Hyperbolic sine

Percentage Accurate: 53.4% → 100.0%

Time: 4.9s

Alternatives: 7

Speedup: 1.9×

• 48.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{e^{x} - e^{-x}}{2} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ (- (exp x) (exp (- x))) 2.0))

C

double code(double x) {
	return (exp(x) - exp(-x)) / 2.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (exp(x) - exp(-x)) / 2.0d0
end function

Java

public static double code(double x) {
	return (Math.exp(x) - Math.exp(-x)) / 2.0;
}

Python

def code(x):
	return (math.exp(x) - math.exp(-x)) / 2.0

Julia

function code(x)
	return Float64(Float64(exp(x) - exp(Float64(-x))) / 2.0)
end

MATLAB

function tmp = code(x)
	tmp = (exp(x) - exp(-x)) / 2.0;
end

Wolfram

code[x_] := N[(N[(N[Exp[x], $MachinePrecision] - N[Exp[(-x)], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]

Initial Program: 53.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{e^{x} - e^{-x}}{2} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ (- (exp x) (exp (- x))) 2.0))

C

double code(double x) {
	return (exp(x) - exp(-x)) / 2.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (exp(x) - exp(-x)) / 2.0d0
end function

Java

public static double code(double x) {
	return (Math.exp(x) - Math.exp(-x)) / 2.0;
}

Python

def code(x):
	return (math.exp(x) - math.exp(-x)) / 2.0

Julia

function code(x)
	return Float64(Float64(exp(x) - exp(Float64(-x))) / 2.0)
end

MATLAB

function tmp = code(x)
	tmp = (exp(x) - exp(-x)) / 2.0;
end

Wolfram

code[x_] := N[(N[(N[Exp[x], $MachinePrecision] - N[Exp[(-x)], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := e^{x\_m} - e^{-x\_m}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_0 \leq 0.1:\\ \;\;\;\;x\_m + \left(0.0001984126984126984 \cdot {x\_m}^{7} + \left(0.008333333333333333 \cdot {x\_m}^{5} + 0.16666666666666666 \cdot {x\_m}^{3}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_0}{2}\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m)
 :precision binary64
 (let* ((t_0 (- (exp x_m) (exp (- x_m)))))
   (*
    x_s
    (if (<= t_0 0.1)
      (+
       x_m
       (+
        (* 0.0001984126984126984 (pow x_m 7.0))
        (+
         (* 0.008333333333333333 (pow x_m 5.0))
         (* 0.16666666666666666 (pow x_m 3.0)))))
      (/ t_0 2.0)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	double t_0 = exp(x_m) - exp(-x_m);
	double tmp;
	if (t_0 <= 0.1) {
		tmp = x_m + ((0.0001984126984126984 * pow(x_m, 7.0)) + ((0.008333333333333333 * pow(x_m, 5.0)) + (0.16666666666666666 * pow(x_m, 3.0))));
	} else {
		tmp = t_0 / 2.0;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8) :: t_0
    real(8) :: tmp
    t_0 = exp(x_m) - exp(-x_m)
    if (t_0 <= 0.1d0) then
        tmp = x_m + ((0.0001984126984126984d0 * (x_m ** 7.0d0)) + ((0.008333333333333333d0 * (x_m ** 5.0d0)) + (0.16666666666666666d0 * (x_m ** 3.0d0))))
    else
        tmp = t_0 / 2.0d0
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m) {
	double t_0 = Math.exp(x_m) - Math.exp(-x_m);
	double tmp;
	if (t_0 <= 0.1) {
		tmp = x_m + ((0.0001984126984126984 * Math.pow(x_m, 7.0)) + ((0.008333333333333333 * Math.pow(x_m, 5.0)) + (0.16666666666666666 * Math.pow(x_m, 3.0))));
	} else {
		tmp = t_0 / 2.0;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m):
	t_0 = math.exp(x_m) - math.exp(-x_m)
	tmp = 0
	if t_0 <= 0.1:
		tmp = x_m + ((0.0001984126984126984 * math.pow(x_m, 7.0)) + ((0.008333333333333333 * math.pow(x_m, 5.0)) + (0.16666666666666666 * math.pow(x_m, 3.0))))
	else:
		tmp = t_0 / 2.0
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m)
	t_0 = Float64(exp(x_m) - exp(Float64(-x_m)))
	tmp = 0.0
	if (t_0 <= 0.1)
		tmp = Float64(x_m + Float64(Float64(0.0001984126984126984 * (x_m ^ 7.0)) + Float64(Float64(0.008333333333333333 * (x_m ^ 5.0)) + Float64(0.16666666666666666 * (x_m ^ 3.0)))));
	else
		tmp = Float64(t_0 / 2.0);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m)
	t_0 = exp(x_m) - exp(-x_m);
	tmp = 0.0;
	if (t_0 <= 0.1)
		tmp = x_m + ((0.0001984126984126984 * (x_m ^ 7.0)) + ((0.008333333333333333 * (x_m ^ 5.0)) + (0.16666666666666666 * (x_m ^ 3.0))));
	else
		tmp = t_0 / 2.0;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_] := Block[{t$95$0 = N[(N[Exp[x$95$m], $MachinePrecision] - N[Exp[(-x$95$m)], $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$0, 0.1], N[(x$95$m + N[(N[(0.0001984126984126984 * N[Power[x$95$m, 7.0], $MachinePrecision]), $MachinePrecision] + N[(N[(0.008333333333333333 * N[Power[x$95$m, 5.0], $MachinePrecision]), $MachinePrecision] + N[(0.16666666666666666 * N[Power[x$95$m, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 / 2.0), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) < 0.10000000000000001

