e+82)
		tmp = t_3;
	elseif (y <= -3.7e-95)
		tmp = t_4;
	elseif (y <= -1.7e-153)
		tmp = t_1;
	elseif (y <= -7.6e-188)
		tmp = t_2;
	elseif (y <= 1.95e-39)
		tmp = t_1;
	else
		tmp = t_4;
	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[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$3 = N[((-x$95$m) / N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -6e+190], t$95$3, If[LessEqual[y, -3.5e+116], t$95$2, If[LessEqual[y, -1.4e+82], t$95$3, If[LessEqual[y, -3.7e-95], t$95$4, If[LessEqual[y, -1.7e-153], t$95$1, If[LessEqual[y, -7.6e-188], t$95$2, If[LessEqual[y, 1.95e-39], t$95$1, t$95$4]]]]]]]), $MachinePrecision]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 49.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{-x_m}{z \cdot t}\\ t_2 := \frac{\frac{x_m}{y}}{t}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.05 \cdot 10^{-187}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x_m}{t}}{y}\\ \end{array} \end{array} \end{array} \]

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))) (t_2 (/ (/ x_m y) t)))
   (*
    x_s
    (if (<= y -1.55e-29)
      t_2
      (if (<= y -2e-149)
        t_1
        (if (<= y -3.05e-187) t_2 (if (<= y 1.1e-46) 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);
	double t_2 = (x_m / y) / t;
	double tmp;
	if (y <= -1.55e-29) {
		tmp = t_2;
	} else if (y <= -2e-149) {
		tmp = t_1;
	} else if (y <= -3.05e-187) {
		tmp = t_2;
	} else if (y <= 1.1e-46) {
		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) :: t_2
    real(8) :: tmp
    t_1 = -x_m / (z * t)
    t_2 = (x_m / y) / t
    if (y <= (-1.55d-29)) then
        tmp = t_2
    else if (y <= (-2d-149)) then
        tmp = t_1
    else if (y <= (-3.05d-187)) then
        tmp = t_2
    else if (y <= 1.1d-46) 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);
	double t_2 = (x_m / y) / t;
	double tmp;
	if (y <= -1.55e-29) {
		tmp = t_2;
	} else if (y <= -2e-149) {
		tmp = t_1;
	} else if (y <= -3.05e-187) {
		tmp = t_2;
	} else if (y <= 1.1e-46) {
		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)
	t_2 = (x_m / y) / t
	tmp = 0
	if y <= -1.55e-29:
		tmp = t_2
	elif y <= -2e-149:
		tmp = t_1
	elif y <= -3.05e-187:
		tmp = t_2
	elif y <= 1.1e-46:
		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(-x_m) / Float64(z * t))
	t_2 = Float64(Float64(x_m / y) / t)
	tmp = 0.0
	if (y <= -1.55e-29)
		tmp = t_2;
	elseif (y <= -2e-149)
		tmp = t_1;
	elseif (y <= -3.05e-187)
		tmp = t_2;
	elseif (y <= 1.1e-46)
		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);
	t_2 = (x_m / y) / t;
	tmp = 0.0;
	if (y <= -1.55e-29)
		tmp = t_2;
	elseif (y <= -2e-149)
		tmp = t_1;
	elseif (y <= -3.05e-187)
		tmp = t_2;
	elseif (y <= 1.1e-46)
		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[((-x$95$m) / N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -1.55e-29], t$95$2, If[LessEqual[y, -2e-149], t$95$1, If[LessEqual[y, -3.05e-187], t$95$2, If[LessEqual[y, 1.1e-46], t$95$1, N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]]]]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 93.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+160}:\\ \;\;\;\;\frac{-\frac{x_m}{z}}{y - z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+93}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{t - z} \cdot \frac{x_m}{z}\\ \end{array} \end{array} \]

