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

Percentage Accurate: 89.4% → 96.7%

Time: 14.1s

Alternatives: 11

Speedup: 0.3×

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: 89.4% 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: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_2 \leq -4 \cdot 10^{+22}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{y} \cdot \frac{t_1}{z}}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+236}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{t \cdot \left(x + 1\right)} + \frac{x}{x + 1}\right) - \frac{x}{t \cdot \left(z \cdot \left(x + 1\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 -4e+22)
     (/ 1.0 (* (/ (+ x 1.0) y) (/ t_1 z)))
     (if (<= t_2 5e+236)
       t_2
       (-
        (+ (/ y (* t (+ x 1.0))) (/ x (+ x 1.0)))
        (/ x (* t (* z (+ x 1.0)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -4e+22) {
		tmp = 1.0 / (((x + 1.0) / y) * (t_1 / z));
	} else if (t_2 <= 5e+236) {
		tmp = t_2;
	} else {
		tmp = ((y / (t * (x + 1.0))) + (x / (x + 1.0))) - (x / (t * (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) :: t_2
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-4d+22)) then
        tmp = 1.0d0 / (((x + 1.0d0) / y) * (t_1 / z))
    else if (t_2 <= 5d+236) then
        tmp = t_2
    else
        tmp = ((y / (t * (x + 1.0d0))) + (x / (x + 1.0d0))) - (x / (t * (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 t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -4e+22) {
		tmp = 1.0 / (((x + 1.0) / y) * (t_1 / z));
	} else if (t_2 <= 5e+236) {
		tmp = t_2;
	} else {
		tmp = ((y / (t * (x + 1.0))) + (x / (x + 1.0))) - (x / (t * (z * (x + 1.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -4e+22:
		tmp = 1.0 / (((x + 1.0) / y) * (t_1 / z))
	elif t_2 <= 5e+236:
		tmp = t_2
	else:
		tmp = ((y / (t * (x + 1.0))) + (x / (x + 1.0))) - (x / (t * (z * (x + 1.0))))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -4e+22)
		tmp = Float64(1.0 / Float64(Float64(Float64(x + 1.0) / y) * Float64(t_1 / z)));
	elseif (t_2 <= 5e+236)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(y / Float64(t * Float64(x + 1.0))) + Float64(x / Float64(x + 1.0))) - Float64(x / Float64(t * Float64(z * Float64(x + 1.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -4e+22)
		tmp = 1.0 / (((x + 1.0) / y) * (t_1 / z));
	elseif (t_2 <= 5e+236)
		tmp = t_2;
	else
		tmp = ((y / (t * (x + 1.0))) + (x / (x + 1.0))) - (x / (t * (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]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+22], N[(1.0 / N[(N[(N[(x + 1.0), $MachinePrecision] / y), $MachinePrecision] * N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+236], t$95$2, N[(N[(N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(t * N[(z * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 2: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_2 \leq -4 \cdot 10^{+22}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{y} \cdot \frac{t_1}{z}}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+236}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 -4e+22)
     (/ 1.0 (* (/ (+ x 1.0) y) (/ t_1 z)))
     (if (<= t_2 5e+236) t_2 (/ (+ x (/ y t)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -4e+22) {
		tmp = 1.0 / (((x + 1.0) / y) * (t_1 / z));
	} else if (t_2 <= 5e+236) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (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) :: t_2
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-4d+22)) then
        tmp = 1.0d0 / (((x + 1.0d0) / y) * (t_1 / z))
    else if (t_2 <= 5d+236) then
        tmp = t_2
    else
        tmp = (x + (y / t)) / (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 t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -4e+22) {
		tmp = 1.0 / (((x + 1.0) / y) * (t_1 / z));
	} else if (t_2 <= 5e+236) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -4e+22:
		tmp = 1.0 / (((x + 1.0) / y) * (t_1 / z))
	elif t_2 <= 5e+236:
		tmp = t_2
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -4e+22)
		tmp = Float64(1.0 / Float64(Float64(Float64(x + 1.0) / y) * Float64(t_1 / z)));
	elseif (t_2 <= 5e+236)
		tmp = t_2;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -4e+22)