   1. Initial program 41.3%

      \[\frac{e^{x} - e^{-x}}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 92.2%

      \[\leadsto \frac{\color{blue}{0.0003968253968253968 \cdot {x}^{7} + \left(0.016666666666666666 \cdot {x}^{5} + \left(0.3333333333333333 \cdot {x}^{3} + 2 \cdot x\right)\right)}}{2} \]

   4. Taylor expanded in x around 0 92.2%

      \[\leadsto \color{blue}{x + \left(0.0001984126984126984 \cdot {x}^{7} + \left(0.008333333333333333 \cdot {x}^{5} + 0.16666666666666666 \cdot {x}^{3}\right)\right)} \]

   if 0.10000000000000001 < (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

   1. Initial program 100.0%

      \[\frac{e^{x} - e^{-x}}{2} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{x} - e^{-x} \leq 0.1:\\ \;\;\;\;x + \left(0.0001984126984126984 \cdot {x}^{7} + \left(0.008333333333333333 \cdot {x}^{5} + 0.16666666666666666 \cdot {x}^{3}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{x} - e^{-x}}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := e^{x\_m} - e^{-x\_m}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_0 \leq 5 \cdot 10^{-7}:\\ \;\;\;\;x\_m + 0.16666666666666666 \cdot {x\_m}^{3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_0}{2}\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m)
 :precision binary64
 (let* ((t_0 (- (exp x_m) (exp (- x_m)))))
   (*
    x_s
    (if (<= t_0 5e-7)
      (+ x_m (* 0.16666666666666666 (pow x_m 3.0)))
      (/ t_0 2.0)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	double t_0 = exp(x_m) - exp(-x_m);
	double tmp;
	if (t_0 <= 5e-7) {
		tmp = x_m + (0.16666666666666666 * pow(x_m, 3.0));
	} else {
		tmp = t_0 / 2.0;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8) :: t_0
    real(8) :: tmp
    t_0 = exp(x_m) - exp(-x_m)
    if (t_0 <= 5d-7) then
        tmp = x_m + (0.16666666666666666d0 * (x_m ** 3.0d0))
    else
        tmp = t_0 / 2.0d0
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m) {
	double t_0 = Math.exp(x_m) - Math.exp(-x_m);
	double tmp;
	if (t_0 <= 5e-7) {
		tmp = x_m + (0.16666666666666666 * Math.pow(x_m, 3.0));
	} else {
		tmp = t_0 / 2.0;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m):
	t_0 = math.exp(x_m) - math.exp(-x_m)
	tmp = 0
	if t_0 <= 5e-7:
		tmp = x_m + (0.16666666666666666 * math.pow(x_m, 3.0))
	else:
		tmp = t_0 / 2.0
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m)
	t_0 = Float64(exp(x_m) - exp(Float64(-x_m)))
	tmp = 0.0
	if (t_0 <= 5e-7)
		tmp = Float64(x_m + Float64(0.16666666666666666 * (x_m ^ 3.0)));
	else
		tmp = Float64(t_0 / 2.0);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m)
	t_0 = exp(x_m) - exp(-x_m);
	tmp = 0.0;
	if (t_0 <= 5e-7)
		tmp = x_m + (0.16666666666666666 * (x_m ^ 3.0));
	else
		tmp = t_0 / 2.0;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_] := Block[{t$95$0 = N[(N[Exp[x$95$m], $MachinePrecision] - N[Exp[(-x$95$m)], $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$0, 5e-7], N[(x$95$m + N[(0.16666666666666666 * N[Power[x$95$m, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 / 2.0), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) < 4.99999999999999977e-7

