exp2 (problem 3.3.7)

Percentage Accurate: 54.2% → 100.0%

Time: 14.3s

Alternatives: 6

Speedup: 68.7×

Specification

\[\left|x\right| \leq 710\]

Math

\[\begin{array}{l} \\ \left(e^{x} - 2\right) + e^{-x} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(e^{x} - 2\right) + e^{-x} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} t_0 := \left(e^{x\_m} - 2\right) + e^{-x\_m}\\ \mathbf{if}\;t\_0 \leq 0.005:\\ \;\;\;\;{x\_m}^{2} \cdot \left(1 + {x\_m}^{2} \cdot \left(0.08333333333333333 + {x\_m}^{2} \cdot \left(0.002777777777777778 + {x\_m}^{2} \cdot 4.96031746031746 \cdot 10^{-5}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m)
 :precision binary64
 (let* ((t_0 (+ (- (exp x_m) 2.0) (exp (- x_m)))))
   (if (<= t_0 0.005)
     (*
      (pow x_m 2.0)
      (+
       1.0
       (*
        (pow x_m 2.0)
        (+
         0.08333333333333333
         (*
          (pow x_m 2.0)
          (+ 0.002777777777777778 (* (pow x_m 2.0) 4.96031746031746e-5)))))))
     t_0)))

C

x_m = fabs(x);
double code(double x_m) {
	double t_0 = (exp(x_m) - 2.0) + exp(-x_m);
	double tmp;
	if (t_0 <= 0.005) {
		tmp = pow(x_m, 2.0) * (1.0 + (pow(x_m, 2.0) * (0.08333333333333333 + (pow(x_m, 2.0) * (0.002777777777777778 + (pow(x_m, 2.0) * 4.96031746031746e-5))))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

x_m = abs(x)
real(8) function code(x_m)
    real(8), intent (in) :: x_m
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (exp(x_m) - 2.0d0) + exp(-x_m)
    if (t_0 <= 0.005d0) then
        tmp = (x_m ** 2.0d0) * (1.0d0 + ((x_m ** 2.0d0) * (0.08333333333333333d0 + ((x_m ** 2.0d0) * (0.002777777777777778d0 + ((x_m ** 2.0d0) * 4.96031746031746d-5))))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

x_m = Math.abs(x);
public static double code(double x_m) {
	double t_0 = (Math.exp(x_m) - 2.0) + Math.exp(-x_m);
	double tmp;
	if (t_0 <= 0.005) {
		tmp = Math.pow(x_m, 2.0) * (1.0 + (Math.pow(x_m, 2.0) * (0.08333333333333333 + (Math.pow(x_m, 2.0) * (0.002777777777777778 + (Math.pow(x_m, 2.0) * 4.96031746031746e-5))))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

x_m = math.fabs(x)
def code(x_m):
	t_0 = (math.exp(x_m) - 2.0) + math.exp(-x_m)
	tmp = 0
	if t_0 <= 0.005:
		tmp = math.pow(x_m, 2.0) * (1.0 + (math.pow(x_m, 2.0) * (0.08333333333333333 + (math.pow(x_m, 2.0) * (0.002777777777777778 + (math.pow(x_m, 2.0) * 4.96031746031746e-5))))))
	else:
		tmp = t_0
	return tmp

Julia

x_m = abs(x)
function code(x_m)
	t_0 = Float64(Float64(exp(x_m) - 2.0) + exp(Float64(-x_m)))
	tmp = 0.0
	if (t_0 <= 0.005)
		tmp = Float64((x_m ^ 2.0) * Float64(1.0 + Float64((x_m ^ 2.0) * Float64(0.08333333333333333 + Float64((x_m ^ 2.0) * Float64(0.002777777777777778 + Float64((x_m ^ 2.0) * 4.96031746031746e-5)))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x_m = abs(x);
function tmp_2 = code(x_m)
	t_0 = (exp(x_m) - 2.0) + exp(-x_m);
	tmp = 0.0;
	if (t_0 <= 0.005)
		tmp = (x_m ^ 2.0) * (1.0 + ((x_m ^ 2.0) * (0.08333333333333333 + ((x_m ^ 2.0) * (0.002777777777777778 + ((x_m ^ 2.0) * 4.96031746031746e-5))))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_] := Block[{t$95$0 = N[(N[(N[Exp[x$95$m], $MachinePrecision] - 2.0), $MachinePrecision] + N[Exp[(-x$95$m)], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.005], N[(N[Power[x$95$m, 2.0], $MachinePrecision] * N[(1.0 + N[(N[Power[x$95$m, 2.0], $MachinePrecision] * N[(0.08333333333333333 + N[(N[Power[x$95$m, 2.0], $MachinePrecision] * N[(0.002777777777777778 + N[(N[Power[x$95$m, 2.0], $MachinePrecision] * 4.96031746031746e-5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x))) < 0.0050000000000000001

