2sin (example 3.3)

Percentage Accurate: 41.9% → 99.4%

Time: 11.8s

Alternatives: 10

Speedup: 2.0×

Specification

Math

\[\begin{array}{l} \\ \sin \left(x + \varepsilon\right) - \sin x \end{array} \]

FPCore

(FPCore (x eps) :precision binary64 (- (sin (+ x eps)) (sin x)))

C

double code(double x, double eps) {
	return sin((x + eps)) - sin(x);
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    code = sin((x + eps)) - sin(x)
end function

Java

public static double code(double x, double eps) {
	return Math.sin((x + eps)) - Math.sin(x);
}

Python

def code(x, eps):
	return math.sin((x + eps)) - math.sin(x)

Julia

function code(x, eps)
	return Float64(sin(Float64(x + eps)) - sin(x))
end

MATLAB

function tmp = code(x, eps)
	tmp = sin((x + eps)) - sin(x);
end

Wolfram

code[x_, eps_] := N[(N[Sin[N[(x + eps), $MachinePrecision]], $MachinePrecision] - N[Sin[x], $MachinePrecision]), $MachinePrecision]

Initial Program: 41.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sin \left(x + \varepsilon\right) - \sin x \end{array} \]

FPCore

(FPCore (x eps) :precision binary64 (- (sin (+ x eps)) (sin x)))

C

double code(double x, double eps) {
	return sin((x + eps)) - sin(x);
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    code = sin((x + eps)) - sin(x)
end function

Java

public static double code(double x, double eps) {
	return Math.sin((x + eps)) - Math.sin(x);
}

Python

def code(x, eps):
	return math.sin((x + eps)) - math.sin(x)

Julia

function code(x, eps)
	return Float64(sin(Float64(x + eps)) - sin(x))
end

MATLAB

function tmp = code(x, eps)
	tmp = sin((x + eps)) - sin(x);
end

Wolfram

code[x_, eps_] := N[(N[Sin[N[(x + eps), $MachinePrecision]], $MachinePrecision] - N[Sin[x], $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\cos x, \sin \varepsilon, \sin x \cdot \left(\cos \varepsilon + -1\right)\right) \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (fma (cos x) (sin eps) (* (sin x) (+ (cos eps) -1.0))))

C

double code(double x, double eps) {
	return fma(cos(x), sin(eps), (sin(x) * (cos(eps) + -1.0)));
}

Julia

function code(x, eps)
	return fma(cos(x), sin(eps), Float64(sin(x) * Float64(cos(eps) + -1.0)))
end

Wolfram

code[x_, eps_] := N[(N[Cos[x], $MachinePrecision] * N[Sin[eps], $MachinePrecision] + N[(N[Sin[x], $MachinePrecision] * N[(N[Cos[eps], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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Alternative 2: 77.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(x + \varepsilon\right) - \sin x\\ \mathbf{if}\;t_0 \leq -0.04 \lor \neg \left(t_0 \leq 5 \cdot 10^{-36}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\cos x \cdot \left(2 \cdot \sin \left(\varepsilon \cdot 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (let* ((t_0 (- (sin (+ x eps)) (sin x))))
   (if (or (<= t_0 -0.04) (not (<= t_0 5e-36)))
     t_0
     (* (cos x) (* 2.0 (sin (* eps 0.5)))))))

C

double code(double x, double eps) {
	double t_0 = sin((x + eps)) - sin(x);
	double tmp;
	if ((t_0 <= -0.04) || !(t_0 <= 5e-36)) {
		tmp = t_0;
	} else {
		tmp = cos(x) * (2.0 * sin((eps * 0.5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sin((x + eps)) - sin(x)
    if ((t_0 <= (-0.04d0)) .or. (.not. (t_0 <= 5d-36))) then
        tmp = t_0
    else
        tmp = cos(x) * (2.0d0 * sin((eps * 0.5d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double eps) {
	double t_0 = Math.sin((x + eps)) - Math.sin(x);
	double tmp;
	if ((t_0 <= -0.04) || !(t_0 <= 5e-36)) {
		tmp = t_0;
	} else {
		tmp = Math.cos(x) * (2.0 * Math.sin((eps * 0.5)));
	}
	return tmp;
}