   1. Initial program 41.0%

      \[\frac{e^{x} - e^{-x}}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 92.1%

      \[\leadsto \frac{\color{blue}{0.0003968253968253968 \cdot {x}^{7} + \left(0.016666666666666666 \cdot {x}^{5} + \left(0.3333333333333333 \cdot {x}^{3} + 2 \cdot x\right)\right)}}{2} \]

   4. Taylor expanded in x around 0 85.9%

      \[\leadsto \color{blue}{x + 0.16666666666666666 \cdot {x}^{3}} \]

   if 4.99999999999999977e-7 < (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

   1. Initial program 99.9%

      \[\frac{e^{x} - e^{-x}}{2} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{x} - e^{-x} \leq 5 \cdot 10^{-7}:\\ \;\;\;\;x + 0.16666666666666666 \cdot {x}^{3}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{x} - e^{-x}}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 5.6:\\ \;\;\;\;x\_m + 0.16666666666666666 \cdot {x\_m}^{3}\\ \mathbf{else}:\\ \;\;\;\;{\left({x\_m}^{42} \cdot 6.101221350130783 \cdot 10^{-23}\right)}^{0.16666666666666666}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m)
 :precision binary64
 (*
  x_s
  (if (<= x_m 5.6)
    (+ x_m (* 0.16666666666666666 (pow x_m 3.0)))
    (pow (* (pow x_m 42.0) 6.101221350130783e-23) 0.16666666666666666))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	double tmp;
	if (x_m <= 5.6) {
		tmp = x_m + (0.16666666666666666 * pow(x_m, 3.0));
	} else {
		tmp = pow((pow(x_m, 42.0) * 6.101221350130783e-23), 0.16666666666666666);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8) :: tmp
    if (x_m <= 5.6d0) then
        tmp = x_m + (0.16666666666666666d0 * (x_m ** 3.0d0))
    else
        tmp = ((x_m ** 42.0d0) * 6.101221350130783d-23) ** 0.16666666666666666d0
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m) {
	double tmp;
	if (x_m <= 5.6) {
		tmp = x_m + (0.16666666666666666 * Math.pow(x_m, 3.0));
	} else {
		tmp = Math.pow((Math.pow(x_m, 42.0) * 6.101221350130783e-23), 0.16666666666666666);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m):
	tmp = 0
	if x_m <= 5.6:
		tmp = x_m + (0.16666666666666666 * math.pow(x_m, 3.0))
	else:
		tmp = math.pow((math.pow(x_m, 42.0) * 6.101221350130783e-23), 0.16666666666666666)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m)
	tmp = 0.0
	if (x_m <= 5.6)
		tmp = Float64(x_m + Float64(0.16666666666666666 * (x_m ^ 3.0)));
	else
		tmp = Float64((x_m ^ 42.0) * 6.101221350130783e-23) ^ 0.16666666666666666;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m)
	tmp = 0.0;
	if (x_m <= 5.6)
		tmp = x_m + (0.16666666666666666 * (x_m ^ 3.0));
	else
		tmp = ((x_m ^ 42.0) * 6.101221350130783e-23) ^ 0.16666666666666666;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_] := N[(x$95$s * If[LessEqual[x$95$m, 5.6], N[(x$95$m + N[(0.16666666666666666 * N[Power[x$95$m, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[(N[Power[x$95$m, 42.0], $MachinePrecision] * 6.101221350130783e-23), $MachinePrecision], 0.16666666666666666], $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 5.5999999999999996

   1. Initial program 41.6%

      \[\frac{e^{x} - e^{-x}}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 92.0%

      \[\leadsto \frac{\color{blue}{0.0003968253968253968 \cdot {x}^{7} + \left(0.016666666666666666 \cdot {x}^{5} + \left(0.3333333333333333 \cdot {x}^{3} + 2 \cdot x\right)\right)}}{2} \]