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 -2.55e+160)
    (/ (- (/ x_m z)) (- y z))
    (if (<= z 2.4e+93)
      (/ x_m (* (- y z) (- t z)))
      (* (/ -1.0 (- t z)) (/ x_m 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 <= -2.55e+160) {
		tmp = -(x_m / z) / (y - z);
	} else if (z <= 2.4e+93) {
		tmp = x_m / ((y - z) * (t - z));
	} else {
		tmp = (-1.0 / (t - z)) * (x_m / 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 <= (-2.55d+160)) then
        tmp = -(x_m / z) / (y - z)
    else if (z <= 2.4d+93) then
        tmp = x_m / ((y - z) * (t - z))
    else
        tmp = ((-1.0d0) / (t - z)) * (x_m / 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 <= -2.55e+160) {
		tmp = -(x_m / z) / (y - z);
	} else if (z <= 2.4e+93) {
		tmp = x_m / ((y - z) * (t - z));
	} else {
		tmp = (-1.0 / (t - z)) * (x_m / 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 <= -2.55e+160:
		tmp = -(x_m / z) / (y - z)
	elif z <= 2.4e+93:
		tmp = x_m / ((y - z) * (t - z))
	else:
		tmp = (-1.0 / (t - z)) * (x_m / 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 <= -2.55e+160)
		tmp = Float64(Float64(-Float64(x_m / z)) / Float64(y - z));
	elseif (z <= 2.4e+93)
		tmp = Float64(x_m / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(Float64(-1.0 / Float64(t - z)) * Float64(x_m / 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 <= -2.55e+160)
		tmp = -(x_m / z) / (y - z);
	elseif (z <= 2.4e+93)
		tmp = x_m / ((y - z) * (t - z));
	else
		tmp = (-1.0 / (t - z)) * (x_m / 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, -2.55e+160], N[((-N[(x$95$m / z), $MachinePrecision]) / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+93], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 48.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+148}:\\ \;\;\;\;\frac{\frac{x_m}{z}}{y}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-107}:\\ \;\;\;\;-\frac{\frac{x_m}{t}}{z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-133}:\\ \;\;\;\;\frac{\frac{x_m}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x_m}{y \cdot z}\\ \end{array} \end{array} \]

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 -1.2e+148)
    (/ (/ x_m z) y)
    (if (<= z -1.35e-107)
      (- (/ (/ x_m t) z))
      (if (<= z 1.2e-133) (/ (/ x_m y) t) (/ (- x_m) (* 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 <= -1.2e+148) {
		tmp = (x_m / z) / y;
	} else if (z <= -1.35e-107) {
		tmp = -((x_m / t) / z);
	} else if (z <= 1.2e-133) {
		tmp = (x_m / y) / t;
	} else {
		tmp = -x_m / (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 <= (-1.2d+148)) then
        tmp = (x_m / z) / y
    else if (z <= (-1.35d-107)) then
        tmp = -((x_m / t) / z)
    else if (z <= 1.2d-133) then
        tmp = (x_m / y) / t
    else
        tmp = -x_m / (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 <= -1.2e+148) {
		tmp = (x_m / z) / y;
	} else if (z <= -1.35e-107) {
		tmp = -((x_m / t) / z);
	} else if (z <= 1.2e-133) {
		tmp = (x_m / y) / t;
	} else {
		tmp = -x_m / (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 <= -1.2e+148:
		tmp = (x_m / z) / y
	elif z <= -1.35e-107:
		tmp = -((x_m / t) / z)
	elif z <= 1.2e-133:
		tmp = (x_m / y) / t
	else:
		tmp = -x_m / (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 <= -1.2e+148)
		tmp = Float64(Float64(x_m / z) / y);
	elseif (z <= -1.35e-107)
		tmp = Float64(-Float64(Float64(x_m / t) / z));
	elseif (z <= 1.2e-133)
		tmp = Float64(Float64(x_m / y) / t);
	else
		tmp = Float64(Float64(-x_m) / 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 <= -1.2e+148)
		tmp = (x_m / z) / y;
	elseif (z <= -1.35e-107)
		tmp = -((x_m / t) / z);
	elseif (z <= 1.2e-133)
		tmp = (x_m / y) / t;
	else
		tmp = -x_m / (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, -1.2e+148], N[(N[(x$95$m / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, -1.35e-107], (-N[(N[(x$95$m / t), $MachinePrecision] / z), $MachinePrecision]), If[LessEqual[z, 1.2e-133], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], N[((-x$95$m) / N[(y * z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 50.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{-\frac{x_m}{z}}{y}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-108}:\\ \;\;\;\;-\frac{\frac{x_m}{t}}{z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-133}:\\ \;\;\;\;\frac{\frac{x_m}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \end{array} \]

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)) y)))
   (*
    x_s
    (if (<= z -2.9e+100)
      t_1
      (if (<= z -4.6e-108)
        (- (/ (/ x_m t) z))
        (if (<= z 1.2e-133) (/ (/ x_m y) t) t_1))))))

