Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, H

Percentage Accurate: 95.8% → 97.9%

Time: 12.7s

Alternatives: 18

Speedup: 1.0×

• 27.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

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 * 3.0d0))) + (t / ((z * 3.0d0) * y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

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 * 3.0d0))) + (t / ((z * 3.0d0) * y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-73} \lor \neg \left(y \leq 1.65 \cdot 10^{-161}\right):\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{3 \cdot \frac{y}{\frac{t}{z}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5e-73) (not (<= y 1.65e-161)))
   (+ x (/ (- (/ t y) y) (* z 3.0)))
   (+ x (/ 1.0 (* 3.0 (/ y (/ t z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5e-73) || !(y <= 1.65e-161)) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = x + (1.0 / (3.0 * (y / (t / z))));
	}
	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 <= (-5d-73)) .or. (.not. (y <= 1.65d-161))) then
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    else
        tmp = x + (1.0d0 / (3.0d0 * (y / (t / z))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5e-73) || !(y <= 1.65e-161)) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = x + (1.0 / (3.0 * (y / (t / z))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5e-73) or not (y <= 1.65e-161):
		tmp = x + (((t / y) - y) / (z * 3.0))
	else:
		tmp = x + (1.0 / (3.0 * (y / (t / z))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5e-73) || !(y <= 1.65e-161))
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(1.0 / Float64(3.0 * Float64(y / Float64(t / z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5e-73) || ~((y <= 1.65e-161)))
		tmp = x + (((t / y) - y) / (z * 3.0));
	else
		tmp = x + (1.0 / (3.0 * (y / (t / z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5e-73], N[Not[LessEqual[y, 1.65e-161]], $MachinePrecision]], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(3.0 * N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 2: 88.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ t_2 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-301}:\\ \;\;\;\;\frac{\frac{0.3333333333333333}{y}}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 2400000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* 0.3333333333333333 (/ t (* y z)))))
        (t_2 (- x (/ y (* z 3.0)))))
   (if (<= y -1.15e+23)
     t_2
     (if (<= y -8.6e-211)
       t_1
       (if (<= y -1.6e-301)
         (/ (/ 0.3333333333333333 y) (/ z t))
         (if (<= y 2400000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (0.3333333333333333 * (t / (y * z)));
	double t_2 = x - (y / (z * 3.0));
	double tmp;
	if (y <= -1.15e+23) {
		tmp = t_2;
	} else if (y <= -8.6e-211) {
		tmp = t_1;
	} else if (y <= -1.6e-301) {
		tmp = (0.3333333333333333 / y) / (z / t);
	} else if (y <= 2400000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 + (0.3333333333333333d0 * (t / (y * z)))
    t_2 = x - (y / (z * 3.0d0))
    if (y <= (-1.15d+23)) then
        tmp = t_2
    else if (y <= (-8.6d-211)) then
        tmp = t_1
    else if (y <= (-1.6d-301)) then
        tmp = (0.3333333333333333d0 / y) / (z / t)
    else if (y <= 2400000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (0.3333333333333333 * (t / (y * z)));
	double t_2 = x - (y / (z * 3.0));
	double tmp;
	if (y <= -1.15e+23) {
		tmp = t_2;
	} else if (y <= -8.6e-211) {
		tmp = t_1;
	} else if (y <= -1.6e-301) {
		tmp = (0.3333333333333333 / y) / (z / t);
	} else if (y <= 2400000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (0.3333333333333333 * (t / (y * z)))
	t_2 = x - (y / (z * 3.0))
	tmp = 0
	if y <= -1.15e+23:
		tmp = t_2
	elif y <= -8.6e-211:
		tmp = t_1
	elif y <= -1.6e-301:
		tmp = (0.3333333333333333 / y) / (z / t)
	elif y <= 2400000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(y * z))))
	t_2 = Float64(x - Float64(y / Float64(z * 3.0)))
	tmp = 0.0
	if (y <= -1.15e+23)
		tmp = t_2;
	elseif (y <= -8.6e-211)
		tmp = t_1;
	elseif (y <= -1.6e-301)
		tmp = Float64(Float64(0.3333333333333333 / y) / Float64(z / t));
	elseif (y <= 2400000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (0.3333333333333333 * (t / (y * z)));
	t_2 = x - (y / (z * 3.0));
	tmp = 0.0;
	if (y <= -1.15e+23)
		tmp = t_2;
	elseif (y <= -8.6e-211)
		tmp = t_1;
	elseif (y <= -1.6e-301)
		tmp = (0.3333333333333333 / y) / (z / t);
	elseif (y <= 2400000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e+23], t$95$2, If[LessEqual[y, -8.6e-211], t$95$1, If[LessEqual[y, -1.6e-301], N[(N[(0.3333333333333333 / y), $MachinePrecision] / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2400000000000.0], t$95$1, t$95$2]]]]]]

