Kahan p13 Example 1

Percentage Accurate: 100.0% → 100.0%

Time: 15.0s

Alternatives: 11

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 \cdot t}{1 + t}\\ t_2 := t_1 \cdot t_1\\ \frac{1 + t_2}{2 + t_2} \end{array} \end{array} \]

FPCore

(FPCore (t)
 :precision binary64
 (let* ((t_1 (/ (* 2.0 t) (+ 1.0 t))) (t_2 (* t_1 t_1)))
   (/ (+ 1.0 t_2) (+ 2.0 t_2))))

C

double code(double t) {
	double t_1 = (2.0 * t) / (1.0 + t);
	double t_2 = t_1 * t_1;
	return (1.0 + t_2) / (2.0 + t_2);
}

Fortran

real(8) function code(t)
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    t_1 = (2.0d0 * t) / (1.0d0 + t)
    t_2 = t_1 * t_1
    code = (1.0d0 + t_2) / (2.0d0 + t_2)
end function

Java

public static double code(double t) {
	double t_1 = (2.0 * t) / (1.0 + t);
	double t_2 = t_1 * t_1;
	return (1.0 + t_2) / (2.0 + t_2);
}

Python

def code(t):
	t_1 = (2.0 * t) / (1.0 + t)
	t_2 = t_1 * t_1
	return (1.0 + t_2) / (2.0 + t_2)

Julia

function code(t)
	t_1 = Float64(Float64(2.0 * t) / Float64(1.0 + t))
	t_2 = Float64(t_1 * t_1)
	return Float64(Float64(1.0 + t_2) / Float64(2.0 + t_2))
end

MATLAB

function tmp = code(t)
	t_1 = (2.0 * t) / (1.0 + t);
	t_2 = t_1 * t_1;
	tmp = (1.0 + t_2) / (2.0 + t_2);
end

Wolfram

code[t_] := Block[{t$95$1 = N[(N[(2.0 * t), $MachinePrecision] / N[(1.0 + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t$95$1), $MachinePrecision]}, N[(N[(1.0 + t$95$2), $MachinePrecision] / N[(2.0 + t$95$2), $MachinePrecision]), $MachinePrecision]]]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 \cdot t}{1 + t}\\ t_2 := t_1 \cdot t_1\\ \frac{1 + t_2}{2 + t_2} \end{array} \end{array} \]

FPCore

(FPCore (t)
 :precision binary64
 (let* ((t_1 (/ (* 2.0 t) (+ 1.0 t))) (t_2 (* t_1 t_1)))
   (/ (+ 1.0 t_2) (+ 2.0 t_2))))

C

double code(double t) {
	double t_1 = (2.0 * t) / (1.0 + t);
	double t_2 = t_1 * t_1;
	return (1.0 + t_2) / (2.0 + t_2);
}

Fortran

real(8) function code(t)
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    t_1 = (2.0d0 * t) / (1.0d0 + t)
    t_2 = t_1 * t_1
    code = (1.0d0 + t_2) / (2.0d0 + t_2)
end function

Java

public static double code(double t) {
	double t_1 = (2.0 * t) / (1.0 + t);
	double t_2 = t_1 * t_1;
	return (1.0 + t_2) / (2.0 + t_2);
}

Python

def code(t):
	t_1 = (2.0 * t) / (1.0 + t)
	t_2 = t_1 * t_1
	return (1.0 + t_2) / (2.0 + t_2)

Julia

function code(t)
	t_1 = Float64(Float64(2.0 * t) / Float64(1.0 + t))
	t_2 = Float64(t_1 * t_1)
	return Float64(Float64(1.0 + t_2) / Float64(2.0 + t_2))
end

MATLAB

function tmp = code(t)
	t_1 = (2.0 * t) / (1.0 + t);
	t_2 = t_1 * t_1;
	tmp = (1.0 + t_2) / (2.0 + t_2);
end

Wolfram

code[t_] := Block[{t$95$1 = N[(N[(2.0 * t), $MachinePrecision] / N[(1.0 + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t$95$1), $MachinePrecision]}, N[(N[(1.0 + t$95$2), $MachinePrecision] / N[(2.0 + t$95$2), $MachinePrecision]), $MachinePrecision]]]

Alternative 1: 100.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 \cdot t}{1 + t}\\ \frac{1 + t_1 \cdot t_1}{2 + \left(\left(1 + {\left(2 \cdot \frac{t}{1 + t}\right)}^{2}\right) + -1\right)} \end{array} \end{array} \]