   4. Taylor expanded in x around 0 85.4%

      \[\leadsto \color{blue}{x + 0.16666666666666666 \cdot {x}^{3}} \]

   if 5.5999999999999996 < x

   1. Initial program 100.0%

      \[\frac{e^{x} - e^{-x}}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.0%

      \[\leadsto \frac{\color{blue}{0.0003968253968253968 \cdot {x}^{7} + \left(0.016666666666666666 \cdot {x}^{5} + \left(0.3333333333333333 \cdot {x}^{3} + 2 \cdot x\right)\right)}}{2} \]

   4. Taylor expanded in x around inf 88.0%

      \[\leadsto \color{blue}{0.0001984126984126984 \cdot {x}^{7}} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 88.0%

         \[\leadsto \color{blue}{\sqrt{0.0001984126984126984 \cdot {x}^{7}} \cdot \sqrt{0.0001984126984126984 \cdot {x}^{7}}} \]

      2. sqrt-unprod 93.9%

         \[\leadsto \color{blue}{\sqrt{\left(0.0001984126984126984 \cdot {x}^{7}\right) \cdot \left(0.0001984126984126984 \cdot {x}^{7}\right)}} \]

      3. *-commutative 93.9%

         \[\leadsto \sqrt{\color{blue}{\left({x}^{7} \cdot 0.0001984126984126984\right)} \cdot \left(0.0001984126984126984 \cdot {x}^{7}\right)} \]

      4. *-commutative 93.9%

         \[\leadsto \sqrt{\left({x}^{7} \cdot 0.0001984126984126984\right) \cdot \color{blue}{\left({x}^{7} \cdot 0.0001984126984126984\right)}} \]

      5. swap-sqr 93.9%

         \[\leadsto \sqrt{\color{blue}{\left({x}^{7} \cdot {x}^{7}\right) \cdot \left(0.0001984126984126984 \cdot 0.0001984126984126984\right)}} \]

      6. pow-prod-up 93.9%

         \[\leadsto \sqrt{\color{blue}{{x}^{\left(7 + 7\right)}} \cdot \left(0.0001984126984126984 \cdot 0.0001984126984126984\right)} \]

      7. metadata-eval 93.9%

         \[\leadsto \sqrt{{x}^{\color{blue}{14}} \cdot \left(0.0001984126984126984 \cdot 0.0001984126984126984\right)} \]

      8. metadata-eval 93.9%

         \[\leadsto \sqrt{{x}^{14} \cdot \color{blue}{3.936759889140842 \cdot 10^{-8}}} \]

   6. Applied egg-rr 93.9%

      \[\leadsto \color{blue}{\sqrt{{x}^{14} \cdot 3.936759889140842 \cdot 10^{-8}}} \]
   7. Step-by-step derivation

      1. add-cbrt-cube 100.0%

         \[\leadsto \sqrt{\color{blue}{\sqrt[3]{\left(\left({x}^{14} \cdot 3.936759889140842 \cdot 10^{-8}\right) \cdot \left({x}^{14} \cdot 3.936759889140842 \cdot 10^{-8}\right)\right) \cdot \left({x}^{14} \cdot 3.936759889140842 \cdot 10^{-8}\right)}}} \]

      2. pow1/3 100.0%

         \[\leadsto \sqrt{\color{blue}{{\left(\left(\left({x}^{14} \cdot 3.936759889140842 \cdot 10^{-8}\right) \cdot \left({x}^{14} \cdot 3.936759889140842 \cdot 10^{-8}\right)\right) \cdot \left({x}^{14} \cdot 3.936759889140842 \cdot 10^{-8}\right)\right)}^{0.3333333333333333}}} \]

      3. sqrt-pow1 100.0%

         \[\leadsto \color{blue}{{\left(\left(\left({x}^{14} \cdot 3.936759889140842 \cdot 10^{-8}\right) \cdot \left({x}^{14} \cdot 3.936759889140842 \cdot 10^{-8}\right)\right) \cdot \left({x}^{14} \cdot 3.936759889140842 \cdot 10^{-8}\right)\right)}^{\left(\frac{0.3333333333333333}{2}\right)}} \]

      4. pow3 100.0%

         \[\leadsto {\color{blue}{\left({\left({x}^{14} \cdot 3.936759889140842 \cdot 10^{-8}\right)}^{3}\right)}}^{\left(\frac{0.3333333333333333}{2}\right)} \]

      5. unpow-prod-down 100.0%

         \[\leadsto {\color{blue}{\left({\left({x}^{14}\right)}^{3} \cdot {\left( 3.936759889140842 \cdot 10^{-8} \right)}^{3}\right)}}^{\left(\frac{0.3333333333333333}{2}\right)} \]