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) / y;
	double tmp;
	if (z <= -2.9e+100) {
		tmp = t_1;
	} else if (z <= -4.6e-108) {
		tmp = -((x_m / t) / z);
	} else if (z <= 1.2e-133) {
		tmp = (x_m / y) / t;
	} else {
		tmp = t_1;
	}
	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) / y
    if (z <= (-2.9d+100)) then
        tmp = t_1
    else if (z <= (-4.6d-108)) then
        tmp = -((x_m / t) / z)
    else if (z <= 1.2d-133) then
        tmp = (x_m / y) / t
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = -(x_m / z) / y;
	double tmp;
	if (z <= -2.9e+100) {
		tmp = t_1;
	} else if (z <= -4.6e-108) {
		tmp = -((x_m / t) / z);
	} else if (z <= 1.2e-133) {
		tmp = (x_m / y) / t;
	} else {
		tmp = t_1;
	}
	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) / y
	tmp = 0
	if z <= -2.9e+100:
		tmp = t_1
	elif z <= -4.6e-108:
		tmp = -((x_m / t) / z)
	elif z <= 1.2e-133:
		tmp = (x_m / y) / t
	else:
		tmp = t_1
	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)) / y)
	tmp = 0.0
	if (z <= -2.9e+100)
		tmp = t_1;
	elseif (z <= -4.6e-108)
		tmp = Float64(-Float64(Float64(x_m / t) / z));
	elseif (z <= 1.2e-133)
		tmp = Float64(Float64(x_m / y) / t);
	else
		tmp = t_1;
	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) / y;
	tmp = 0.0;
	if (z <= -2.9e+100)
		tmp = t_1;
	elseif (z <= -4.6e-108)
		tmp = -((x_m / t) / z);
	elseif (z <= 1.2e-133)
		tmp = (x_m / y) / t;
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[((-N[(x$95$m / z), $MachinePrecision]) / y), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -2.9e+100], t$95$1, If[LessEqual[z, -4.6e-108], (-N[(N[(x$95$m / t), $MachinePrecision] / z), $MachinePrecision]), If[LessEqual[z, 1.2e-133], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 72.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-28}:\\ \;\;\;\;\frac{\frac{x_m}{y}}{t - z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-111}:\\ \;\;\;\;\frac{-x_m}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -2.6e-28)
    (/ (/ x_m y) (- t z))
    (if (<= y 9.5e-111) (/ (- x_m) (* z (- t z))) (/ (/ x_m t) (- y z))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e-28) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 9.5e-111) {
		tmp = -x_m / (z * (t - z));
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.6d-28)) then
        tmp = (x_m / y) / (t - z)
    else if (y <= 9.5d-111) then
        tmp = -x_m / (z * (t - z))
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e-28) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 9.5e-111) {
		tmp = -x_m / (z * (t - z));
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -2.6e-28:
		tmp = (x_m / y) / (t - z)
	elif y <= 9.5e-111:
		tmp = -x_m / (z * (t - z))
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -2.6e-28)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (y <= 9.5e-111)
		tmp = Float64(Float64(-x_m) / Float64(z * Float64(t - z)));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -2.6e-28)
		tmp = (x_m / y) / (t - z);
	elseif (y <= 9.5e-111)
		tmp = -x_m / (z * (t - z));
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -2.6e-28], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e-111], N[((-x$95$m) / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{x_m}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-121}:\\ \;\;\;\;\frac{-\frac{x_m}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -5.2e-26)
    (/ (/ x_m y) (- t z))
    (if (<= y 2.9e-121) (/ (- (/ x_m z)) (- t z)) (/ (/ x_m t) (- y z))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e-26) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 2.9e-121) {
		tmp = -(x_m / z) / (t - z);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.2d-26)) then
        tmp = (x_m / y) / (t - z)