FPCore

(FPCore (t)
 :precision binary64
 (let* ((t_1 (/ (* 2.0 t) (+ 1.0 t))))
   (/
    (+ 1.0 (* t_1 t_1))
    (+ 2.0 (+ (+ 1.0 (pow (* 2.0 (/ t (+ 1.0 t))) 2.0)) -1.0)))))

C

double code(double t) {
	double t_1 = (2.0 * t) / (1.0 + t);
	return (1.0 + (t_1 * t_1)) / (2.0 + ((1.0 + pow((2.0 * (t / (1.0 + t))), 2.0)) + -1.0));
}

Fortran

real(8) function code(t)
    real(8), intent (in) :: t
    real(8) :: t_1
    t_1 = (2.0d0 * t) / (1.0d0 + t)
    code = (1.0d0 + (t_1 * t_1)) / (2.0d0 + ((1.0d0 + ((2.0d0 * (t / (1.0d0 + t))) ** 2.0d0)) + (-1.0d0)))
end function

Java

public static double code(double t) {
	double t_1 = (2.0 * t) / (1.0 + t);
	return (1.0 + (t_1 * t_1)) / (2.0 + ((1.0 + Math.pow((2.0 * (t / (1.0 + t))), 2.0)) + -1.0));
}

Python

def code(t):
	t_1 = (2.0 * t) / (1.0 + t)
	return (1.0 + (t_1 * t_1)) / (2.0 + ((1.0 + math.pow((2.0 * (t / (1.0 + t))), 2.0)) + -1.0))

Julia

function code(t)
	t_1 = Float64(Float64(2.0 * t) / Float64(1.0 + t))
	return Float64(Float64(1.0 + Float64(t_1 * t_1)) / Float64(2.0 + Float64(Float64(1.0 + (Float64(2.0 * Float64(t / Float64(1.0 + t))) ^ 2.0)) + -1.0)))
end

MATLAB

function tmp = code(t)
	t_1 = (2.0 * t) / (1.0 + t);
	tmp = (1.0 + (t_1 * t_1)) / (2.0 + ((1.0 + ((2.0 * (t / (1.0 + t))) ^ 2.0)) + -1.0));
end

Wolfram

code[t_] := Block[{t$95$1 = N[(N[(2.0 * t), $MachinePrecision] / N[(1.0 + t), $MachinePrecision]), $MachinePrecision]}, N[(N[(1.0 + N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision] / N[(2.0 + N[(N[(1.0 + N[Power[N[(2.0 * N[(t / N[(1.0 + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 2: 99.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 + t}\\ t_2 := 2 \cdot t_1\\ \frac{1 + \frac{t_1 \cdot \left(t \cdot 4\right)}{1 + t}}{2 + \left(\left(1 + t_2 \cdot t_2\right) + -1\right)} \end{array} \end{array} \]

FPCore

(FPCore (t)
 :precision binary64
 (let* ((t_1 (/ t (+ 1.0 t))) (t_2 (* 2.0 t_1)))
   (/
    (+ 1.0 (/ (* t_1 (* t 4.0)) (+ 1.0 t)))
    (+ 2.0 (+ (+ 1.0 (* t_2 t_2)) -1.0)))))

C

double code(double t) {
	double t_1 = t / (1.0 + t);
	double t_2 = 2.0 * t_1;
	return (1.0 + ((t_1 * (t * 4.0)) / (1.0 + t))) / (2.0 + ((1.0 + (t_2 * t_2)) + -1.0));
}

Fortran

real(8) function code(t)
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    t_1 = t / (1.0d0 + t)
    t_2 = 2.0d0 * t_1
    code = (1.0d0 + ((t_1 * (t * 4.0d0)) / (1.0d0 + t))) / (2.0d0 + ((1.0d0 + (t_2 * t_2)) + (-1.0d0)))
end function

Java

public static double code(double t) {
	double t_1 = t / (1.0 + t);
	double t_2 = 2.0 * t_1;
	return (1.0 + ((t_1 * (t * 4.0)) / (1.0 + t))) / (2.0 + ((1.0 + (t_2 * t_2)) + -1.0));
}

Python

def code(t):
	t_1 = t / (1.0 + t)
	t_2 = 2.0 * t_1
	return (1.0 + ((t_1 * (t * 4.0)) / (1.0 + t))) / (2.0 + ((1.0 + (t_2 * t_2)) + -1.0))

Julia

function code(t)
	t_1 = Float64(t / Float64(1.0 + t))
	t_2 = Float64(2.0 * t_1)
	return Float64(Float64(1.0 + Float64(Float64(t_1 * Float64(t * 4.0)) / Float64(1.0 + t))) / Float64(2.0 + Float64(Float64(1.0 + Float64(t_2 * t_2)) + -1.0)))
end