   1. Initial program 56.5%

      \[\left(e^{x} - 2\right) + e^{-x} \]
   2. Step-by-step derivation

      1. associate-+l- 56.4%

         \[\leadsto \color{blue}{e^{x} - \left(2 - e^{-x}\right)} \]

      2. sub-neg 56.4%

         \[\leadsto \color{blue}{e^{x} + \left(-\left(2 - e^{-x}\right)\right)} \]

      3. sub-neg 56.4%

         \[\leadsto e^{x} + \left(-\color{blue}{\left(2 + \left(-e^{-x}\right)\right)}\right) \]

      4. distribute-neg-in 56.4%

         \[\leadsto e^{x} + \color{blue}{\left(\left(-2\right) + \left(-\left(-e^{-x}\right)\right)\right)} \]

      5. remove-double-neg 56.4%

         \[\leadsto e^{x} + \left(\left(-2\right) + \color{blue}{e^{-x}}\right) \]

      6. +-commutative 56.4%

         \[\leadsto e^{x} + \color{blue}{\left(e^{-x} + \left(-2\right)\right)} \]

      7. metadata-eval 56.4%

         \[\leadsto e^{x} + \left(e^{-x} + \color{blue}{-2}\right) \]

   3. Simplified 56.4%

      \[\leadsto \color{blue}{e^{x} + \left(e^{-x} + -2\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{{x}^{2} \cdot \left(1 + {x}^{2} \cdot \left(0.08333333333333333 + {x}^{2} \cdot \left(0.002777777777777778 + 4.96031746031746 \cdot 10^{-5} \cdot {x}^{2}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto {x}^{2} \cdot \left(1 + {x}^{2} \cdot \left(0.08333333333333333 + {x}^{2} \cdot \left(0.002777777777777778 + \color{blue}{{x}^{2} \cdot 4.96031746031746 \cdot 10^{-5}}\right)\right)\right) \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{{x}^{2} \cdot \left(1 + {x}^{2} \cdot \left(0.08333333333333333 + {x}^{2} \cdot \left(0.002777777777777778 + {x}^{2} \cdot 4.96031746031746 \cdot 10^{-5}\right)\right)\right)} \]

   if 0.0050000000000000001 < (+.f64 (-.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x)))

   1. Initial program 99.1%

      \[\left(e^{x} - 2\right) + e^{-x} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(e^{x} - 2\right) + e^{-x} \leq 0.005:\\ \;\;\;\;{x}^{2} \cdot \left(1 + {x}^{2} \cdot \left(0.08333333333333333 + {x}^{2} \cdot \left(0.002777777777777778 + {x}^{2} \cdot 4.96031746031746 \cdot 10^{-5}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(e^{x} - 2\right) + e^{-x}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} t_0 := \left(e^{x\_m} - 2\right) + e^{-x\_m}\\ \mathbf{if}\;t\_0 \leq 10^{-9}:\\ \;\;\;\;x\_m \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m)
 :precision binary64
 (let* ((t_0 (+ (- (exp x_m) 2.0) (exp (- x_m)))))
   (if (<= t_0 1e-9) (* x_m x_m) t_0)))

C

x_m = fabs(x);
double code(double x_m) {
	double t_0 = (exp(x_m) - 2.0) + exp(-x_m);
	double tmp;
	if (t_0 <= 1e-9) {
		tmp = x_m * x_m;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

x_m = abs(x)
real(8) function code(x_m)
    real(8), intent (in) :: x_m
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (exp(x_m) - 2.0d0) + exp(-x_m)
    if (t_0 <= 1d-9) then
        tmp = x_m * x_m
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

x_m = Math.abs(x);
public static double code(double x_m) {
	double t_0 = (Math.exp(x_m) - 2.0) + Math.exp(-x_m);
	double tmp;
	if (t_0 <= 1e-9) {
		tmp = x_m * x_m;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

x_m = math.fabs(x)
def code(x_m):
	t_0 = (math.exp(x_m) - 2.0) + math.exp(-x_m)
	tmp = 0
	if t_0 <= 1e-9:
		tmp = x_m * x_m
	else:
		tmp = t_0
	return tmp