      6. pow-pow 100.0%

         \[\leadsto {\left(\color{blue}{{x}^{\left(14 \cdot 3\right)}} \cdot {\left( 3.936759889140842 \cdot 10^{-8} \right)}^{3}\right)}^{\left(\frac{0.3333333333333333}{2}\right)} \]

      7. metadata-eval 100.0%

         \[\leadsto {\left({x}^{\color{blue}{42}} \cdot {\left( 3.936759889140842 \cdot 10^{-8} \right)}^{3}\right)}^{\left(\frac{0.3333333333333333}{2}\right)} \]

      8. metadata-eval 100.0%

         \[\leadsto {\left({x}^{42} \cdot \color{blue}{6.101221350130783 \cdot 10^{-23}}\right)}^{\left(\frac{0.3333333333333333}{2}\right)} \]

      9. metadata-eval 100.0%

         \[\leadsto {\left({x}^{42} \cdot 6.101221350130783 \cdot 10^{-23}\right)}^{\color{blue}{0.16666666666666666}} \]

   8. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{{\left({x}^{42} \cdot 6.101221350130783 \cdot 10^{-23}\right)}^{0.16666666666666666}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.6:\\ \;\;\;\;x + 0.16666666666666666 \cdot {x}^{3}\\ \mathbf{else}:\\ \;\;\;\;{\left({x}^{42} \cdot 6.101221350130783 \cdot 10^{-23}\right)}^{0.16666666666666666}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 5.6:\\ \;\;\;\;x\_m + 0.16666666666666666 \cdot {x\_m}^{3}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{x\_m}^{21} \cdot 7.811031526073099 \cdot 10^{-12}}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m)
 :precision binary64
 (*
  x_s
  (if (<= x_m 5.6)
    (+ x_m (* 0.16666666666666666 (pow x_m 3.0)))
    (cbrt (* (pow x_m 21.0) 7.811031526073099e-12)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	double tmp;
	if (x_m <= 5.6) {
		tmp = x_m + (0.16666666666666666 * pow(x_m, 3.0));
	} else {
		tmp = cbrt((pow(x_m, 21.0) * 7.811031526073099e-12));
	}
	return x_s * tmp;
}

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m) {
	double tmp;
	if (x_m <= 5.6) {
		tmp = x_m + (0.16666666666666666 * Math.pow(x_m, 3.0));
	} else {
		tmp = Math.cbrt((Math.pow(x_m, 21.0) * 7.811031526073099e-12));
	}
	return x_s * tmp;
}

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m)
	tmp = 0.0
	if (x_m <= 5.6)
		tmp = Float64(x_m + Float64(0.16666666666666666 * (x_m ^ 3.0)));
	else
		tmp = cbrt(Float64((x_m ^ 21.0) * 7.811031526073099e-12));
	end
	return Float64(x_s * tmp)
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_] := N[(x$95$s * If[LessEqual[x$95$m, 5.6], N[(x$95$m + N[(0.16666666666666666 * N[Power[x$95$m, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[(N[Power[x$95$m, 21.0], $MachinePrecision] * 7.811031526073099e-12), $MachinePrecision], 1/3], $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 5.5999999999999996

   1. Initial program 41.6%

      \[\frac{e^{x} - e^{-x}}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 92.0%

      \[\leadsto \frac{\color{blue}{0.0003968253968253968 \cdot {x}^{7} + \left(0.016666666666666666 \cdot {x}^{5} + \left(0.3333333333333333 \cdot {x}^{3} + 2 \cdot x\right)\right)}}{2} \]

   4. Taylor expanded in x around 0 85.4%

      \[\leadsto \color{blue}{x + 0.16666666666666666 \cdot {x}^{3}} \]

   if 5.5999999999999996 < x

   1. Initial program 100.0%

      \[\frac{e^{x} - e^{-x}}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.0%

      \[\leadsto \frac{\color{blue}{0.0003968253968253968 \cdot {x}^{7} + \left(0.016666666666666666 \cdot {x}^{5} + \left(0.3333333333333333 \cdot {x}^{3} + 2 \cdot x\right)\right)}}{2} \]

   4. Taylor expanded in x around inf 88.0%

      \[\leadsto \color{blue}{0.0001984126984126984 \cdot {x}^{7}} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 88.0%

         \[\leadsto \color{blue}{\sqrt{0.0001984126984126984 \cdot {x}^{7}} \cdot \sqrt{0.0001984126984126984 \cdot {x}^{7}}} \]