MATLAB

function tmp = code(t)
	t_1 = t / (1.0 + t);
	t_2 = 2.0 * t_1;
	tmp = (1.0 + ((t_1 * (t * 4.0)) / (1.0 + t))) / (2.0 + ((1.0 + (t_2 * t_2)) + -1.0));
end

Wolfram

code[t_] := Block[{t$95$1 = N[(t / N[(1.0 + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * t$95$1), $MachinePrecision]}, N[(N[(1.0 + N[(N[(t$95$1 * N[(t * 4.0), $MachinePrecision]), $MachinePrecision] / N[(1.0 + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(2.0 + N[(N[(1.0 + N[(t$95$2 * t$95$2), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 3: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot \left(t \cdot 4\right)}{\left(1 + t\right) \cdot \left(1 + t\right)}\\ \mathbf{if}\;t \leq -5 \cdot 10^{+153}:\\ \;\;\;\;0.8333333333333334\\ \mathbf{elif}\;t \leq 1000000:\\ \;\;\;\;\frac{1 + t_1}{2 + t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-5 - \frac{-8}{t}}{-6 + \frac{8}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (t)
 :precision binary64
 (let* ((t_1 (/ (* t (* t 4.0)) (* (+ 1.0 t) (+ 1.0 t)))))
   (if (<= t -5e+153)
     0.8333333333333334
     (if (<= t 1000000.0)
       (/ (+ 1.0 t_1) (+ 2.0 t_1))
       (/ (- -5.0 (/ -8.0 t)) (+ -6.0 (/ 8.0 t)))))))

C

double code(double t) {
	double t_1 = (t * (t * 4.0)) / ((1.0 + t) * (1.0 + t));
	double tmp;
	if (t <= -5e+153) {
		tmp = 0.8333333333333334;
	} else if (t <= 1000000.0) {
		tmp = (1.0 + t_1) / (2.0 + t_1);
	} else {
		tmp = (-5.0 - (-8.0 / t)) / (-6.0 + (8.0 / t));
	}
	return tmp;
}

Fortran

real(8) function code(t)
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * (t * 4.0d0)) / ((1.0d0 + t) * (1.0d0 + t))
    if (t <= (-5d+153)) then
        tmp = 0.8333333333333334d0
    else if (t <= 1000000.0d0) then
        tmp = (1.0d0 + t_1) / (2.0d0 + t_1)
    else
        tmp = ((-5.0d0) - ((-8.0d0) / t)) / ((-6.0d0) + (8.0d0 / t))
    end if
    code = tmp
end function

Java

public static double code(double t) {
	double t_1 = (t * (t * 4.0)) / ((1.0 + t) * (1.0 + t));
	double tmp;
	if (t <= -5e+153) {
		tmp = 0.8333333333333334;
	} else if (t <= 1000000.0) {
		tmp = (1.0 + t_1) / (2.0 + t_1);
	} else {
		tmp = (-5.0 - (-8.0 / t)) / (-6.0 + (8.0 / t));
	}
	return tmp;
}

Python

def code(t):
	t_1 = (t * (t * 4.0)) / ((1.0 + t) * (1.0 + t))
	tmp = 0
	if t <= -5e+153:
		tmp = 0.8333333333333334
	elif t <= 1000000.0:
		tmp = (1.0 + t_1) / (2.0 + t_1)
	else:
		tmp = (-5.0 - (-8.0 / t)) / (-6.0 + (8.0 / t))
	return tmp

Julia

function code(t)
	t_1 = Float64(Float64(t * Float64(t * 4.0)) / Float64(Float64(1.0 + t) * Float64(1.0 + t)))
	tmp = 0.0
	if (t <= -5e+153)
		tmp = 0.8333333333333334;
	elseif (t <= 1000000.0)
		tmp = Float64(Float64(1.0 + t_1) / Float64(2.0 + t_1));
	else
		tmp = Float64(Float64(-5.0 - Float64(-8.0 / t)) / Float64(-6.0 + Float64(8.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(t)
	t_1 = (t * (t * 4.0)) / ((1.0 + t) * (1.0 + t));
	tmp = 0.0;
	if (t <= -5e+153)
		tmp = 0.8333333333333334;
	elseif (t <= 1000000.0)
		tmp = (1.0 + t_1) / (2.0 + t_1);
	else
		tmp = (-5.0 - (-8.0 / t)) / (-6.0 + (8.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[t_] := Block[{t$95$1 = N[(N[(t * N[(t * 4.0), $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 + t), $MachinePrecision] * N[(1.0 + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e+153], 0.8333333333333334, If[LessEqual[t, 1000000.0], N[(N[(1.0 + t$95$1), $MachinePrecision] / N[(2.0 + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(-5.0 - N[(-8.0 / t), $MachinePrecision]), $MachinePrecision] / N[(-6.0 + N[(8.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 4: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 \cdot t}{1 + t}\\ t_2 := t_1 \cdot t_1\\ \frac{1 + t_2}{2 + t_2} \end{array} \end{array} \]

