Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, A

Percentage Accurate: 89.2% → 96.3%

Time: 14.3s

Alternatives: 15

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))

C

double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

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) - x) / ((t * z) - x))) / (x + 1.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

Python

def code(x, y, z, t):
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))

C

double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

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) - x) / ((t * z) - x))) / (x + 1.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

Python

def code(x, y, z, t):
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ \mathbf{if}\;z \leq -4 \cdot 10^{+131}:\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+142}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{t_1}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t_1}{z}}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)))
   (if (<= z -4e+131)
     (/ (+ x (/ y (- t (/ x z)))) (+ x 1.0))
     (if (<= z 8.5e+142)
       (/ (+ x (/ (- (* z y) x) t_1)) (+ x 1.0))
       (/ (+ x (/ y (/ t_1 z))) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if (z <= -4e+131) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else if (z <= 8.5e+142) {
		tmp = (x + (((z * y) - x) / t_1)) / (x + 1.0);
	} else {
		tmp = (x + (y / (t_1 / z))) / (x + 1.0);
	}
	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 = (z * t) - x
    if (z <= (-4d+131)) then
        tmp = (x + (y / (t - (x / z)))) / (x + 1.0d0)
    else if (z <= 8.5d+142) then
        tmp = (x + (((z * y) - x) / t_1)) / (x + 1.0d0)
    else
        tmp = (x + (y / (t_1 / z))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if (z <= -4e+131) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else if (z <= 8.5e+142) {
		tmp = (x + (((z * y) - x) / t_1)) / (x + 1.0);
	} else {
		tmp = (x + (y / (t_1 / z))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	tmp = 0
	if z <= -4e+131:
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0)
	elif z <= 8.5e+142:
		tmp = (x + (((z * y) - x) / t_1)) / (x + 1.0)
	else:
		tmp = (x + (y / (t_1 / z))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	tmp = 0.0
	if (z <= -4e+131)
		tmp = Float64(Float64(x + Float64(y / Float64(t - Float64(x / z)))) / Float64(x + 1.0));
	elseif (z <= 8.5e+142)
		tmp = Float64(Float64(x + Float64(Float64(Float64(z * y) - x) / t_1)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(y / Float64(t_1 / z))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	tmp = 0.0;
	if (z <= -4e+131)
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	elseif (z <= 8.5e+142)
		tmp = (x + (((z * y) - x) / t_1)) / (x + 1.0);
	else
		tmp = (x + (y / (t_1 / z))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[z, -4e+131], N[(N[(x + N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+142], N[(N[(x + N[(N[(N[(z * y), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 2: 75.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ t_2 := \frac{y}{\left(t - \frac{x}{z}\right) \cdot \left(x + 1\right)}\\ \mathbf{if}\;x \leq -1.1:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.16 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{-121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \left(1 + \frac{\frac{-1}{t}}{z}\right)\\ \mathbf{elif}\;x \leq 0.00022:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0)))