Python

def code(x, eps):
	t_0 = math.sin((x + eps)) - math.sin(x)
	tmp = 0
	if (t_0 <= -0.04) or not (t_0 <= 5e-36):
		tmp = t_0
	else:
		tmp = math.cos(x) * (2.0 * math.sin((eps * 0.5)))
	return tmp

Julia

function code(x, eps)
	t_0 = Float64(sin(Float64(x + eps)) - sin(x))
	tmp = 0.0
	if ((t_0 <= -0.04) || !(t_0 <= 5e-36))
		tmp = t_0;
	else
		tmp = Float64(cos(x) * Float64(2.0 * sin(Float64(eps * 0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, eps)
	t_0 = sin((x + eps)) - sin(x);
	tmp = 0.0;
	if ((t_0 <= -0.04) || ~((t_0 <= 5e-36)))
		tmp = t_0;
	else
		tmp = cos(x) * (2.0 * sin((eps * 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, eps_] := Block[{t$95$0 = N[(N[Sin[N[(x + eps), $MachinePrecision]], $MachinePrecision] - N[Sin[x], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -0.04], N[Not[LessEqual[t$95$0, 5e-36]], $MachinePrecision]], t$95$0, N[(N[Cos[x], $MachinePrecision] * N[(2.0 * N[Sin[N[(eps * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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Alternative 3: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \cos x \cdot \sin \varepsilon - \sin x \cdot \left(1 - \cos \varepsilon\right) \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (- (* (cos x) (sin eps)) (* (sin x) (- 1.0 (cos eps)))))

C

double code(double x, double eps) {
	return (cos(x) * sin(eps)) - (sin(x) * (1.0 - cos(eps)));
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    code = (cos(x) * sin(eps)) - (sin(x) * (1.0d0 - cos(eps)))
end function

Java

public static double code(double x, double eps) {
	return (Math.cos(x) * Math.sin(eps)) - (Math.sin(x) * (1.0 - Math.cos(eps)));
}

Python

def code(x, eps):
	return (math.cos(x) * math.sin(eps)) - (math.sin(x) * (1.0 - math.cos(eps)))

Julia

function code(x, eps)
	return Float64(Float64(cos(x) * sin(eps)) - Float64(sin(x) * Float64(1.0 - cos(eps))))
end

MATLAB

function tmp = code(x, eps)
	tmp = (cos(x) * sin(eps)) - (sin(x) * (1.0 - cos(eps)));
end

Wolfram

code[x_, eps_] := N[(N[(N[Cos[x], $MachinePrecision] * N[Sin[eps], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] * N[(1.0 - N[Cos[eps], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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Alternative 4: 78.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\varepsilon \leq -0.0016 \lor \neg \left(\varepsilon \leq 0.0002\right):\\ \;\;\;\;\sin \varepsilon - \sin x \cdot \left(1 - \cos \varepsilon\right)\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(\sin x \cdot {\varepsilon}^{2}\right) + \cos x \cdot \varepsilon\\ \end{array} \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (if (or (<= eps -0.0016) (not (<= eps 0.0002)))
   (- (sin eps) (* (sin x) (- 1.0 (cos eps))))
   (+ (* -0.5 (* (sin x) (pow eps 2.0))) (* (cos x) eps))))

C

double code(double x, double eps) {
	double tmp;
	if ((eps <= -0.0016) || !(eps <= 0.0002)) {
		tmp = sin(eps) - (sin(x) * (1.0 - cos(eps)));
	} else {
		tmp = (-0.5 * (sin(x) * pow(eps, 2.0))) + (cos(x) * eps);
	}
	return tmp;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    real(8) :: tmp
    if ((eps <= (-0.0016d0)) .or. (.not. (eps <= 0.0002d0))) then
        tmp = sin(eps) - (sin(x) * (1.0d0 - cos(eps)))
    else
        tmp = ((-0.5d0) * (sin(x) * (eps ** 2.0d0))) + (cos(x) * eps)
    end if
    code = tmp
end function