FPCore

(FPCore (t)
 :precision binary64
 (let* ((t_1 (/ (* 2.0 t) (+ 1.0 t))) (t_2 (* t_1 t_1)))
   (/ (+ 1.0 t_2) (+ 2.0 t_2))))

C

double code(double t) {
	double t_1 = (2.0 * t) / (1.0 + t);
	double t_2 = t_1 * t_1;
	return (1.0 + t_2) / (2.0 + t_2);
}

Fortran

real(8) function code(t)
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    t_1 = (2.0d0 * t) / (1.0d0 + t)
    t_2 = t_1 * t_1
    code = (1.0d0 + t_2) / (2.0d0 + t_2)
end function

Java

public static double code(double t) {
	double t_1 = (2.0 * t) / (1.0 + t);
	double t_2 = t_1 * t_1;
	return (1.0 + t_2) / (2.0 + t_2);
}

Python

def code(t):
	t_1 = (2.0 * t) / (1.0 + t)
	t_2 = t_1 * t_1
	return (1.0 + t_2) / (2.0 + t_2)

Julia

function code(t)
	t_1 = Float64(Float64(2.0 * t) / Float64(1.0 + t))
	t_2 = Float64(t_1 * t_1)
	return Float64(Float64(1.0 + t_2) / Float64(2.0 + t_2))
end

MATLAB

function tmp = code(t)
	t_1 = (2.0 * t) / (1.0 + t);
	t_2 = t_1 * t_1;
	tmp = (1.0 + t_2) / (2.0 + t_2);
end

Wolfram

code[t_] := Block[{t$95$1 = N[(N[(2.0 * t), $MachinePrecision] / N[(1.0 + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t$95$1), $MachinePrecision]}, N[(N[(1.0 + t$95$2), $MachinePrecision] / N[(2.0 + t$95$2), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 5: 99.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 \cdot t}{1 + t} \cdot \left(2 \cdot t\right)\\ \mathbf{if}\;t \leq -1.15:\\ \;\;\;\;0.8333333333333334 - \frac{0.2222222222222222}{t}\\ \mathbf{elif}\;t \leq 2.3:\\ \;\;\;\;\frac{1 + t_1}{2 + t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-5 - \frac{-8}{t}}{-6 + \frac{8}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (t)
 :precision binary64
 (let* ((t_1 (* (/ (* 2.0 t) (+ 1.0 t)) (* 2.0 t))))
   (if (<= t -1.15)
     (- 0.8333333333333334 (/ 0.2222222222222222 t))
     (if (<= t 2.3)
       (/ (+ 1.0 t_1) (+ 2.0 t_1))
       (/ (- -5.0 (/ -8.0 t)) (+ -6.0 (/ 8.0 t)))))))

C

double code(double t) {
	double t_1 = ((2.0 * t) / (1.0 + t)) * (2.0 * t);
	double tmp;
	if (t <= -1.15) {
		tmp = 0.8333333333333334 - (0.2222222222222222 / t);
	} else if (t <= 2.3) {
		tmp = (1.0 + t_1) / (2.0 + t_1);
	} else {
		tmp = (-5.0 - (-8.0 / t)) / (-6.0 + (8.0 / t));
	}
	return tmp;
}

Fortran

real(8) function code(t)
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((2.0d0 * t) / (1.0d0 + t)) * (2.0d0 * t)
    if (t <= (-1.15d0)) then
        tmp = 0.8333333333333334d0 - (0.2222222222222222d0 / t)
    else if (t <= 2.3d0) then
        tmp = (1.0d0 + t_1) / (2.0d0 + t_1)
    else
        tmp = ((-5.0d0) - ((-8.0d0) / t)) / ((-6.0d0) + (8.0d0 / t))
    end if
    code = tmp
end function

Java

public static double code(double t) {
	double t_1 = ((2.0 * t) / (1.0 + t)) * (2.0 * t);
	double tmp;
	if (t <= -1.15) {
		tmp = 0.8333333333333334 - (0.2222222222222222 / t);
	} else if (t <= 2.3) {
		tmp = (1.0 + t_1) / (2.0 + t_1);
	} else {
		tmp = (-5.0 - (-8.0 / t)) / (-6.0 + (8.0 / t));
	}
	return tmp;
}