        (t_2 (/ y (* (- t (/ x z)) (+ x 1.0)))))
   (if (<= x -1.1)
     (/ x (+ x 1.0))
     (if (<= x -2.6e-100)
       t_2
       (if (<= x -1.16e-234)
         t_1
         (if (<= x 2.95e-121)
           t_2
           (if (<= x 8.6e-114)
             (* x (+ 1.0 (/ (/ -1.0 t) z)))
             (if (<= x 0.00022) t_1 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double t_2 = y / ((t - (x / z)) * (x + 1.0));
	double tmp;
	if (x <= -1.1) {
		tmp = x / (x + 1.0);
	} else if (x <= -2.6e-100) {
		tmp = t_2;
	} else if (x <= -1.16e-234) {
		tmp = t_1;
	} else if (x <= 2.95e-121) {
		tmp = t_2;
	} else if (x <= 8.6e-114) {
		tmp = x * (1.0 + ((-1.0 / t) / z));
	} else if (x <= 0.00022) {
		tmp = t_1;
	} else {
		tmp = 1.0;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    t_2 = y / ((t - (x / z)) * (x + 1.0d0))
    if (x <= (-1.1d0)) then
        tmp = x / (x + 1.0d0)
    else if (x <= (-2.6d-100)) then
        tmp = t_2
    else if (x <= (-1.16d-234)) then
        tmp = t_1
    else if (x <= 2.95d-121) then
        tmp = t_2
    else if (x <= 8.6d-114) then
        tmp = x * (1.0d0 + (((-1.0d0) / t) / z))
    else if (x <= 0.00022d0) then
        tmp = t_1
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double t_2 = y / ((t - (x / z)) * (x + 1.0));
	double tmp;
	if (x <= -1.1) {
		tmp = x / (x + 1.0);
	} else if (x <= -2.6e-100) {
		tmp = t_2;
	} else if (x <= -1.16e-234) {
		tmp = t_1;
	} else if (x <= 2.95e-121) {
		tmp = t_2;
	} else if (x <= 8.6e-114) {
		tmp = x * (1.0 + ((-1.0 / t) / z));
	} else if (x <= 0.00022) {
		tmp = t_1;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	t_2 = y / ((t - (x / z)) * (x + 1.0))
	tmp = 0
	if x <= -1.1:
		tmp = x / (x + 1.0)
	elif x <= -2.6e-100:
		tmp = t_2
	elif x <= -1.16e-234:
		tmp = t_1
	elif x <= 2.95e-121:
		tmp = t_2
	elif x <= 8.6e-114:
		tmp = x * (1.0 + ((-1.0 / t) / z))
	elif x <= 0.00022:
		tmp = t_1
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	t_2 = Float64(y / Float64(Float64(t - Float64(x / z)) * Float64(x + 1.0)))
	tmp = 0.0
	if (x <= -1.1)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= -2.6e-100)
		tmp = t_2;
	elseif (x <= -1.16e-234)
		tmp = t_1;
	elseif (x <= 2.95e-121)
		tmp = t_2;
	elseif (x <= 8.6e-114)
		tmp = Float64(x * Float64(1.0 + Float64(Float64(-1.0 / t) / z)));
	elseif (x <= 0.00022)
		tmp = t_1;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	t_2 = y / ((t - (x / z)) * (x + 1.0));
	tmp = 0.0;
	if (x <= -1.1)
		tmp = x / (x + 1.0);
	elseif (x <= -2.6e-100)
		tmp = t_2;
	elseif (x <= -1.16e-234)
		tmp = t_1;
	elseif (x <= 2.95e-121)
		tmp = t_2;
	elseif (x <= 8.6e-114)
		tmp = x * (1.0 + ((-1.0 / t) / z));
	elseif (x <= 0.00022)
		tmp = t_1;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision] * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.1], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.6e-100], t$95$2, If[LessEqual[x, -1.16e-234], t$95$1, If[LessEqual[x, 2.95e-121], t$95$2, If[LessEqual[x, 8.6e-114], N[(x * N[(1.0 + N[(N[(-1.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.00022], t$95$1, 1.0]]]]]]]]