		tmp = 1.0 / (((x + 1.0) / y) * (t_1 / z));
	elseif (t_2 <= 5e+236)
		tmp = t_2;
	else
		tmp = (x + (y / t)) / (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]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+22], N[(1.0 / N[(N[(N[(x + 1.0), $MachinePrecision] / y), $MachinePrecision] * N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+236], t$95$2, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 3: 80.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x + 1\right) - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{if}\;t \leq -8 \cdot 10^{-15}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-92}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;t \leq 55000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- (+ x 1.0) (/ y (/ x z))) (+ x 1.0))))
   (if (<= t -8e-15)
     (/ (+ x (/ y t)) (+ x 1.0))
     (if (<= t 7.8e-178)
       t_1
       (if (<= t 2.1e-92)
         (* (/ y (+ x 1.0)) (/ z (- (* z t) x)))
         (if (<= t 55000000000.0)
           t_1
           (+ (/ x (+ x 1.0)) (/ (/ y t) (+ x 1.0)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	double tmp;
	if (t <= -8e-15) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (t <= 7.8e-178) {
		tmp = t_1;
	} else if (t <= 2.1e-92) {
		tmp = (y / (x + 1.0)) * (z / ((z * t) - x));
	} else if (t <= 55000000000.0) {
		tmp = t_1;
	} else {
		tmp = (x / (x + 1.0)) + ((y / t) / (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 = ((x + 1.0d0) - (y / (x / z))) / (x + 1.0d0)
    if (t <= (-8d-15)) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else if (t <= 7.8d-178) then
        tmp = t_1
    else if (t <= 2.1d-92) then
        tmp = (y / (x + 1.0d0)) * (z / ((z * t) - x))
    else if (t <= 55000000000.0d0) then
        tmp = t_1
    else
        tmp = (x / (x + 1.0d0)) + ((y / t) / (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 = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	double tmp;
	if (t <= -8e-15) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (t <= 7.8e-178) {
		tmp = t_1;
	} else if (t <= 2.1e-92) {
		tmp = (y / (x + 1.0)) * (z / ((z * t) - x));
	} else if (t <= 55000000000.0) {
		tmp = t_1;
	} else {
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x + 1.0) - (y / (x / z))) / (x + 1.0)
	tmp = 0
	if t <= -8e-15:
		tmp = (x + (y / t)) / (x + 1.0)
	elif t <= 7.8e-178:
		tmp = t_1
	elif t <= 2.1e-92:
		tmp = (y / (x + 1.0)) * (z / ((z * t) - x))
	elif t <= 55000000000.0:
		tmp = t_1
	else:
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x + 1.0) - Float64(y / Float64(x / z))) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -8e-15)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	elseif (t <= 7.8e-178)
		tmp = t_1;
	elseif (t <= 2.1e-92)
		tmp = Float64(Float64(y / Float64(x + 1.0)) * Float64(z / Float64(Float64(z * t) - x)));
	elseif (t <= 55000000000.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(Float64(y / t) / Float64(x + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	tmp = 0.0;
	if (t <= -8e-15)
		tmp = (x + (y / t)) / (x + 1.0);
	elseif (t <= 7.8e-178)
		tmp = t_1;
	elseif (t <= 2.1e-92)
		tmp = (y / (x + 1.0)) * (z / ((z * t) - x));
	elseif (t <= 55000000000.0)
		tmp = t_1;
	else
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x + 1.0), $MachinePrecision] - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8e-15], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e-178], t$95$1, If[LessEqual[t, 2.1e-92], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 55000000000.0], t$95$1, N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 4: 67.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-39}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z \cdot t}\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+137}:\\ \;\;\;\;1 + \frac{\frac{y}{t} + -1}{x}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.4e-39)
   1.0
   (if (<= x 3.5e-78)
     (/ y t)
     (if (<= x 7.2e-10)
       (* x (+ 1.0 (/ -1.0 (* z t))))
       (if (<= x 4.8e+137)
         (+ 1.0 (/ (+ (/ y t) -1.0) x))
         (+ 1.0 (/ -1.0 x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.4e-39) {
		tmp = 1.0;
	} else if (x <= 3.5e-78) {
		tmp = y / t;
	} else if (x <= 7.2e-10) {
		tmp = x * (1.0 + (-1.0 / (z * t)));