Python

def code(t):
	t_1 = ((2.0 * t) / (1.0 + t)) * (2.0 * t)
	tmp = 0
	if t <= -1.15:
		tmp = 0.8333333333333334 - (0.2222222222222222 / t)
	elif t <= 2.3:
		tmp = (1.0 + t_1) / (2.0 + t_1)
	else:
		tmp = (-5.0 - (-8.0 / t)) / (-6.0 + (8.0 / t))
	return tmp

Julia

function code(t)
	t_1 = Float64(Float64(Float64(2.0 * t) / Float64(1.0 + t)) * Float64(2.0 * t))
	tmp = 0.0
	if (t <= -1.15)
		tmp = Float64(0.8333333333333334 - Float64(0.2222222222222222 / t));
	elseif (t <= 2.3)
		tmp = Float64(Float64(1.0 + t_1) / Float64(2.0 + t_1));
	else
		tmp = Float64(Float64(-5.0 - Float64(-8.0 / t)) / Float64(-6.0 + Float64(8.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(t)
	t_1 = ((2.0 * t) / (1.0 + t)) * (2.0 * t);
	tmp = 0.0;
	if (t <= -1.15)
		tmp = 0.8333333333333334 - (0.2222222222222222 / t);
	elseif (t <= 2.3)
		tmp = (1.0 + t_1) / (2.0 + t_1);
	else
		tmp = (-5.0 - (-8.0 / t)) / (-6.0 + (8.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[t_] := Block[{t$95$1 = N[(N[(N[(2.0 * t), $MachinePrecision] / N[(1.0 + t), $MachinePrecision]), $MachinePrecision] * N[(2.0 * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15], N[(0.8333333333333334 - N[(0.2222222222222222 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3], N[(N[(1.0 + t$95$1), $MachinePrecision] / N[(2.0 + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(-5.0 - N[(-8.0 / t), $MachinePrecision]), $MachinePrecision] / N[(-6.0 + N[(8.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 6: 99.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot \left(t \cdot 4\right)}{1 + 2 \cdot t}\\ \mathbf{if}\;t \leq -0.6:\\ \;\;\;\;0.8333333333333334 - \frac{0.2222222222222222}{t}\\ \mathbf{elif}\;t \leq 2.6:\\ \;\;\;\;\frac{1 + t_1}{2 + t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-5 - \frac{-8}{t}}{-6 + \frac{8}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (t)
 :precision binary64
 (let* ((t_1 (/ (* t (* t 4.0)) (+ 1.0 (* 2.0 t)))))
   (if (<= t -0.6)
     (- 0.8333333333333334 (/ 0.2222222222222222 t))
     (if (<= t 2.6)
       (/ (+ 1.0 t_1) (+ 2.0 t_1))
       (/ (- -5.0 (/ -8.0 t)) (+ -6.0 (/ 8.0 t)))))))

C

double code(double t) {
	double t_1 = (t * (t * 4.0)) / (1.0 + (2.0 * t));
	double tmp;
	if (t <= -0.6) {
		tmp = 0.8333333333333334 - (0.2222222222222222 / t);
	} else if (t <= 2.6) {
		tmp = (1.0 + t_1) / (2.0 + t_1);
	} else {
		tmp = (-5.0 - (-8.0 / t)) / (-6.0 + (8.0 / t));
	}
	return tmp;
}

Fortran

real(8) function code(t)
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * (t * 4.0d0)) / (1.0d0 + (2.0d0 * t))
    if (t <= (-0.6d0)) then
        tmp = 0.8333333333333334d0 - (0.2222222222222222d0 / t)
    else if (t <= 2.6d0) then
        tmp = (1.0d0 + t_1) / (2.0d0 + t_1)
    else
        tmp = ((-5.0d0) - ((-8.0d0) / t)) / ((-6.0d0) + (8.0d0 / t))
    end if
    code = tmp
end function

Java

public static double code(double t) {
	double t_1 = (t * (t * 4.0)) / (1.0 + (2.0 * t));
	double tmp;
	if (t <= -0.6) {
		tmp = 0.8333333333333334 - (0.2222222222222222 / t);
	} else if (t <= 2.6) {
		tmp = (1.0 + t_1) / (2.0 + t_1);
	} else {
		tmp = (-5.0 - (-8.0 / t)) / (-6.0 + (8.0 / t));
	}
	return tmp;
}