Derivation

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

Alternative 3: 66.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 + \frac{\frac{-1}{t}}{z}\right)\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{-100}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-159}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-147}:\\ \;\;\;\;\frac{-y}{-t}\\ \mathbf{elif}\;x \leq 4.12 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-5}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ 1.0 (/ (/ -1.0 t) z)))))
   (if (<= x -3.1e-100)
     1.0
     (if (<= x -6e-157)
       t_1
       (if (<= x -1.85e-159)
         1.0
         (if (<= x 3.6e-147)
           (/ (- y) (- t))
           (if (<= x 4.12e-63)
             t_1
             (if (<= x 6e-5) (/ y (* t (+ x 1.0))) 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 + ((-1.0 / t) / z));
	double tmp;
	if (x <= -3.1e-100) {
		tmp = 1.0;
	} else if (x <= -6e-157) {
		tmp = t_1;
	} else if (x <= -1.85e-159) {
		tmp = 1.0;
	} else if (x <= 3.6e-147) {
		tmp = -y / -t;
	} else if (x <= 4.12e-63) {
		tmp = t_1;
	} else if (x <= 6e-5) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = 1.0;
	}
	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 = x * (1.0d0 + (((-1.0d0) / t) / z))
    if (x <= (-3.1d-100)) then
        tmp = 1.0d0
    else if (x <= (-6d-157)) then
        tmp = t_1
    else if (x <= (-1.85d-159)) then
        tmp = 1.0d0
    else if (x <= 3.6d-147) then
        tmp = -y / -t
    else if (x <= 4.12d-63) then
        tmp = t_1
    else if (x <= 6d-5) then
        tmp = y / (t * (x + 1.0d0))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 + ((-1.0 / t) / z));
	double tmp;
	if (x <= -3.1e-100) {
		tmp = 1.0;
	} else if (x <= -6e-157) {
		tmp = t_1;
	} else if (x <= -1.85e-159) {
		tmp = 1.0;
	} else if (x <= 3.6e-147) {
		tmp = -y / -t;
	} else if (x <= 4.12e-63) {
		tmp = t_1;
	} else if (x <= 6e-5) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 + ((-1.0 / t) / z))
	tmp = 0
	if x <= -3.1e-100:
		tmp = 1.0
	elif x <= -6e-157:
		tmp = t_1
	elif x <= -1.85e-159:
		tmp = 1.0
	elif x <= 3.6e-147:
		tmp = -y / -t
	elif x <= 4.12e-63:
		tmp = t_1
	elif x <= 6e-5:
		tmp = y / (t * (x + 1.0))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 + Float64(Float64(-1.0 / t) / z)))
	tmp = 0.0
	if (x <= -3.1e-100)
		tmp = 1.0;
	elseif (x <= -6e-157)
		tmp = t_1;
	elseif (x <= -1.85e-159)
		tmp = 1.0;
	elseif (x <= 3.6e-147)
		tmp = Float64(Float64(-y) / Float64(-t));
	elseif (x <= 4.12e-63)
		tmp = t_1;
	elseif (x <= 6e-5)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 + ((-1.0 / t) / z));
	tmp = 0.0;
	if (x <= -3.1e-100)
		tmp = 1.0;
	elseif (x <= -6e-157)
		tmp = t_1;
	elseif (x <= -1.85e-159)
		tmp = 1.0;
	elseif (x <= 3.6e-147)
		tmp = -y / -t;
	elseif (x <= 4.12e-63)
		tmp = t_1;
	elseif (x <= 6e-5)
		tmp = y / (t * (x + 1.0));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 + N[(N[(-1.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.1e-100], 1.0, If[LessEqual[x, -6e-157], t$95$1, If[LessEqual[x, -1.85e-159], 1.0, If[LessEqual[x, 3.6e-147], N[((-y) / (-t)), $MachinePrecision], If[LessEqual[x, 4.12e-63], t$95$1, If[LessEqual[x, 6e-5], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]]]]

Derivation

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

Alternative 4: 69.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ t_2 := y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.12 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(1 + \frac{\frac{-1}{t}}{z}\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))) (t_2 (* y (/ z (- (* z t) x)))))
   (if (<= x -1.15e-9)
     t_1
     (if (<= x 1.05e-145)
       t_2
       (if (<= x 4.12e-63)
         (* x (+ 1.0 (/ (/ -1.0 t) z)))
         (if (<= x 5e-23) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double t_2 = y * (z / ((z * t) - x));
	double tmp;
	if (x <= -1.15e-9) {
		tmp = t_1;
	} else if (x <= 1.05e-145) {
		tmp = t_2;
	} else if (x <= 4.12e-63) {
		tmp = x * (1.0 + ((-1.0 / t) / z));
	} else if (x <= 5e-23) {
		tmp = t_2;
	} else {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = x / (x + 1.0d0)
    t_2 = y * (z / ((z * t) - x))
    if (x <= (-1.15d-9)) then
        tmp = t_1
    else if (x <= 1.05d-145) then
        tmp = t_2
    else if (x <= 4.12d-63) then
        tmp = x * (1.0d0 + (((-1.0d0) / t) / z))
    else if (x <= 5d-23) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double t_2 = y * (z / ((z * t) - x));
	double tmp;
	if (x <= -1.15e-9) {
		tmp = t_1;
	} else if (x <= 1.05e-145) {
		tmp = t_2;
	} else if (x <= 4.12e-63) {
		tmp = x * (1.0 + ((-1.0 / t) / z));
	} else if (x <= 5e-23) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	t_2 = y * (z / ((z * t) - x))
	tmp = 0
	if x <= -1.15e-9:
		tmp = t_1
	elif x <= 1.05e-145:
		tmp = t_2
	elif x <= 4.12e-63:
		tmp = x * (1.0 + ((-1.0 / t) / z))
	elif x <= 5e-23:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	t_2 = Float64(y * Float64(z / Float64(Float64(z * t) - x)))
	tmp = 0.0
	if (x <= -1.15e-9)
		tmp = t_1;
	elseif (x <= 1.05e-145)
		tmp = t_2;
	elseif (x <= 4.12e-63)
		tmp = Float64(x * Float64(1.0 + Float64(Float64(-1.0 / t) / z)));
	elseif (x <= 5e-23)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	t_2 = y * (z / ((z * t) - x));
	tmp = 0.0;
	if (x <= -1.15e-9)
		tmp = t_1;
	elseif (x <= 1.05e-145)
		tmp = t_2;
	elseif (x <= 4.12e-63)
		tmp = x * (1.0 + ((-1.0 / t) / z));
	elseif (x <= 5e-23)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e-9], t$95$1, If[LessEqual[x, 1.05e-145], t$95$2, If[LessEqual[x, 4.12e-63], N[(x * N[(1.0 + N[(N[(-1.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e-23], t$95$2, t$95$1]]]]]]