    else if (y <= 2.9d-121) then
        tmp = -(x_m / z) / (t - z)
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e-26) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 2.9e-121) {
		tmp = -(x_m / z) / (t - z);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -5.2e-26:
		tmp = (x_m / y) / (t - z)
	elif y <= 2.9e-121:
		tmp = -(x_m / z) / (t - z)
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -5.2e-26)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (y <= 2.9e-121)
		tmp = Float64(Float64(-Float64(x_m / z)) / Float64(t - z));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -5.2e-26)
		tmp = (x_m / y) / (t - z);
	elseif (y <= 2.9e-121)
		tmp = -(x_m / z) / (t - z);
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -5.2e-26], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e-121], N[((-N[(x$95$m / z), $MachinePrecision]) / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 67.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+99} \lor \neg \left(z \leq 2.7 \cdot 10^{+109}\right):\\ \;\;\;\;\frac{x_m}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 -9e+99) (not (<= z 2.7e+109)))
    (/ 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 <= -9e+99) || !(z <= 2.7e+109)) {
		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 <= (-9d+99)) .or. (.not. (z <= 2.7d+109))) 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 <= -9e+99) || !(z <= 2.7e+109)) {
		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 <= -9e+99) or not (z <= 2.7e+109):
		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 <= -9e+99) || !(z <= 2.7e+109))
		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 <= -9e+99) || ~((z <= 2.7e+109)))
		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, -9e+99], N[Not[LessEqual[z, 2.7e+109]], $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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 57.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-86}:\\ \;\;\;\;x_m \cdot \frac{\frac{1}{y}}{t}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-88}:\\ \;\;\;\;\frac{-\frac{x_m}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -2.3e-86)
    (* x_m (/ (/ 1.0 y) t))
    (if (<= t 7.2e-88) (/ (- (/ x_m z)) y) (/ x_m (* (- y z) t))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -2.3e-86) {
		tmp = x_m * ((1.0 / y) / t);
	} else if (t <= 7.2e-88) {
		tmp = -(x_m / z) / y;
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.3d-86)) then
        tmp = x_m * ((1.0d0 / y) / t)
    else if (t <= 7.2d-88) then
        tmp = -(x_m / z) / y
    else
        tmp = x_m / ((y - z) * t)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -2.3e-86) {
		tmp = x_m * ((1.0 / y) / t);
	} else if (t <= 7.2e-88) {
		tmp = -(x_m / z) / y;
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= -2.3e-86:
		tmp = x_m * ((1.0 / y) / t)
	elif t <= 7.2e-88:
		tmp = -(x_m / z) / y
	else:
		tmp = x_m / ((y - z) * t)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= -2.3e-86)
		tmp = Float64(x_m * Float64(Float64(1.0 / y) / t));
	elseif (t <= 7.2e-88)
		tmp = Float64(Float64(-Float64(x_m / z)) / y);
	else
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -2.3e-86)
		tmp = x_m * ((1.0 / y) / t);
	elseif (t <= 7.2e-88)
		tmp = -(x_m / z) / y;
	else
		tmp = x_m / ((y - z) * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -2.3e-86], N[(x$95$m * N[(N[(1.0 / y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e-88], N[((-N[(x$95$m / z), $MachinePrecision]) / y), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 46.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+95} \lor \neg \left(z \leq 4400\right):\\ \;\;\;\;\frac{x_m}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{y \cdot t}\\ \end{array} \end{array} \]