Python

def code(t):
	t_1 = (t * (t * 4.0)) / (1.0 + (2.0 * t))
	tmp = 0
	if t <= -0.6:
		tmp = 0.8333333333333334 - (0.2222222222222222 / t)
	elif t <= 2.6:
		tmp = (1.0 + t_1) / (2.0 + t_1)
	else:
		tmp = (-5.0 - (-8.0 / t)) / (-6.0 + (8.0 / t))
	return tmp

Julia

function code(t)
	t_1 = Float64(Float64(t * Float64(t * 4.0)) / Float64(1.0 + Float64(2.0 * t)))
	tmp = 0.0
	if (t <= -0.6)
		tmp = Float64(0.8333333333333334 - Float64(0.2222222222222222 / t));
	elseif (t <= 2.6)
		tmp = Float64(Float64(1.0 + t_1) / Float64(2.0 + t_1));
	else
		tmp = Float64(Float64(-5.0 - Float64(-8.0 / t)) / Float64(-6.0 + Float64(8.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(t)
	t_1 = (t * (t * 4.0)) / (1.0 + (2.0 * t));
	tmp = 0.0;
	if (t <= -0.6)
		tmp = 0.8333333333333334 - (0.2222222222222222 / t);
	elseif (t <= 2.6)
		tmp = (1.0 + t_1) / (2.0 + t_1);
	else
		tmp = (-5.0 - (-8.0 / t)) / (-6.0 + (8.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[t_] := Block[{t$95$1 = N[(N[(t * N[(t * 4.0), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(2.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.6], N[(0.8333333333333334 - N[(0.2222222222222222 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6], N[(N[(1.0 + t$95$1), $MachinePrecision] / N[(2.0 + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(-5.0 - N[(-8.0 / t), $MachinePrecision]), $MachinePrecision] / N[(-6.0 + N[(8.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 7: 99.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(t \cdot 4\right)\\ \mathbf{if}\;t \leq -0.6:\\ \;\;\;\;0.8333333333333334 - \frac{0.2222222222222222}{t}\\ \mathbf{elif}\;t \leq 2.1:\\ \;\;\;\;\frac{1 + t_1}{2 + t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-5 - \frac{-8}{t}}{-6 + \frac{8}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (t)
 :precision binary64
 (let* ((t_1 (* t (* t 4.0))))
   (if (<= t -0.6)
     (- 0.8333333333333334 (/ 0.2222222222222222 t))
     (if (<= t 2.1)
       (/ (+ 1.0 t_1) (+ 2.0 t_1))
       (/ (- -5.0 (/ -8.0 t)) (+ -6.0 (/ 8.0 t)))))))

C

double code(double t) {
	double t_1 = t * (t * 4.0);
	double tmp;
	if (t <= -0.6) {
		tmp = 0.8333333333333334 - (0.2222222222222222 / t);
	} else if (t <= 2.1) {
		tmp = (1.0 + t_1) / (2.0 + t_1);
	} else {
		tmp = (-5.0 - (-8.0 / t)) / (-6.0 + (8.0 / t));
	}
	return tmp;
}

Fortran

real(8) function code(t)
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (t * 4.0d0)
    if (t <= (-0.6d0)) then
        tmp = 0.8333333333333334d0 - (0.2222222222222222d0 / t)
    else if (t <= 2.1d0) then
        tmp = (1.0d0 + t_1) / (2.0d0 + t_1)
    else
        tmp = ((-5.0d0) - ((-8.0d0) / t)) / ((-6.0d0) + (8.0d0 / t))
    end if
    code = tmp
end function

Java

public static double code(double t) {
	double t_1 = t * (t * 4.0);
	double tmp;
	if (t <= -0.6) {
		tmp = 0.8333333333333334 - (0.2222222222222222 / t);
	} else if (t <= 2.1) {
		tmp = (1.0 + t_1) / (2.0 + t_1);
	} else {
		tmp = (-5.0 - (-8.0 / t)) / (-6.0 + (8.0 / t));
	}
	return tmp;
}

Python

def code(t):
	t_1 = t * (t * 4.0)
	tmp = 0
	if t <= -0.6:
		tmp = 0.8333333333333334 - (0.2222222222222222 / t)
	elif t <= 2.1:
		tmp = (1.0 + t_1) / (2.0 + t_1)
	else:
		tmp = (-5.0 - (-8.0 / t)) / (-6.0 + (8.0 / t))
	return tmp