	} else if (x <= 4.8e+137) {
		tmp = 1.0 + (((y / t) + -1.0) / x);
	} else {
		tmp = 1.0 + (-1.0 / 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 (x <= (-3.4d-39)) then
        tmp = 1.0d0
    else if (x <= 3.5d-78) then
        tmp = y / t
    else if (x <= 7.2d-10) then
        tmp = x * (1.0d0 + ((-1.0d0) / (z * t)))
    else if (x <= 4.8d+137) then
        tmp = 1.0d0 + (((y / t) + (-1.0d0)) / x)
    else
        tmp = 1.0d0 + ((-1.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.4e-39) {
		tmp = 1.0;
	} else if (x <= 3.5e-78) {
		tmp = y / t;
	} else if (x <= 7.2e-10) {
		tmp = x * (1.0 + (-1.0 / (z * t)));
	} else if (x <= 4.8e+137) {
		tmp = 1.0 + (((y / t) + -1.0) / x);
	} else {
		tmp = 1.0 + (-1.0 / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.4e-39:
		tmp = 1.0
	elif x <= 3.5e-78:
		tmp = y / t
	elif x <= 7.2e-10:
		tmp = x * (1.0 + (-1.0 / (z * t)))
	elif x <= 4.8e+137:
		tmp = 1.0 + (((y / t) + -1.0) / x)
	else:
		tmp = 1.0 + (-1.0 / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.4e-39)
		tmp = 1.0;
	elseif (x <= 3.5e-78)
		tmp = Float64(y / t);
	elseif (x <= 7.2e-10)
		tmp = Float64(x * Float64(1.0 + Float64(-1.0 / Float64(z * t))));
	elseif (x <= 4.8e+137)
		tmp = Float64(1.0 + Float64(Float64(Float64(y / t) + -1.0) / x));
	else
		tmp = Float64(1.0 + Float64(-1.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.4e-39)
		tmp = 1.0;
	elseif (x <= 3.5e-78)
		tmp = y / t;
	elseif (x <= 7.2e-10)
		tmp = x * (1.0 + (-1.0 / (z * t)));
	elseif (x <= 4.8e+137)
		tmp = 1.0 + (((y / t) + -1.0) / x);
	else
		tmp = 1.0 + (-1.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.4e-39], 1.0, If[LessEqual[x, 3.5e-78], N[(y / t), $MachinePrecision], If[LessEqual[x, 7.2e-10], N[(x * N[(1.0 + N[(-1.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e+137], N[(1.0 + N[(N[(N[(y / t), $MachinePrecision] + -1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 5: 81.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-57} \lor \neg \left(z \leq 8.5 \cdot 10^{-42}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.7e-57) (not (<= z 8.5e-42)))
   (/ (+ x (/ y t)) (+ 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 ((z <= -1.7e-57) || !(z <= 8.5e-42)) {
		tmp = (x + (y / t)) / (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 ((z <= (-1.7d-57)) .or. (.not. (z <= 8.5d-42))) then
        tmp = (x + (y / t)) / (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 ((z <= -1.7e-57) || !(z <= 8.5e-42)) {
		tmp = (x + (y / t)) / (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 (z <= -1.7e-57) or not (z <= 8.5e-42):
		tmp = (x + (y / t)) / (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 ((z <= -1.7e-57) || !(z <= 8.5e-42))
		tmp = Float64(Float64(x + Float64(y / t)) / 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 ((z <= -1.7e-57) || ~((z <= 8.5e-42)))
		tmp = (x + (y / t)) / (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[z, -1.7e-57], N[Not[LessEqual[z, 8.5e-42]], $MachinePrecision]], N[(N[(x + N[(y / t), $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 6: 74.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-39}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7e-39) 1.0 (+ (/ x (+ x 1.0)) (/ (/ y t) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7e-39) {
		tmp = 1.0;
	} else {
		tmp = (x / (x + 1.0)) + ((y / t) / (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 <= (-7d-39)) then
        tmp = 1.0d0
    else
        tmp = (x / (x + 1.0d0)) + ((y / t) / (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 <= -7e-39) {
		tmp = 1.0;
	} else {
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7e-39:
		tmp = 1.0
	else:
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7e-39)
		tmp = 1.0;
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(Float64(y / t) / Float64(x + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7e-39)
		tmp = 1.0;
	else
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7e-39], 1.0, N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 7: 69.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-39}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-83}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.9e-39) 1.0 (if (<= x 3.3e-83) (/ y t) (/ 1.0 (/ (+ x 1.0) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.9e-39) {