Derivation

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

Alternative 3: 81.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+85} \lor \neg \left(z \cdot 3 \leq 4 \cdot 10^{+101}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z 3.0) -2e+85) (not (<= (* z 3.0) 4e+101)))
   (- x (/ y (* z 3.0)))
   (* -0.3333333333333333 (/ (- y (/ t y)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -2e+85) || !((z * 3.0) <= 4e+101)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	}
	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 (((z * 3.0d0) <= (-2d+85)) .or. (.not. ((z * 3.0d0) <= 4d+101))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = (-0.3333333333333333d0) * ((y - (t / y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -2e+85) || !((z * 3.0) <= 4e+101)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * 3.0) <= -2e+85) or not ((z * 3.0) <= 4e+101):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = -0.3333333333333333 * ((y - (t / y)) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * 3.0) <= -2e+85) || !(Float64(z * 3.0) <= 4e+101))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * 3.0) <= -2e+85) || ~(((z * 3.0) <= 4e+101)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * 3.0), $MachinePrecision], -2e+85], N[Not[LessEqual[N[(z * 3.0), $MachinePrecision], 4e+101]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 4: 97.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+77}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5e+77)
   (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0))))
   (+ x (/ (- (/ t y) y) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5e+77) {
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	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 (t <= (-5d+77)) then
        tmp = (x - (y / (z * 3.0d0))) + (t / (y * (z * 3.0d0)))
    else
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5e+77) {
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5e+77:
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)))
	else:
		tmp = x + (((t / y) - y) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5e+77)
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(y * Float64(z * 3.0))));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5e+77)
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	else
		tmp = x + (((t / y) - y) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5e+77], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 5: 97.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+69}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.4e+69)
   (+ (- x (/ y (* z 3.0))) (/ t (* z (* y 3.0))))
   (+ x (/ (- (/ t y) y) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.4e+69) {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	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 (t <= (-2.4d+69)) then
        tmp = (x - (y / (z * 3.0d0))) + (t / (z * (y * 3.0d0)))
    else
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.4e+69) {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.4e+69:
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)))
	else:
		tmp = x + (((t / y) - y) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.4e+69)
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(z * Float64(y * 3.0))));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.4e+69)
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)));
	else
		tmp = x + (((t / y) - y) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.4e+69], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 6: 97.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-41} \lor \neg \left(y \leq 2.1 \cdot 10^{-161}\right):\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.9e-41) (not (<= y 2.1e-161)))
   (+ x (* 0.3333333333333333 (/ (- (/ t y) y) z)))
   (+ x (* (/ t z) (/ 0.3333333333333333 y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.9e-41) || !(y <= 2.1e-161)) {
		tmp = x + (0.3333333333333333 * (((t / y) - y) / z));
	} else {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	}
	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 <= (-1.9d-41)) .or. (.not. (y <= 2.1d-161))) then
        tmp = x + (0.3333333333333333d0 * (((t / y) - y) / z))
    else
        tmp = x + ((t / z) * (0.3333333333333333d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.9e-41) || !(y <= 2.1e-161)) {
		tmp = x + (0.3333333333333333 * (((t / y) - y) / z));
	} else {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.9e-41) or not (y <= 2.1e-161):
		tmp = x + (0.3333333333333333 * (((t / y) - y) / z))
	else:
		tmp = x + ((t / z) * (0.3333333333333333 / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.9e-41) || !(y <= 2.1e-161))
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(Float64(Float64(t / y) - y) / z)));
	else
		tmp = Float64(x + Float64(Float64(t / z) * Float64(0.3333333333333333 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.9e-41) || ~((y <= 2.1e-161)))
		tmp = x + (0.3333333333333333 * (((t / y) - y) / z));
	else