Julia

function code(t)
	t_1 = Float64(t * Float64(t * 4.0))
	tmp = 0.0
	if (t <= -0.6)
		tmp = Float64(0.8333333333333334 - Float64(0.2222222222222222 / t));
	elseif (t <= 2.1)
		tmp = Float64(Float64(1.0 + t_1) / Float64(2.0 + t_1));
	else
		tmp = Float64(Float64(-5.0 - Float64(-8.0 / t)) / Float64(-6.0 + Float64(8.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(t)
	t_1 = t * (t * 4.0);
	tmp = 0.0;
	if (t <= -0.6)
		tmp = 0.8333333333333334 - (0.2222222222222222 / t);
	elseif (t <= 2.1)
		tmp = (1.0 + t_1) / (2.0 + t_1);
	else
		tmp = (-5.0 - (-8.0 / t)) / (-6.0 + (8.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[t_] := Block[{t$95$1 = N[(t * N[(t * 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.6], N[(0.8333333333333334 - N[(0.2222222222222222 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1], N[(N[(1.0 + t$95$1), $MachinePrecision] / N[(2.0 + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(-5.0 - N[(-8.0 / t), $MachinePrecision]), $MachinePrecision] / N[(-6.0 + N[(8.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 8: 98.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.48:\\ \;\;\;\;0.8333333333333334 - \frac{0.2222222222222222}{t}\\ \mathbf{elif}\;t \leq 2:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{-5 - \frac{-8}{t}}{-6 + \frac{8}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (t)
 :precision binary64
 (if (<= t -0.48)
   (- 0.8333333333333334 (/ 0.2222222222222222 t))
   (if (<= t 2.0) 0.5 (/ (- -5.0 (/ -8.0 t)) (+ -6.0 (/ 8.0 t))))))

C

double code(double t) {
	double tmp;
	if (t <= -0.48) {
		tmp = 0.8333333333333334 - (0.2222222222222222 / t);
	} else if (t <= 2.0) {
		tmp = 0.5;
	} else {
		tmp = (-5.0 - (-8.0 / t)) / (-6.0 + (8.0 / t));
	}
	return tmp;
}

Fortran

real(8) function code(t)
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-0.48d0)) then
        tmp = 0.8333333333333334d0 - (0.2222222222222222d0 / t)
    else if (t <= 2.0d0) then
        tmp = 0.5d0
    else
        tmp = ((-5.0d0) - ((-8.0d0) / t)) / ((-6.0d0) + (8.0d0 / t))
    end if
    code = tmp
end function

Java

public static double code(double t) {
	double tmp;
	if (t <= -0.48) {
		tmp = 0.8333333333333334 - (0.2222222222222222 / t);
	} else if (t <= 2.0) {
		tmp = 0.5;
	} else {
		tmp = (-5.0 - (-8.0 / t)) / (-6.0 + (8.0 / t));
	}
	return tmp;
}

Python

def code(t):
	tmp = 0
	if t <= -0.48:
		tmp = 0.8333333333333334 - (0.2222222222222222 / t)
	elif t <= 2.0:
		tmp = 0.5
	else:
		tmp = (-5.0 - (-8.0 / t)) / (-6.0 + (8.0 / t))
	return tmp

Julia

function code(t)
	tmp = 0.0
	if (t <= -0.48)
		tmp = Float64(0.8333333333333334 - Float64(0.2222222222222222 / t));
	elseif (t <= 2.0)
		tmp = 0.5;
	else
		tmp = Float64(Float64(-5.0 - Float64(-8.0 / t)) / Float64(-6.0 + Float64(8.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(t)
	tmp = 0.0;
	if (t <= -0.48)
		tmp = 0.8333333333333334 - (0.2222222222222222 / t);
	elseif (t <= 2.0)
		tmp = 0.5;
	else
		tmp = (-5.0 - (-8.0 / t)) / (-6.0 + (8.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[t_] := If[LessEqual[t, -0.48], N[(0.8333333333333334 - N[(0.2222222222222222 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.0], 0.5, N[(N[(-5.0 - N[(-8.0 / t), $MachinePrecision]), $MachinePrecision] / N[(-6.0 + N[(8.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 9: 99.0% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.48 \lor \neg \left(t \leq 0.65\right):\\ \;\;\;\;0.8333333333333334 - \frac{0.2222222222222222}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (t)
 :precision binary64
 (if (or (<= t -0.48) (not (<= t 0.65)))
   (- 0.8333333333333334 (/ 0.2222222222222222 t))
   0.5))

C

double code(double t) {
	double tmp;
	if ((t <= -0.48) || !(t <= 0.65)) {
		tmp = 0.8333333333333334 - (0.2222222222222222 / t);
	} else {
		tmp = 0.5;
	}
	return tmp;
}