Derivation

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

Alternative 5: 69.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ t_2 := \frac{y}{\frac{z \cdot t - x}{z}}\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.38 \cdot 10^{-145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.12 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(1 + \frac{\frac{-1}{t}}{z}\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))) (t_2 (/ y (/ (- (* z t) x) z))))
   (if (<= x -1.2e-10)
     t_1
     (if (<= x 1.38e-145)
       t_2
       (if (<= x 4.12e-63)
         (* x (+ 1.0 (/ (/ -1.0 t) z)))
         (if (<= x 5.8e-15) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double t_2 = y / (((z * t) - x) / z);
	double tmp;
	if (x <= -1.2e-10) {
		tmp = t_1;
	} else if (x <= 1.38e-145) {
		tmp = t_2;
	} else if (x <= 4.12e-63) {
		tmp = x * (1.0 + ((-1.0 / t) / z));
	} else if (x <= 5.8e-15) {
		tmp = t_2;
	} else {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = x / (x + 1.0d0)
    t_2 = y / (((z * t) - x) / z)
    if (x <= (-1.2d-10)) then
        tmp = t_1
    else if (x <= 1.38d-145) then
        tmp = t_2
    else if (x <= 4.12d-63) then
        tmp = x * (1.0d0 + (((-1.0d0) / t) / z))
    else if (x <= 5.8d-15) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double t_2 = y / (((z * t) - x) / z);
	double tmp;
	if (x <= -1.2e-10) {
		tmp = t_1;
	} else if (x <= 1.38e-145) {
		tmp = t_2;
	} else if (x <= 4.12e-63) {
		tmp = x * (1.0 + ((-1.0 / t) / z));
	} else if (x <= 5.8e-15) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	t_2 = y / (((z * t) - x) / z)
	tmp = 0
	if x <= -1.2e-10:
		tmp = t_1
	elif x <= 1.38e-145:
		tmp = t_2
	elif x <= 4.12e-63:
		tmp = x * (1.0 + ((-1.0 / t) / z))
	elif x <= 5.8e-15:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	t_2 = Float64(y / Float64(Float64(Float64(z * t) - x) / z))
	tmp = 0.0
	if (x <= -1.2e-10)
		tmp = t_1;
	elseif (x <= 1.38e-145)
		tmp = t_2;
	elseif (x <= 4.12e-63)
		tmp = Float64(x * Float64(1.0 + Float64(Float64(-1.0 / t) / z)));
	elseif (x <= 5.8e-15)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	t_2 = y / (((z * t) - x) / z);
	tmp = 0.0;
	if (x <= -1.2e-10)
		tmp = t_1;
	elseif (x <= 1.38e-145)
		tmp = t_2;
	elseif (x <= 4.12e-63)
		tmp = x * (1.0 + ((-1.0 / t) / z));
	elseif (x <= 5.8e-15)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e-10], t$95$1, If[LessEqual[x, 1.38e-145], t$95$2, If[LessEqual[x, 4.12e-63], N[(x * N[(1.0 + N[(N[(-1.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e-15], t$95$2, t$95$1]]]]]]