Julia

x_m = abs(x)
function code(x_m)
	t_0 = Float64(Float64(exp(x_m) - 2.0) + exp(Float64(-x_m)))
	tmp = 0.0
	if (t_0 <= 1e-9)
		tmp = Float64(x_m * x_m);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x_m = abs(x);
function tmp_2 = code(x_m)
	t_0 = (exp(x_m) - 2.0) + exp(-x_m);
	tmp = 0.0;
	if (t_0 <= 1e-9)
		tmp = x_m * x_m;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_] := Block[{t$95$0 = N[(N[(N[Exp[x$95$m], $MachinePrecision] - 2.0), $MachinePrecision] + N[Exp[(-x$95$m)], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 1e-9], N[(x$95$m * x$95$m), $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x))) < 1.00000000000000006e-9

   1. Initial program 56.4%

      \[\left(e^{x} - 2\right) + e^{-x} \]
   2. Step-by-step derivation

      1. associate-+l- 56.3%

         \[\leadsto \color{blue}{e^{x} - \left(2 - e^{-x}\right)} \]

      2. sub-neg 56.3%

         \[\leadsto \color{blue}{e^{x} + \left(-\left(2 - e^{-x}\right)\right)} \]

      3. sub-neg 56.3%

         \[\leadsto e^{x} + \left(-\color{blue}{\left(2 + \left(-e^{-x}\right)\right)}\right) \]

      4. distribute-neg-in 56.3%

         \[\leadsto e^{x} + \color{blue}{\left(\left(-2\right) + \left(-\left(-e^{-x}\right)\right)\right)} \]

      5. remove-double-neg 56.3%

         \[\leadsto e^{x} + \left(\left(-2\right) + \color{blue}{e^{-x}}\right) \]

      6. +-commutative 56.3%

         \[\leadsto e^{x} + \color{blue}{\left(e^{-x} + \left(-2\right)\right)} \]

      7. metadata-eval 56.3%

         \[\leadsto e^{x} + \left(e^{-x} + \color{blue}{-2}\right) \]

   3. Simplified 56.3%

      \[\leadsto \color{blue}{e^{x} + \left(e^{-x} + -2\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cbrt-cube 56.3%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(e^{x} + \left(e^{-x} + -2\right)\right) \cdot \left(e^{x} + \left(e^{-x} + -2\right)\right)\right) \cdot \left(e^{x} + \left(e^{-x} + -2\right)\right)}} \]

      2. pow1/3 56.3%

         \[\leadsto \color{blue}{{\left(\left(\left(e^{x} + \left(e^{-x} + -2\right)\right) \cdot \left(e^{x} + \left(e^{-x} + -2\right)\right)\right) \cdot \left(e^{x} + \left(e^{-x} + -2\right)\right)\right)}^{0.3333333333333333}} \]

      3. pow3 56.3%

         \[\leadsto {\color{blue}{\left({\left(e^{x} + \left(e^{-x} + -2\right)\right)}^{3}\right)}}^{0.3333333333333333} \]

      4. associate-+r+ 56.2%

         \[\leadsto {\left({\color{blue}{\left(\left(e^{x} + e^{-x}\right) + -2\right)}}^{3}\right)}^{0.3333333333333333} \]

      5. +-commutative 56.2%

         \[\leadsto {\left({\color{blue}{\left(-2 + \left(e^{x} + e^{-x}\right)\right)}}^{3}\right)}^{0.3333333333333333} \]

      6. cosh-undef 56.2%

         \[\leadsto {\left({\left(-2 + \color{blue}{2 \cdot \cosh x}\right)}^{3}\right)}^{0.3333333333333333} \]

   6. Applied egg-rr 56.2%

      \[\leadsto \color{blue}{{\left({\left(-2 + 2 \cdot \cosh x\right)}^{3}\right)}^{0.3333333333333333}} \]

   7. Taylor expanded in x around 0 69.6%

      \[\leadsto {\color{blue}{\left({x}^{6}\right)}}^{0.3333333333333333} \]
   8. Step-by-step derivation