Fortran

real(8) function code(t)
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-0.48d0)) .or. (.not. (t <= 0.65d0))) then
        tmp = 0.8333333333333334d0 - (0.2222222222222222d0 / t)
    else
        tmp = 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double t) {
	double tmp;
	if ((t <= -0.48) || !(t <= 0.65)) {
		tmp = 0.8333333333333334 - (0.2222222222222222 / t);
	} else {
		tmp = 0.5;
	}
	return tmp;
}

Python

def code(t):
	tmp = 0
	if (t <= -0.48) or not (t <= 0.65):
		tmp = 0.8333333333333334 - (0.2222222222222222 / t)
	else:
		tmp = 0.5
	return tmp

Julia

function code(t)
	tmp = 0.0
	if ((t <= -0.48) || !(t <= 0.65))
		tmp = Float64(0.8333333333333334 - Float64(0.2222222222222222 / t));
	else
		tmp = 0.5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(t)
	tmp = 0.0;
	if ((t <= -0.48) || ~((t <= 0.65)))
		tmp = 0.8333333333333334 - (0.2222222222222222 / t);
	else
		tmp = 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[t_] := If[Or[LessEqual[t, -0.48], N[Not[LessEqual[t, 0.65]], $MachinePrecision]], N[(0.8333333333333334 - N[(0.2222222222222222 / t), $MachinePrecision]), $MachinePrecision], 0.5]

Derivation

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

Alternative 10: 98.4% accurate, 6.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.34:\\ \;\;\;\;0.8333333333333334\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;0.8333333333333334\\ \end{array} \end{array} \]

FPCore

(FPCore (t)
 :precision binary64
 (if (<= t -0.34) 0.8333333333333334 (if (<= t 1.0) 0.5 0.8333333333333334)))

C

double code(double t) {
	double tmp;
	if (t <= -0.34) {
		tmp = 0.8333333333333334;
	} else if (t <= 1.0) {
		tmp = 0.5;
	} else {
		tmp = 0.8333333333333334;
	}
	return tmp;
}

Fortran

real(8) function code(t)
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-0.34d0)) then
        tmp = 0.8333333333333334d0
    else if (t <= 1.0d0) then
        tmp = 0.5d0
    else
        tmp = 0.8333333333333334d0
    end if
    code = tmp
end function

Java

public static double code(double t) {
	double tmp;
	if (t <= -0.34) {
		tmp = 0.8333333333333334;
	} else if (t <= 1.0) {
		tmp = 0.5;
	} else {
		tmp = 0.8333333333333334;
	}
	return tmp;
}

Python

def code(t):
	tmp = 0
	if t <= -0.34:
		tmp = 0.8333333333333334
	elif t <= 1.0:
		tmp = 0.5
	else:
		tmp = 0.8333333333333334
	return tmp

Julia

function code(t)
	tmp = 0.0
	if (t <= -0.34)
		tmp = 0.8333333333333334;
	elseif (t <= 1.0)
		tmp = 0.5;
	else
		tmp = 0.8333333333333334;
	end
	return tmp
end

MATLAB

function tmp_2 = code(t)
	tmp = 0.0;
	if (t <= -0.34)
		tmp = 0.8333333333333334;
	elseif (t <= 1.0)
		tmp = 0.5;
	else
		tmp = 0.8333333333333334;
	end
	tmp_2 = tmp;
end

Wolfram

code[t_] := If[LessEqual[t, -0.34], 0.8333333333333334, If[LessEqual[t, 1.0], 0.5, 0.8333333333333334]]

Derivation

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

Alternative 11: 58.1% accurate, 35.0× speedup

Math

\[\begin{array}{l} \\ 0.5 \end{array} \]

FPCore

(FPCore (t) :precision binary64 0.5)

C

double code(double t) {
	return 0.5;
}

Fortran

real(8) function code(t)
    real(8), intent (in) :: t
    code = 0.5d0
end function

Java

public static double code(double t) {
	return 0.5;
}

Python

def code(t):
	return 0.5

Julia

function code(t)
	return 0.5
end

MATLAB

function tmp = code(t)
	tmp = 0.5;
end

Wolfram

code[t_] := 0.5

Derivation

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

Reproduce

herbie shell --seed 2023347 
(FPCore (t)
  :name "Kahan p13 Example 1"
  :precision binary64
  (/ (+ 1.0 (* (/ (* 2.0 t) (+ 1.0 t)) (/ (* 2.0 t) (+ 1.0 t)))) (+ 2.0 (* (/ (* 2.0 t) (+ 1.0 t)) (/ (* 2.0 t) (+ 1.0 t))))))