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 -1.25e+95) (not (<= z 4400.0)))
    (/ 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 <= -1.25e+95) || !(z <= 4400.0)) {
		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 <= (-1.25d+95)) .or. (.not. (z <= 4400.0d0))) 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 <= -1.25e+95) || !(z <= 4400.0)) {
		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 <= -1.25e+95) or not (z <= 4400.0):
		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 <= -1.25e+95) || !(z <= 4400.0))
		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 <= -1.25e+95) || ~((z <= 4400.0)))
		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, -1.25e+95], N[Not[LessEqual[z, 4400.0]], $MachinePrecision]], N[(x$95$m / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 12: 48.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+101} \lor \neg \left(z \leq 4400\right):\\ \;\;\;\;\frac{x_m}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x_m}{t}}{y}\\ \end{array} \end{array} \]

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 -9e+101) (not (<= z 4400.0)))
    (/ 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 <= -9e+101) || !(z <= 4400.0)) {
		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 <= (-9d+101)) .or. (.not. (z <= 4400.0d0))) 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 <= -9e+101) || !(z <= 4400.0)) {
		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 <= -9e+101) or not (z <= 4400.0):
		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 <= -9e+101) || !(z <= 4400.0))
		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 <= -9e+101) || ~((z <= 4400.0)))
		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, -9e+101], N[Not[LessEqual[z, 4400.0]], $MachinePrecision]], N[(x$95$m / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 13: 48.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+102} \lor \neg \left(z \leq 1.12 \cdot 10^{+169}\right):\\ \;\;\;\;\frac{x_m}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x_m}{y}}{t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -7.8e+102) (not (<= z 1.12e+169)))
    (/ 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 <= -7.8e+102) || !(z <= 1.12e+169)) {
		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 <= (-7.8d+102)) .or. (.not. (z <= 1.12d+169))) 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 <= -7.8e+102) || !(z <= 1.12e+169)) {
		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 <= -7.8e+102) or not (z <= 1.12e+169):
		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 <= -7.8e+102) || !(z <= 1.12e+169))
		tmp = Float64(x_m / Float64(y * z));
	else
		tmp = Float64(Float64(x_m / y) / t);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -7.8e+102) || ~((z <= 1.12e+169)))
		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, -7.8e+102], N[Not[LessEqual[z, 1.12e+169]], $MachinePrecision]], N[(x$95$m / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 14: 50.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+102} \lor \neg \left(z \leq 4400\right):\\ \;\;\;\;\frac{\frac{x_m}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x_m}{y}}{t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -2.5e+102) (not (<= z 4400.0)))
    (/ (/ x_m z) y)
    (/ (/ 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 <= -2.5e+102) || !(z <= 4400.0)) {
		tmp = (x_m / z) / y;
	} 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 <= (-2.5d+102)) .or. (.not. (z <= 4400.0d0))) then
        tmp = (x_m / z) / y
    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 <= -2.5e+102) || !(z <= 4400.0)) {
		tmp = (x_m / z) / y;
	} 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 <= -2.5e+102) or not (z <= 4400.0):
		tmp = (x_m / z) / y
	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 <= -2.5e+102) || !(z <= 4400.0))
		tmp = Float64(Float64(x_m / z) / y);
	else
		tmp = Float64(Float64(x_m / y) / t);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -2.5e+102) || ~((z <= 4400.0)))
		tmp = (x_m / z) / y;
	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, -2.5e+102], N[Not[LessEqual[z, 4400.0]], $MachinePrecision]], N[(N[(x$95$m / z), $MachinePrecision] / y), $MachinePrecision], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 15: 63.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;t \leq 4.2 \cdot 10^{-49}:\\ \;\;\;\;\frac{x_m}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 4.2e-49) (/ 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 <= 4.2e-49) {
		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 <= 4.2d-49) 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 <= 4.2e-49) {
		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 <= 4.2e-49:
		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 <= 4.2e-49)
		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 <= 4.2e-49)
		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, 4.2e-49], 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 16: 64.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;t \leq 2.85 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{x_m}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 2.85e-39) (/ (/ 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 <= 2.85e-39) {
		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 <= 2.85d-39) 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 <= 2.85e-39) {
		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 <= 2.85e-39:
		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 <= 2.85e-39)
		tmp = Float64(Float64(x_m / 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 <= 2.85e-39)
		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, 2.85e-39], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 17: 67.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;t \leq 1.45 \cdot 10^{-46}:\\ \;\;\;\;\frac{\frac{x_m}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= t 1.45e-46) (/ (/ x_m (- t z)) y) (/ x_m (* (- y z) t)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= 1.45e-46) {
		tmp = (x_m / (t - z)) / y;
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 1.45d-46) then
        tmp = (x_m / (t - z)) / y
    else
        tmp = x_m / ((y - z) * t)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= 1.45e-46) {
		tmp = (x_m / (t - z)) / y;
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= 1.45e-46:
		tmp = (x_m / (t - z)) / y
	else:
		tmp = x_m / ((y - z) * t)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= 1.45e-46)
		tmp = Float64(Float64(x_m / Float64(t - z)) / y);
	else
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= 1.45e-46)
		tmp = (x_m / (t - z)) / y;
	else
		tmp = x_m / ((y - z) * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, 1.45e-46], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 18: 96.9% accurate, 1.0× speedup

Math

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

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 (- t z)) (- y z))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * ((x_m / (t - z)) / (y - 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 / (t - z)) / (y - 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 / (t - z)) / (y - 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 / (t - z)) / (y - 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(t - z)) / Float64(y - 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 / (t - z)) / (y - 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[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 19: 96.9% 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 20: 39.7% accurate, 1.8× speedup

Math

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

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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Developer target: 88.4% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023343 
(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))))