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.9e-41], N[Not[LessEqual[y, 2.1e-161]], $MachinePrecision]], N[(x + N[(0.3333333333333333 * N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 7: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-71} \lor \neg \left(y \leq 9 \cdot 10^{-162}\right):\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{3 \cdot \frac{y}{\frac{t}{z}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.15e-71) (not (<= y 9e-162)))
   (+ x (* 0.3333333333333333 (/ (- (/ t y) y) z)))
   (+ x (/ 1.0 (* 3.0 (/ y (/ t z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.15e-71) || !(y <= 9e-162)) {
		tmp = x + (0.3333333333333333 * (((t / y) - y) / z));
	} else {
		tmp = x + (1.0 / (3.0 * (y / (t / z))));
	}
	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 <= (-1.15d-71)) .or. (.not. (y <= 9d-162))) then
        tmp = x + (0.3333333333333333d0 * (((t / y) - y) / z))
    else
        tmp = x + (1.0d0 / (3.0d0 * (y / (t / z))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.15e-71) || !(y <= 9e-162)) {
		tmp = x + (0.3333333333333333 * (((t / y) - y) / z));
	} else {
		tmp = x + (1.0 / (3.0 * (y / (t / z))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.15e-71) or not (y <= 9e-162):
		tmp = x + (0.3333333333333333 * (((t / y) - y) / z))
	else:
		tmp = x + (1.0 / (3.0 * (y / (t / z))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.15e-71) || !(y <= 9e-162))
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(Float64(Float64(t / y) - y) / z)));
	else
		tmp = Float64(x + Float64(1.0 / Float64(3.0 * Float64(y / Float64(t / z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.15e-71) || ~((y <= 9e-162)))
		tmp = x + (0.3333333333333333 * (((t / y) - y) / z));
	else
		tmp = x + (1.0 / (3.0 * (y / (t / z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.15e-71], N[Not[LessEqual[y, 9e-162]], $MachinePrecision]], N[(x + N[(0.3333333333333333 * N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(3.0 * N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 8: 92.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+22} \lor \neg \left(y \leq 1960000000000\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.6e+22) (not (<= y 1960000000000.0)))
   (- x (/ y (* z 3.0)))
   (+ x (* (/ t z) (/ 0.3333333333333333 y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.6e+22) || !(y <= 1960000000000.0)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	}
	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 <= (-2.6d+22)) .or. (.not. (y <= 1960000000000.0d0))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = x + ((t / z) * (0.3333333333333333d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.6e+22) || !(y <= 1960000000000.0)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.6e+22) or not (y <= 1960000000000.0):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = x + ((t / z) * (0.3333333333333333 / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.6e+22) || !(y <= 1960000000000.0))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(Float64(t / z) * Float64(0.3333333333333333 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.6e+22) || ~((y <= 1960000000000.0)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.6e+22], N[Not[LessEqual[y, 1960000000000.0]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 9: 60.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z \cdot -3}\\ \mathbf{if}\;y \leq -9.8 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-80}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (* z -3.0))))
   (if (<= y -9.8e+70)
     t_1
     (if (<= y 3.3e-80)
       (* 0.3333333333333333 (/ t (* y z)))
       (if (<= y 6.9e+36) x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (z * -3.0);
	double tmp;
	if (y <= -9.8e+70) {
		tmp = t_1;
	} else if (y <= 3.3e-80) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else if (y <= 6.9e+36) {
		tmp = x;
	} 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 = y / (z * (-3.0d0))
    if (y <= (-9.8d+70)) then
        tmp = t_1
    else if (y <= 3.3d-80) then
        tmp = 0.3333333333333333d0 * (t / (y * z))
    else if (y <= 6.9d+36) then
        tmp = x
    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 = y / (z * -3.0);
	double tmp;
	if (y <= -9.8e+70) {
		tmp = t_1;
	} else if (y <= 3.3e-80) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else if (y <= 6.9e+36) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (z * -3.0)
	tmp = 0
	if y <= -9.8e+70:
		tmp = t_1
	elif y <= 3.3e-80:
		tmp = 0.3333333333333333 * (t / (y * z))
	elif y <= 6.9e+36:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(z * -3.0))
	tmp = 0.0
	if (y <= -9.8e+70)
		tmp = t_1;
	elseif (y <= 3.3e-80)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	elseif (y <= 6.9e+36)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (z * -3.0);
	tmp = 0.0;
	if (y <= -9.8e+70)
		tmp = t_1;
	elseif (y <= 3.3e-80)
		tmp = 0.3333333333333333 * (t / (y * z));
	elseif (y <= 6.9e+36)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.8e+70], t$95$1, If[LessEqual[y, 3.3e-80], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.9e+36], x, t$95$1]]]]