Derivation

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

Alternative 6: 75.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-95}:\\ \;\;\;\;\frac{x - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-53}:\\ \;\;\;\;\frac{y}{\left(t - \frac{x}{z}\right) \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t \leq 0.001:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -5.4e-185)
     t_1
     (if (<= t 1.5e-95)
       (/ (- x (/ y (/ x z))) (+ x 1.0))
       (if (<= t 1.45e-53)
         (/ y (* (- t (/ x z)) (+ x 1.0)))
         (if (<= t 0.001) (/ x (+ x 1.0)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -5.4e-185) {
		tmp = t_1;
	} else if (t <= 1.5e-95) {
		tmp = (x - (y / (x / z))) / (x + 1.0);
	} else if (t <= 1.45e-53) {
		tmp = y / ((t - (x / z)) * (x + 1.0));
	} else if (t <= 0.001) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 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 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-5.4d-185)) then
        tmp = t_1
    else if (t <= 1.5d-95) then
        tmp = (x - (y / (x / z))) / (x + 1.0d0)
    else if (t <= 1.45d-53) then
        tmp = y / ((t - (x / z)) * (x + 1.0d0))
    else if (t <= 0.001d0) then
        tmp = x / (x + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -5.4e-185) {
		tmp = t_1;
	} else if (t <= 1.5e-95) {
		tmp = (x - (y / (x / z))) / (x + 1.0);
	} else if (t <= 1.45e-53) {
		tmp = y / ((t - (x / z)) * (x + 1.0));
	} else if (t <= 0.001) {
		tmp = x / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -5.4e-185:
		tmp = t_1
	elif t <= 1.5e-95:
		tmp = (x - (y / (x / z))) / (x + 1.0)
	elif t <= 1.45e-53:
		tmp = y / ((t - (x / z)) * (x + 1.0))
	elif t <= 0.001:
		tmp = x / (x + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -5.4e-185)
		tmp = t_1;
	elseif (t <= 1.5e-95)
		tmp = Float64(Float64(x - Float64(y / Float64(x / z))) / Float64(x + 1.0));
	elseif (t <= 1.45e-53)
		tmp = Float64(y / Float64(Float64(t - Float64(x / z)) * Float64(x + 1.0)));
	elseif (t <= 0.001)
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -5.4e-185)
		tmp = t_1;
	elseif (t <= 1.5e-95)
		tmp = (x - (y / (x / z))) / (x + 1.0);
	elseif (t <= 1.45e-53)
		tmp = y / ((t - (x / z)) * (x + 1.0));
	elseif (t <= 0.001)
		tmp = x / (x + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.4e-185], t$95$1, If[LessEqual[t, 1.5e-95], N[(N[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e-53], N[(y / N[(N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision] * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.001], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