Java

public static double code(double x, double eps) {
	double tmp;
	if ((eps <= -0.0016) || !(eps <= 0.0002)) {
		tmp = Math.sin(eps) - (Math.sin(x) * (1.0 - Math.cos(eps)));
	} else {
		tmp = (-0.5 * (Math.sin(x) * Math.pow(eps, 2.0))) + (Math.cos(x) * eps);
	}
	return tmp;
}

Python

def code(x, eps):
	tmp = 0
	if (eps <= -0.0016) or not (eps <= 0.0002):
		tmp = math.sin(eps) - (math.sin(x) * (1.0 - math.cos(eps)))
	else:
		tmp = (-0.5 * (math.sin(x) * math.pow(eps, 2.0))) + (math.cos(x) * eps)
	return tmp

Julia

function code(x, eps)
	tmp = 0.0
	if ((eps <= -0.0016) || !(eps <= 0.0002))
		tmp = Float64(sin(eps) - Float64(sin(x) * Float64(1.0 - cos(eps))));
	else
		tmp = Float64(Float64(-0.5 * Float64(sin(x) * (eps ^ 2.0))) + Float64(cos(x) * eps));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, eps)
	tmp = 0.0;
	if ((eps <= -0.0016) || ~((eps <= 0.0002)))
		tmp = sin(eps) - (sin(x) * (1.0 - cos(eps)));
	else
		tmp = (-0.5 * (sin(x) * (eps ^ 2.0))) + (cos(x) * eps);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, eps_] := If[Or[LessEqual[eps, -0.0016], N[Not[LessEqual[eps, 0.0002]], $MachinePrecision]], N[(N[Sin[eps], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] * N[(1.0 - N[Cos[eps], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-0.5 * N[(N[Sin[x], $MachinePrecision] * N[Power[eps, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[x], $MachinePrecision] * eps), $MachinePrecision]), $MachinePrecision]]

Derivation

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Alternative 5: 78.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin x \cdot \left(1 - \cos \varepsilon\right)\\ \mathbf{if}\;\varepsilon \leq -0.0014 \lor \neg \left(\varepsilon \leq 0.0001\right):\\ \;\;\;\;\sin \varepsilon - t_0\\ \mathbf{else}:\\ \;\;\;\;\cos x \cdot \varepsilon - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (let* ((t_0 (* (sin x) (- 1.0 (cos eps)))))
   (if (or (<= eps -0.0014) (not (<= eps 0.0001)))
     (- (sin eps) t_0)
     (- (* (cos x) eps) t_0))))

C

double code(double x, double eps) {
	double t_0 = sin(x) * (1.0 - cos(eps));
	double tmp;
	if ((eps <= -0.0014) || !(eps <= 0.0001)) {
		tmp = sin(eps) - t_0;
	} else {
		tmp = (cos(x) * eps) - t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sin(x) * (1.0d0 - cos(eps))
    if ((eps <= (-0.0014d0)) .or. (.not. (eps <= 0.0001d0))) then
        tmp = sin(eps) - t_0
    else
        tmp = (cos(x) * eps) - t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double eps) {
	double t_0 = Math.sin(x) * (1.0 - Math.cos(eps));
	double tmp;
	if ((eps <= -0.0014) || !(eps <= 0.0001)) {
		tmp = Math.sin(eps) - t_0;
	} else {
		tmp = (Math.cos(x) * eps) - t_0;
	}
	return tmp;
}

Python

def code(x, eps):
	t_0 = math.sin(x) * (1.0 - math.cos(eps))
	tmp = 0
	if (eps <= -0.0014) or not (eps <= 0.0001):
		tmp = math.sin(eps) - t_0
	else:
		tmp = (math.cos(x) * eps) - t_0
	return tmp