Derivation

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

Alternative 10: 62.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+70} \lor \neg \left(y \leq 550000000000\right):\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9e+70) (not (<= y 550000000000.0)))
   (/ y (* z -3.0))
   (* (/ t z) (/ 0.3333333333333333 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9e+70) || !(y <= 550000000000.0)) {
		tmp = y / (z * -3.0);
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	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 <= (-9d+70)) .or. (.not. (y <= 550000000000.0d0))) then
        tmp = y / (z * (-3.0d0))
    else
        tmp = (t / z) * (0.3333333333333333d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9e+70) || !(y <= 550000000000.0)) {
		tmp = y / (z * -3.0);
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9e+70) or not (y <= 550000000000.0):
		tmp = y / (z * -3.0)
	else:
		tmp = (t / z) * (0.3333333333333333 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9e+70) || !(y <= 550000000000.0))
		tmp = Float64(y / Float64(z * -3.0));
	else
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9e+70) || ~((y <= 550000000000.0)))
		tmp = y / (z * -3.0);
	else
		tmp = (t / z) * (0.3333333333333333 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9e+70], N[Not[LessEqual[y, 550000000000.0]], $MachinePrecision]], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 11: 79.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-67} \lor \neg \left(y \leq 1.66 \cdot 10^{-66}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.5e-67) (not (<= y 1.66e-66)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* (/ t z) (/ 0.3333333333333333 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.5e-67) || !(y <= 1.66e-66)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	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 <= (-7.5d-67)) .or. (.not. (y <= 1.66d-66))) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else
        tmp = (t / z) * (0.3333333333333333d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.5e-67) || !(y <= 1.66e-66)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.5e-67) or not (y <= 1.66e-66):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = (t / z) * (0.3333333333333333 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.5e-67) || !(y <= 1.66e-66))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7.5e-67) || ~((y <= 1.66e-66)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = (t / z) * (0.3333333333333333 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.5e-67], N[Not[LessEqual[y, 1.66e-66]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 12: 78.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-66} \lor \neg \left(y \leq 1.6 \cdot 10^{-64}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.2e-66) (not (<= y 1.6e-64)))
   (- x (/ y (* z 3.0)))
   (* (/ t z) (/ 0.3333333333333333 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.2e-66) || !(y <= 1.6e-64)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	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 <= (-3.2d-66)) .or. (.not. (y <= 1.6d-64))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = (t / z) * (0.3333333333333333d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.2e-66) || !(y <= 1.6e-64)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.2e-66) or not (y <= 1.6e-64):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = (t / z) * (0.3333333333333333 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.2e-66) || !(y <= 1.6e-64))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.2e-66) || ~((y <= 1.6e-64)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = (t / z) * (0.3333333333333333 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.2e-66], N[Not[LessEqual[y, 1.6e-64]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 13: 78.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-66}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-69}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.05e-66)
   (- x (* 0.3333333333333333 (/ y z)))
   (if (<= y 3.4e-69)
     (* (/ t z) (/ 0.3333333333333333 y))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e-66) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 3.4e-69) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	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 <= (-1.05d-66)) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else if (y <= 3.4d-69) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e-66) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 3.4e-69) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.05e-66:
		tmp = x - (0.3333333333333333 * (y / z))
	elif y <= 3.4e-69:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.05e-66)
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	elseif (y <= 3.4e-69)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.05e-66)
		tmp = x - (0.3333333333333333 * (y / z));
	elseif (y <= 3.4e-69)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.05e-66], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-69], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 14: 47.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+101} \lor \neg \left(y \leq 56000000000000\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.9e+101) (not (<= y 56000000000000.0)))
   (* -0.3333333333333333 (/ y z))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.9e+101) || !(y <= 56000000000000.0)) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	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 <= (-1.9d+101)) .or. (.not. (y <= 56000000000000.0d0))) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.9e+101) || !(y <= 56000000000000.0)) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.9e+101) or not (y <= 56000000000000.0):
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.9e+101) || !(y <= 56000000000000.0))
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.9e+101) || ~((y <= 56000000000000.0)))
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.9e+101], N[Not[LessEqual[y, 56000000000000.0]], $MachinePrecision]], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