      2. sqrt-unprod 93.9%

         \[\leadsto \color{blue}{\sqrt{\left(0.0001984126984126984 \cdot {x}^{7}\right) \cdot \left(0.0001984126984126984 \cdot {x}^{7}\right)}} \]

      3. *-commutative 93.9%

         \[\leadsto \sqrt{\color{blue}{\left({x}^{7} \cdot 0.0001984126984126984\right)} \cdot \left(0.0001984126984126984 \cdot {x}^{7}\right)} \]

      4. *-commutative 93.9%

         \[\leadsto \sqrt{\left({x}^{7} \cdot 0.0001984126984126984\right) \cdot \color{blue}{\left({x}^{7} \cdot 0.0001984126984126984\right)}} \]

      5. swap-sqr 93.9%

         \[\leadsto \sqrt{\color{blue}{\left({x}^{7} \cdot {x}^{7}\right) \cdot \left(0.0001984126984126984 \cdot 0.0001984126984126984\right)}} \]

      6. pow-prod-up 93.9%

         \[\leadsto \sqrt{\color{blue}{{x}^{\left(7 + 7\right)}} \cdot \left(0.0001984126984126984 \cdot 0.0001984126984126984\right)} \]

      7. metadata-eval 93.9%

         \[\leadsto \sqrt{{x}^{\color{blue}{14}} \cdot \left(0.0001984126984126984 \cdot 0.0001984126984126984\right)} \]

      8. metadata-eval 93.9%

         \[\leadsto \sqrt{{x}^{14} \cdot \color{blue}{3.936759889140842 \cdot 10^{-8}}} \]

   6. Applied egg-rr 93.9%

      \[\leadsto \color{blue}{\sqrt{{x}^{14} \cdot 3.936759889140842 \cdot 10^{-8}}} \]
   7. Step-by-step derivation

      1. pow1 93.9%

         \[\leadsto \color{blue}{{\left(\sqrt{{x}^{14} \cdot 3.936759889140842 \cdot 10^{-8}}\right)}^{1}} \]

      2. metadata-eval 93.9%

         \[\leadsto {\left(\sqrt{{x}^{14} \cdot 3.936759889140842 \cdot 10^{-8}}\right)}^{\color{blue}{\left(3 \cdot 0.3333333333333333\right)}} \]

      3. pow-pow 93.9%

         \[\leadsto \color{blue}{{\left({\left(\sqrt{{x}^{14} \cdot 3.936759889140842 \cdot 10^{-8}}\right)}^{3}\right)}^{0.3333333333333333}} \]

      4. sqrt-prod 93.9%

         \[\leadsto {\left({\color{blue}{\left(\sqrt{{x}^{14}} \cdot \sqrt{3.936759889140842 \cdot 10^{-8}}\right)}}^{3}\right)}^{0.3333333333333333} \]

      5. unpow-prod-down 95.4%

         \[\leadsto {\color{blue}{\left({\left(\sqrt{{x}^{14}}\right)}^{3} \cdot {\left(\sqrt{3.936759889140842 \cdot 10^{-8}}\right)}^{3}\right)}}^{0.3333333333333333} \]

      6. pow3 95.4%

         \[\leadsto {\left(\color{blue}{\left(\left(\sqrt{{x}^{14}} \cdot \sqrt{{x}^{14}}\right) \cdot \sqrt{{x}^{14}}\right)} \cdot {\left(\sqrt{3.936759889140842 \cdot 10^{-8}}\right)}^{3}\right)}^{0.3333333333333333} \]

      7. add-sqr-sqrt 95.4%

         \[\leadsto {\left(\left(\color{blue}{{x}^{14}} \cdot \sqrt{{x}^{14}}\right) \cdot {\left(\sqrt{3.936759889140842 \cdot 10^{-8}}\right)}^{3}\right)}^{0.3333333333333333} \]

      8. sqrt-pow1 95.4%

         \[\leadsto {\left(\left({x}^{14} \cdot \color{blue}{{x}^{\left(\frac{14}{2}\right)}}\right) \cdot {\left(\sqrt{3.936759889140842 \cdot 10^{-8}}\right)}^{3}\right)}^{0.3333333333333333} \]

      9. pow-prod-up 95.4%

         \[\leadsto {\left(\color{blue}{{x}^{\left(14 + \frac{14}{2}\right)}} \cdot {\left(\sqrt{3.936759889140842 \cdot 10^{-8}}\right)}^{3}\right)}^{0.3333333333333333} \]