Julia

function code(x, eps)
	t_0 = Float64(sin(x) * Float64(1.0 - cos(eps)))
	tmp = 0.0
	if ((eps <= -0.0014) || !(eps <= 0.0001))
		tmp = Float64(sin(eps) - t_0);
	else
		tmp = Float64(Float64(cos(x) * eps) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, eps)
	t_0 = sin(x) * (1.0 - cos(eps));
	tmp = 0.0;
	if ((eps <= -0.0014) || ~((eps <= 0.0001)))
		tmp = sin(eps) - t_0;
	else
		tmp = (cos(x) * eps) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, eps_] := Block[{t$95$0 = N[(N[Sin[x], $MachinePrecision] * N[(1.0 - N[Cos[eps], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[eps, -0.0014], N[Not[LessEqual[eps, 0.0001]], $MachinePrecision]], N[(N[Sin[eps], $MachinePrecision] - t$95$0), $MachinePrecision], N[(N[(N[Cos[x], $MachinePrecision] * eps), $MachinePrecision] - t$95$0), $MachinePrecision]]]

Derivation

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Alternative 6: 78.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\varepsilon \leq -0.0015 \lor \neg \left(\varepsilon \leq 3.5 \cdot 10^{-6}\right):\\ \;\;\;\;\sin \varepsilon - \sin x \cdot \left(1 - \cos \varepsilon\right)\\ \mathbf{else}:\\ \;\;\;\;\cos x \cdot \varepsilon\\ \end{array} \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (if (or (<= eps -0.0015) (not (<= eps 3.5e-6)))
   (- (sin eps) (* (sin x) (- 1.0 (cos eps))))
   (* (cos x) eps)))

C

double code(double x, double eps) {
	double tmp;
	if ((eps <= -0.0015) || !(eps <= 3.5e-6)) {
		tmp = sin(eps) - (sin(x) * (1.0 - cos(eps)));
	} else {
		tmp = cos(x) * eps;
	}
	return tmp;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    real(8) :: tmp
    if ((eps <= (-0.0015d0)) .or. (.not. (eps <= 3.5d-6))) then
        tmp = sin(eps) - (sin(x) * (1.0d0 - cos(eps)))
    else
        tmp = cos(x) * eps
    end if
    code = tmp
end function

Java

public static double code(double x, double eps) {
	double tmp;
	if ((eps <= -0.0015) || !(eps <= 3.5e-6)) {
		tmp = Math.sin(eps) - (Math.sin(x) * (1.0 - Math.cos(eps)));
	} else {
		tmp = Math.cos(x) * eps;
	}
	return tmp;
}

Python

def code(x, eps):
	tmp = 0
	if (eps <= -0.0015) or not (eps <= 3.5e-6):
		tmp = math.sin(eps) - (math.sin(x) * (1.0 - math.cos(eps)))
	else:
		tmp = math.cos(x) * eps
	return tmp

Julia

function code(x, eps)
	tmp = 0.0
	if ((eps <= -0.0015) || !(eps <= 3.5e-6))
		tmp = Float64(sin(eps) - Float64(sin(x) * Float64(1.0 - cos(eps))));
	else
		tmp = Float64(cos(x) * eps);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, eps)
	tmp = 0.0;
	if ((eps <= -0.0015) || ~((eps <= 3.5e-6)))
		tmp = sin(eps) - (sin(x) * (1.0 - cos(eps)));
	else
		tmp = cos(x) * eps;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, eps_] := If[Or[LessEqual[eps, -0.0015], N[Not[LessEqual[eps, 3.5e-6]], $MachinePrecision]], N[(N[Sin[eps], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] * N[(1.0 - N[Cos[eps], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[x], $MachinePrecision] * eps), $MachinePrecision]]

Derivation

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Alternative 7: 77.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \cos \left(0.5 \cdot \mathsf{fma}\left(2, x, \varepsilon\right)\right) \cdot \left(2 \cdot \sin \left(\varepsilon \cdot 0.5\right)\right) \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (* (cos (* 0.5 (fma 2.0 x eps))) (* 2.0 (sin (* eps 0.5)))))

C

double code(double x, double eps) {
	return cos((0.5 * fma(2.0, x, eps))) * (2.0 * sin((eps * 0.5)));
}

Julia

function code(x, eps)
	return Float64(cos(Float64(0.5 * fma(2.0, x, eps))) * Float64(2.0 * sin(Float64(eps * 0.5))))
end