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

Alternative 15: 47.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+101} \lor \neg \left(y \leq 1.75 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.15e+101) (not (<= y 1.75e+35))) (/ y (* z -3.0)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.15e+101) || !(y <= 1.75e+35)) {
		tmp = y / (z * -3.0);
	} else {
		tmp = x;
	}
	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 <= (-2.15d+101)) .or. (.not. (y <= 1.75d+35))) then
        tmp = y / (z * (-3.0d0))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.15e+101) || !(y <= 1.75e+35)) {
		tmp = y / (z * -3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.15e+101) or not (y <= 1.75e+35):
		tmp = y / (z * -3.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.15e+101) || !(y <= 1.75e+35))
		tmp = Float64(y / Float64(z * -3.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.15e+101) || ~((y <= 1.75e+35)))
		tmp = y / (z * -3.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.15e+101], N[Not[LessEqual[y, 1.75e+35]], $MachinePrecision]], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision], x]

Derivation

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

Alternative 16: 47.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.06 \cdot 10^{+101}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.56 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.06e+101)
   (* -0.3333333333333333 (/ y z))
   (if (<= y 1.56e+29) x (* y (/ -0.3333333333333333 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.06e+101) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 1.56e+29) {
		tmp = x;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	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 <= (-2.06d+101)) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else if (y <= 1.56d+29) then
        tmp = x
    else
        tmp = y * ((-0.3333333333333333d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.06e+101) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 1.56e+29) {
		tmp = x;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.06e+101:
		tmp = -0.3333333333333333 * (y / z)
	elif y <= 1.56e+29:
		tmp = x
	else:
		tmp = y * (-0.3333333333333333 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.06e+101)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	elseif (y <= 1.56e+29)
		tmp = x;
	else
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.06e+101)
		tmp = -0.3333333333333333 * (y / z);
	elseif (y <= 1.56e+29)
		tmp = x;
	else
		tmp = y * (-0.3333333333333333 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.06e+101], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.56e+29], x, N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 17: 47.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+101}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 49000000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.9e+101)
   (* -0.3333333333333333 (/ y z))
   (if (<= y 49000000000000.0) x (/ -0.3333333333333333 (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.9e+101) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 49000000000000.0) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 / (z / y);
	}
	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 <= (-1.9d+101)) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else if (y <= 49000000000000.0d0) then
        tmp = x
    else
        tmp = (-0.3333333333333333d0) / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.9e+101) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 49000000000000.0) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.9e+101:
		tmp = -0.3333333333333333 * (y / z)
	elif y <= 49000000000000.0:
		tmp = x
	else:
		tmp = -0.3333333333333333 / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.9e+101)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	elseif (y <= 49000000000000.0)
		tmp = x;
	else
		tmp = Float64(-0.3333333333333333 / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.9e+101)
		tmp = -0.3333333333333333 * (y / z);
	elseif (y <= 49000000000000.0)
		tmp = x;
	else
		tmp = -0.3333333333333333 / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.9e+101], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 49000000000000.0], x, N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 18: 30.8% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Developer target: 96.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y)))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
}

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 * 3.0d0))) + ((t / (z * 3.0d0)) / y)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y)

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(Float64(t / Float64(z * 3.0)) / y))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024003 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))