      10. metadata-eval 95.4%

          \[\leadsto {\left({x}^{\left(14 + \color{blue}{7}\right)} \cdot {\left(\sqrt{3.936759889140842 \cdot 10^{-8}}\right)}^{3}\right)}^{0.3333333333333333} \]

      11. metadata-eval 95.4%

          \[\leadsto {\left({x}^{\color{blue}{21}} \cdot {\left(\sqrt{3.936759889140842 \cdot 10^{-8}}\right)}^{3}\right)}^{0.3333333333333333} \]

      12. metadata-eval 95.4%

          \[\leadsto {\left({x}^{21} \cdot {\color{blue}{0.0001984126984126984}}^{3}\right)}^{0.3333333333333333} \]

      13. metadata-eval 95.4%

          \[\leadsto {\left({x}^{21} \cdot \color{blue}{7.811031526073099 \cdot 10^{-12}}\right)}^{0.3333333333333333} \]

   8. Applied egg-rr 95.4%

      \[\leadsto \color{blue}{{\left({x}^{21} \cdot 7.811031526073099 \cdot 10^{-12}\right)}^{0.3333333333333333}} \]
   9. Step-by-step derivation

      1. unpow1/3 95.4%

         \[\leadsto \color{blue}{\sqrt[3]{{x}^{21} \cdot 7.811031526073099 \cdot 10^{-12}}} \]

   10. Simplified 95.4%

       \[\leadsto \color{blue}{\sqrt[3]{{x}^{21} \cdot 7.811031526073099 \cdot 10^{-12}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.6:\\ \;\;\;\;x + 0.16666666666666666 \cdot {x}^{3}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{x}^{21} \cdot 7.811031526073099 \cdot 10^{-12}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 5.6:\\ \;\;\;\;x\_m + 0.16666666666666666 \cdot {x\_m}^{3}\\ \mathbf{else}:\\ \;\;\;\;0.0001984126984126984 \cdot {x\_m}^{7}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m)
 :precision binary64
 (*
  x_s
  (if (<= x_m 5.6)
    (+ x_m (* 0.16666666666666666 (pow x_m 3.0)))
    (* 0.0001984126984126984 (pow x_m 7.0)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	double tmp;
	if (x_m <= 5.6) {
		tmp = x_m + (0.16666666666666666 * pow(x_m, 3.0));
	} else {
		tmp = 0.0001984126984126984 * pow(x_m, 7.0);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8) :: tmp
    if (x_m <= 5.6d0) then
        tmp = x_m + (0.16666666666666666d0 * (x_m ** 3.0d0))
    else
        tmp = 0.0001984126984126984d0 * (x_m ** 7.0d0)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m) {
	double tmp;
	if (x_m <= 5.6) {
		tmp = x_m + (0.16666666666666666 * Math.pow(x_m, 3.0));
	} else {
		tmp = 0.0001984126984126984 * Math.pow(x_m, 7.0);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m):
	tmp = 0
	if x_m <= 5.6:
		tmp = x_m + (0.16666666666666666 * math.pow(x_m, 3.0))
	else:
		tmp = 0.0001984126984126984 * math.pow(x_m, 7.0)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m)
	tmp = 0.0
	if (x_m <= 5.6)
		tmp = Float64(x_m + Float64(0.16666666666666666 * (x_m ^ 3.0)));
	else
		tmp = Float64(0.0001984126984126984 * (x_m ^ 7.0));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m)
	tmp = 0.0;
	if (x_m <= 5.6)
		tmp = x_m + (0.16666666666666666 * (x_m ^ 3.0));
	else
		tmp = 0.0001984126984126984 * (x_m ^ 7.0);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_] := N[(x$95$s * If[LessEqual[x$95$m, 5.6], N[(x$95$m + N[(0.16666666666666666 * N[Power[x$95$m, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.0001984126984126984 * N[Power[x$95$m, 7.0], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 5.5999999999999996

   1. Initial program 41.6%

      \[\frac{e^{x} - e^{-x}}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 92.0%

      \[\leadsto \frac{\color{blue}{0.0003968253968253968 \cdot {x}^{7} + \left(0.016666666666666666 \cdot {x}^{5} + \left(0.3333333333333333 \cdot {x}^{3} + 2 \cdot x\right)\right)}}{2} \]