Wolfram

code[x_, eps_] := N[(N[Cos[N[(0.5 * N[(2.0 * x + eps), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(2.0 * N[Sin[N[(eps * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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Alternative 8: 76.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\varepsilon \leq -0.02 \lor \neg \left(\varepsilon \leq 1950000\right):\\ \;\;\;\;\sin \varepsilon\\ \mathbf{else}:\\ \;\;\;\;\cos x \cdot \varepsilon\\ \end{array} \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (if (or (<= eps -0.02) (not (<= eps 1950000.0))) (sin eps) (* (cos x) eps)))

C

double code(double x, double eps) {
	double tmp;
	if ((eps <= -0.02) || !(eps <= 1950000.0)) {
		tmp = sin(eps);
	} else {
		tmp = cos(x) * eps;
	}
	return tmp;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    real(8) :: tmp
    if ((eps <= (-0.02d0)) .or. (.not. (eps <= 1950000.0d0))) then
        tmp = sin(eps)
    else
        tmp = cos(x) * eps
    end if
    code = tmp
end function

Java

public static double code(double x, double eps) {
	double tmp;
	if ((eps <= -0.02) || !(eps <= 1950000.0)) {
		tmp = Math.sin(eps);
	} else {
		tmp = Math.cos(x) * eps;
	}
	return tmp;
}

Python

def code(x, eps):
	tmp = 0
	if (eps <= -0.02) or not (eps <= 1950000.0):
		tmp = math.sin(eps)
	else:
		tmp = math.cos(x) * eps
	return tmp

Julia

function code(x, eps)
	tmp = 0.0
	if ((eps <= -0.02) || !(eps <= 1950000.0))
		tmp = sin(eps);
	else
		tmp = Float64(cos(x) * eps);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, eps)
	tmp = 0.0;
	if ((eps <= -0.02) || ~((eps <= 1950000.0)))
		tmp = sin(eps);
	else
		tmp = cos(x) * eps;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, eps_] := If[Or[LessEqual[eps, -0.02], N[Not[LessEqual[eps, 1950000.0]], $MachinePrecision]], N[Sin[eps], $MachinePrecision], N[(N[Cos[x], $MachinePrecision] * eps), $MachinePrecision]]

Derivation

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Alternative 9: 55.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \sin \varepsilon \end{array} \]

FPCore

(FPCore (x eps) :precision binary64 (sin eps))

C

double code(double x, double eps) {
	return sin(eps);
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    code = sin(eps)
end function

Java

public static double code(double x, double eps) {
	return Math.sin(eps);
}

Python

def code(x, eps):
	return math.sin(eps)

Julia

function code(x, eps)
	return sin(eps)
end

MATLAB

function tmp = code(x, eps)
	tmp = sin(eps);
end

Wolfram

code[x_, eps_] := N[Sin[eps], $MachinePrecision]

Derivation

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Alternative 10: 29.6% accurate, 205.0× speedup

Math

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

FPCore

(FPCore (x eps) :precision binary64 eps)

C

double code(double x, double eps) {
	return eps;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    code = eps
end function

Java

public static double code(double x, double eps) {
	return eps;
}

Python

def code(x, eps):
	return eps

Julia

function code(x, eps)
	return eps
end

MATLAB

function tmp = code(x, eps)
	tmp = eps;
end

Wolfram

code[x_, eps_] := eps

Derivation

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

Developer target: 99.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\sin x, \cos \varepsilon - 1, \sin \varepsilon \cdot \cos x\right) \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (fma (sin x) (- (cos eps) 1.0) (* (sin eps) (cos x))))

C

double code(double x, double eps) {
	return fma(sin(x), (cos(eps) - 1.0), (sin(eps) * cos(x)));
}

Julia

function code(x, eps)
	return fma(sin(x), Float64(cos(eps) - 1.0), Float64(sin(eps) * cos(x)))
end

Wolfram

code[x_, eps_] := N[(N[Sin[x], $MachinePrecision] * N[(N[Cos[eps], $MachinePrecision] - 1.0), $MachinePrecision] + N[(N[Sin[eps], $MachinePrecision] * N[Cos[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024003 
(FPCore (x eps)
  :name "2sin (example 3.3)"
  :precision binary64

  :herbie-target
  (fma (sin x) (- (cos eps) 1.0) (* (sin eps) (cos x)))

  (- (sin (+ x eps)) (sin x)))