		tmp = 1.0;
	} else if (x <= 3.3e-83) {
		tmp = y / t;
	} else {
		tmp = 1.0 / ((x + 1.0) / 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 (x <= (-3.9d-39)) then
        tmp = 1.0d0
    else if (x <= 3.3d-83) then
        tmp = y / t
    else
        tmp = 1.0d0 / ((x + 1.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.9e-39) {
		tmp = 1.0;
	} else if (x <= 3.3e-83) {
		tmp = y / t;
	} else {
		tmp = 1.0 / ((x + 1.0) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.9e-39:
		tmp = 1.0
	elif x <= 3.3e-83:
		tmp = y / t
	else:
		tmp = 1.0 / ((x + 1.0) / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.9e-39)
		tmp = 1.0;
	elseif (x <= 3.3e-83)
		tmp = Float64(y / t);
	else
		tmp = Float64(1.0 / Float64(Float64(x + 1.0) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.9e-39)
		tmp = 1.0;
	elseif (x <= 3.3e-83)
		tmp = y / t;
	else
		tmp = 1.0 / ((x + 1.0) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.9e-39], 1.0, If[LessEqual[x, 3.3e-83], N[(y / t), $MachinePrecision], N[(1.0 / N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 8: 74.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-39}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7e-39) 1.0 (/ (+ x (/ y t)) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7e-39) {
		tmp = 1.0;
	} else {
		tmp = (x + (y / t)) / (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 <= (-7d-39)) then
        tmp = 1.0d0
    else
        tmp = (x + (y / t)) / (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 <= -7e-39) {
		tmp = 1.0;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7e-39:
		tmp = 1.0
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7e-39)
		tmp = 1.0;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7e-39)
		tmp = 1.0;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7e-39], 1.0, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 9: 69.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-39}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-82}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.9e-39) 1.0 (if (<= x 3.3e-82) (/ y t) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.9e-39) {
		tmp = 1.0;
	} else if (x <= 3.3e-82) {
		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 <= (-3.9d-39)) then
        tmp = 1.0d0
    else if (x <= 3.3d-82) 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 <= -3.9e-39) {
		tmp = 1.0;
	} else if (x <= 3.3e-82) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.9e-39:
		tmp = 1.0
	elif x <= 3.3e-82:
		tmp = y / t
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.9e-39)
		tmp = 1.0;
	elseif (x <= 3.3e-82)
		tmp = Float64(y / 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 <= -3.9e-39)
		tmp = 1.0;
	elseif (x <= 3.3e-82)
		tmp = y / t;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.9e-39], 1.0, If[LessEqual[x, 3.3e-82], N[(y / t), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 10: 69.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-39}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-61}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.5e-39) 1.0 (if (<= x 1.8e-61) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.5e-39) {
		tmp = 1.0;
	} else if (x <= 1.8e-61) {
		tmp = y / 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 <= (-3.5d-39)) then
        tmp = 1.0d0
    else if (x <= 1.8d-61) then
        tmp = y / 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 <= -3.5e-39) {
		tmp = 1.0;
	} else if (x <= 1.8e-61) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.5e-39:
		tmp = 1.0
	elif x <= 1.8e-61:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.5e-39)
		tmp = 1.0;
	elseif (x <= 1.8e-61)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.5e-39)
		tmp = 1.0;
	elseif (x <= 1.8e-61)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.5e-39], 1.0, If[LessEqual[x, 1.8e-61], N[(y / t), $MachinePrecision], 1.0]]

Derivation

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

Alternative 11: 54.3% 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: 99.6% 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 2023350 
(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)))