   4. Taylor expanded in x around 0 85.4%

      \[\leadsto \color{blue}{x + 0.16666666666666666 \cdot {x}^{3}} \]

   if 5.5999999999999996 < x

   1. Initial program 100.0%

      \[\frac{e^{x} - e^{-x}}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.0%

      \[\leadsto \frac{\color{blue}{0.0003968253968253968 \cdot {x}^{7} + \left(0.016666666666666666 \cdot {x}^{5} + \left(0.3333333333333333 \cdot {x}^{3} + 2 \cdot x\right)\right)}}{2} \]

   4. Taylor expanded in x around inf 88.0%

      \[\leadsto \color{blue}{0.0001984126984126984 \cdot {x}^{7}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.6:\\ \;\;\;\;x + 0.16666666666666666 \cdot {x}^{3}\\ \mathbf{else}:\\ \;\;\;\;0.0001984126984126984 \cdot {x}^{7}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 4.2:\\ \;\;\;\;x\_m\\ \mathbf{else}:\\ \;\;\;\;0.0001984126984126984 \cdot {x\_m}^{7}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m)
 :precision binary64
 (* x_s (if (<= x_m 4.2) x_m (* 0.0001984126984126984 (pow x_m 7.0)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	double tmp;
	if (x_m <= 4.2) {
		tmp = x_m;
	} else {
		tmp = 0.0001984126984126984 * pow(x_m, 7.0);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8) :: tmp
    if (x_m <= 4.2d0) then
        tmp = x_m
    else
        tmp = 0.0001984126984126984d0 * (x_m ** 7.0d0)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m) {
	double tmp;
	if (x_m <= 4.2) {
		tmp = x_m;
	} else {
		tmp = 0.0001984126984126984 * Math.pow(x_m, 7.0);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m):
	tmp = 0
	if x_m <= 4.2:
		tmp = x_m
	else:
		tmp = 0.0001984126984126984 * math.pow(x_m, 7.0)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m)
	tmp = 0.0
	if (x_m <= 4.2)
		tmp = x_m;
	else
		tmp = Float64(0.0001984126984126984 * (x_m ^ 7.0));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m)
	tmp = 0.0;
	if (x_m <= 4.2)
		tmp = x_m;
	else
		tmp = 0.0001984126984126984 * (x_m ^ 7.0);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_] := N[(x$95$s * If[LessEqual[x$95$m, 4.2], x$95$m, N[(0.0001984126984126984 * N[Power[x$95$m, 7.0], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 4.20000000000000018

   1. Initial program 41.6%

      \[\frac{e^{x} - e^{-x}}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 92.0%

      \[\leadsto \frac{\color{blue}{0.0003968253968253968 \cdot {x}^{7} + \left(0.016666666666666666 \cdot {x}^{5} + \left(0.3333333333333333 \cdot {x}^{3} + 2 \cdot x\right)\right)}}{2} \]

   4. Taylor expanded in x around 0 66.0%

      \[\leadsto \color{blue}{x} \]

   if 4.20000000000000018 < x

   1. Initial program 100.0%

      \[\frac{e^{x} - e^{-x}}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.0%

      \[\leadsto \frac{\color{blue}{0.0003968253968253968 \cdot {x}^{7} + \left(0.016666666666666666 \cdot {x}^{5} + \left(0.3333333333333333 \cdot {x}^{3} + 2 \cdot x\right)\right)}}{2} \]

   4. Taylor expanded in x around inf 88.0%

      \[\leadsto \color{blue}{0.0001984126984126984 \cdot {x}^{7}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0.0001984126984126984 \cdot {x}^{7}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.0% accurate, 206.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot x\_m \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m) :precision binary64 (* x_s x_m))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	return x_s * x_m;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    code = x_s * x_m
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m) {
	return x_s * x_m;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m):
	return x_s * x_m

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m)
	return Float64(x_s * x_m)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m)
	tmp = x_s * x_m;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_] := N[(x$95$s * x$95$m), $MachinePrecision]

Derivation

1. Initial program 55.9%

   \[\frac{e^{x} - e^{-x}}{2} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 91.0%

   \[\leadsto \frac{\color{blue}{0.0003968253968253968 \cdot {x}^{7} + \left(0.016666666666666666 \cdot {x}^{5} + \left(0.3333333333333333 \cdot {x}^{3} + 2 \cdot x\right)\right)}}{2} \]

4. Taylor expanded in x around 0 51.1%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 51.1%

   \[\leadsto x \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(FPCore (x)
  :name "Hyperbolic sine"
  :precision binary64
  (/ (- (exp x) (exp (- x))) 2.0))