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

Alternative 7: 91.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-138} \lor \neg \left(y \leq 1.15 \cdot 10^{-134}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.6e-138) (not (<= y 1.15e-134)))
   (/ (+ x (/ y (- t (/ x z)))) (+ x 1.0))
   (/ (- x (/ x (- (* z t) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.6e-138) || !(y <= 1.15e-134)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	}
	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) :: tmp
    if ((y <= (-6.6d-138)) .or. (.not. (y <= 1.15d-134))) then
        tmp = (x + (y / (t - (x / z)))) / (x + 1.0d0)
    else
        tmp = (x - (x / ((z * t) - x))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.6e-138) || !(y <= 1.15e-134)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.6e-138) or not (y <= 1.15e-134):
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0)
	else:
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.6e-138) || !(y <= 1.15e-134))
		tmp = Float64(Float64(x + Float64(y / Float64(t - Float64(x / z)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.6e-138) || ~((y <= 1.15e-134)))
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	else
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.6e-138], N[Not[LessEqual[y, 1.15e-134]], $MachinePrecision]], N[(N[(x + N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 8: 76.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-101}:\\ \;\;\;\;\frac{y}{\frac{z \cdot t - x}{z}}\\ \mathbf{elif}\;x \leq 1.15:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.5e-11)
   (/ x (+ x 1.0))
   (if (<= x -6e-101)
     (/ y (/ (- (* z t) x) z))
     (if (<= x 1.15) (/ (+ x (/ y t)) (+ x 1.0)) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.5e-11) {
		tmp = x / (x + 1.0);
	} else if (x <= -6e-101) {
		tmp = y / (((z * t) - x) / z);
	} else if (x <= 1.15) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	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) :: tmp
    if (x <= (-2.5d-11)) then
        tmp = x / (x + 1.0d0)
    else if (x <= (-6d-101)) then
        tmp = y / (((z * t) - x) / z)
    else if (x <= 1.15d0) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.5e-11) {
		tmp = x / (x + 1.0);
	} else if (x <= -6e-101) {
		tmp = y / (((z * t) - x) / z);
	} else if (x <= 1.15) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.5e-11:
		tmp = x / (x + 1.0)
	elif x <= -6e-101:
		tmp = y / (((z * t) - x) / z)
	elif x <= 1.15:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.5e-11)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= -6e-101)
		tmp = Float64(y / Float64(Float64(Float64(z * t) - x) / z));
	elseif (x <= 1.15)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.5e-11)
		tmp = x / (x + 1.0);
	elseif (x <= -6e-101)
		tmp = y / (((z * t) - x) / z);
	elseif (x <= 1.15)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.5e-11], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6e-101], N[(y / N[(N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

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

Alternative 9: 88.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (+ x (/ y (- t (/ x z)))) (+ x 1.0)))

C

double code(double x, double y, double z, double t) {
	return (x + (y / (t - (x / z)))) / (x + 1.0);
}

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 / (t - (x / z)))) / (x + 1.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x + (y / (t - (x / z)))) / (x + 1.0);
}

Python

def code(x, y, z, t):
	return (x + (y / (t - (x / z)))) / (x + 1.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x + Float64(y / Float64(t - Float64(x / z)))) / Float64(x + 1.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x + N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 10: 67.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-128}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.00126:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.02e-128) 1.0 (if (<= x 0.00126) (/ y (* t (+ x 1.0))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.02e-128) {
		tmp = 1.0;
	} else if (x <= 0.00126) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = 1.0;
	}
	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) :: tmp
    if (x <= (-1.02d-128)) then
        tmp = 1.0d0
    else if (x <= 0.00126d0) then
        tmp = y / (t * (x + 1.0d0))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.02e-128) {
		tmp = 1.0;
	} else if (x <= 0.00126) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.02e-128:
		tmp = 1.0
	elif x <= 0.00126:
		tmp = y / (t * (x + 1.0))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.02e-128)
		tmp = 1.0;
	elseif (x <= 0.00126)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.02e-128)
		tmp = 1.0;
	elseif (x <= 0.00126)
		tmp = y / (t * (x + 1.0));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.02e-128], 1.0, If[LessEqual[x, 0.00126], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

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

Alternative 11: 67.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-128}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.65e-128) 1.0 (if (<= x 4.2e-5) (* y (/ 1.0 t)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.65e-128) {
		tmp = 1.0;
	} else if (x <= 4.2e-5) {
		tmp = y * (1.0 / t);
	} else {
		tmp = 1.0;
	}
	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) :: tmp
    if (x <= (-1.65d-128)) then
        tmp = 1.0d0
    else if (x <= 4.2d-5) then
        tmp = y * (1.0d0 / t)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.65e-128) {
		tmp = 1.0;
	} else if (x <= 4.2e-5) {
		tmp = y * (1.0 / t);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.65e-128:
		tmp = 1.0
	elif x <= 4.2e-5:
		tmp = y * (1.0 / t)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.65e-128)
		tmp = 1.0;
	elseif (x <= 4.2e-5)
		tmp = Float64(y * Float64(1.0 / t));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.65e-128)
		tmp = 1.0;
	elseif (x <= 4.2e-5)
		tmp = y * (1.0 / t);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.65e-128], 1.0, If[LessEqual[x, 4.2e-5], N[(y * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

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

Alternative 12: 67.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-128}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-5}:\\ \;\;\;\;\frac{1}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.9e-128) 1.0 (if (<= x 4.2e-5) (/ 1.0 (/ t y)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.9e-128) {
		tmp = 1.0;
	} else if (x <= 4.2e-5) {
		tmp = 1.0 / (t / y);
	} else {
		tmp = 1.0;
	}
	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) :: tmp
    if (x <= (-1.9d-128)) then
        tmp = 1.0d0
    else if (x <= 4.2d-5) then
        tmp = 1.0d0 / (t / y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.9e-128) {
		tmp = 1.0;
	} else if (x <= 4.2e-5) {
		tmp = 1.0 / (t / y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.9e-128:
		tmp = 1.0
	elif x <= 4.2e-5:
		tmp = 1.0 / (t / y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.9e-128)
		tmp = 1.0;
	elseif (x <= 4.2e-5)
		tmp = Float64(1.0 / Float64(t / y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.9e-128)
		tmp = 1.0;
	elseif (x <= 4.2e-5)
		tmp = 1.0 / (t / y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.9e-128], 1.0, If[LessEqual[x, 4.2e-5], N[(1.0 / N[(t / y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

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

Alternative 13: 67.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-128}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{1}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.8e-128) 1.0 (if (<= x 2.8e-22) (/ 1.0 (/ t y)) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.8e-128) {
		tmp = 1.0;
	} else if (x <= 2.8e-22) {
		tmp = 1.0 / (t / y);
	} else {
		tmp = x / (x + 1.0);
	}
	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) :: tmp
    if (x <= (-1.8d-128)) then
        tmp = 1.0d0
    else if (x <= 2.8d-22) then
        tmp = 1.0d0 / (t / y)
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.8e-128) {
		tmp = 1.0;
	} else if (x <= 2.8e-22) {
		tmp = 1.0 / (t / y);
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.8e-128:
		tmp = 1.0
	elif x <= 2.8e-22:
		tmp = 1.0 / (t / y)
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.8e-128)
		tmp = 1.0;
	elseif (x <= 2.8e-22)
		tmp = Float64(1.0 / Float64(t / y));
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.8e-128)
		tmp = 1.0;
	elseif (x <= 2.8e-22)
		tmp = 1.0 / (t / y);
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.8e-128], 1.0, If[LessEqual[x, 2.8e-22], N[(1.0 / N[(t / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 14: 67.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-128}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-15}:\\ \;\;\;\;\frac{-y}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.9e-128) 1.0 (if (<= x 2.9e-15) (/ (- y) (- t)) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.9e-128) {
		tmp = 1.0;
	} else if (x <= 2.9e-15) {
		tmp = -y / -t;
	} else {
		tmp = x / (x + 1.0);
	}
	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) :: tmp
    if (x <= (-1.9d-128)) then
        tmp = 1.0d0
    else if (x <= 2.9d-15) then
        tmp = -y / -t
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.9e-128) {
		tmp = 1.0;
	} else if (x <= 2.9e-15) {
		tmp = -y / -t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.9e-128:
		tmp = 1.0
	elif x <= 2.9e-15:
		tmp = -y / -t
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.9e-128)
		tmp = 1.0;
	elseif (x <= 2.9e-15)
		tmp = Float64(Float64(-y) / Float64(-t));
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.9e-128)
		tmp = 1.0;
	elseif (x <= 2.9e-15)
		tmp = -y / -t;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.9e-128], 1.0, If[LessEqual[x, 2.9e-15], N[((-y) / (-t)), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 15: 53.9% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 1.0)

C

double code(double x, double y, double z, double t) {
	return 1.0;
}

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 = 1.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0;
}

Python

def code(x, y, z, t):
	return 1.0

Julia

function code(x, y, z, t)
	return 1.0
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_, t_] := 1.0

Derivation

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

Developer target: 99.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0)))

C

double code(double x, double y, double z, double t) {
	return (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0);
}

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 / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0);
}

Python

def code(x, y, z, t):
	return (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x + Float64(Float64(y / Float64(t - Float64(x / z))) - Float64(x / Float64(Float64(t * z) - x)))) / Float64(x + 1.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x + N[(N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024003 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))