      1. pow-pow 99.7%

         \[\leadsto \color{blue}{{x}^{\left(6 \cdot 0.3333333333333333\right)}} \]

      2. metadata-eval 99.7%

         \[\leadsto {x}^{\color{blue}{2}} \]

      3. unpow2 99.7%

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

   9. Applied egg-rr 99.7%

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

   if 1.00000000000000006e-9 < (+.f64 (-.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x)))

   1. Initial program 97.5%

      \[\left(e^{x} - 2\right) + e^{-x} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(e^{x} - 2\right) + e^{-x} \leq 10^{-9}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(e^{x} - 2\right) + e^{-x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} t_0 := \left(e^{x\_m} - 2\right) + e^{-x\_m}\\ \mathbf{if}\;t\_0 \leq 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(x\_m, x\_m, 0.08333333333333333 \cdot {x\_m}^{4}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m)
 :precision binary64
 (let* ((t_0 (+ (- (exp x_m) 2.0) (exp (- x_m)))))
   (if (<= t_0 1e-9) (fma x_m x_m (* 0.08333333333333333 (pow x_m 4.0))) t_0)))

C

x_m = fabs(x);
double code(double x_m) {
	double t_0 = (exp(x_m) - 2.0) + exp(-x_m);
	double tmp;
	if (t_0 <= 1e-9) {
		tmp = fma(x_m, x_m, (0.08333333333333333 * pow(x_m, 4.0)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

x_m = abs(x)
function code(x_m)
	t_0 = Float64(Float64(exp(x_m) - 2.0) + exp(Float64(-x_m)))
	tmp = 0.0
	if (t_0 <= 1e-9)
		tmp = fma(x_m, x_m, Float64(0.08333333333333333 * (x_m ^ 4.0)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_] := Block[{t$95$0 = N[(N[(N[Exp[x$95$m], $MachinePrecision] - 2.0), $MachinePrecision] + N[Exp[(-x$95$m)], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 1e-9], N[(x$95$m * x$95$m + N[(0.08333333333333333 * N[Power[x$95$m, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x))) < 1.00000000000000006e-9

   1. Initial program 56.4%

      \[\left(e^{x} - 2\right) + e^{-x} \]
   2. Step-by-step derivation

      1. associate-+l- 56.3%

         \[\leadsto \color{blue}{e^{x} - \left(2 - e^{-x}\right)} \]

      2. sub-neg 56.3%

         \[\leadsto \color{blue}{e^{x} + \left(-\left(2 - e^{-x}\right)\right)} \]

      3. sub-neg 56.3%

         \[\leadsto e^{x} + \left(-\color{blue}{\left(2 + \left(-e^{-x}\right)\right)}\right) \]

      4. distribute-neg-in 56.3%

         \[\leadsto e^{x} + \color{blue}{\left(\left(-2\right) + \left(-\left(-e^{-x}\right)\right)\right)} \]

      5. remove-double-neg 56.3%

         \[\leadsto e^{x} + \left(\left(-2\right) + \color{blue}{e^{-x}}\right) \]

      6. +-commutative 56.3%

         \[\leadsto e^{x} + \color{blue}{\left(e^{-x} + \left(-2\right)\right)} \]

      7. metadata-eval 56.3%

         \[\leadsto e^{x} + \left(e^{-x} + \color{blue}{-2}\right) \]

   3. Simplified 56.3%

      \[\leadsto \color{blue}{e^{x} + \left(e^{-x} + -2\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{{x}^{2} \cdot \left(1 + {x}^{2} \cdot \left(0.08333333333333333 + {x}^{2} \cdot \left(0.002777777777777778 + 4.96031746031746 \cdot 10^{-5} \cdot {x}^{2}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto {x}^{2} \cdot \left(1 + {x}^{2} \cdot \left(0.08333333333333333 + {x}^{2} \cdot \left(0.002777777777777778 + \color{blue}{{x}^{2} \cdot 4.96031746031746 \cdot 10^{-5}}\right)\right)\right) \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{{x}^{2} \cdot \left(1 + {x}^{2} \cdot \left(0.08333333333333333 + {x}^{2} \cdot \left(0.002777777777777778 + {x}^{2} \cdot 4.96031746031746 \cdot 10^{-5}\right)\right)\right)} \]

   8. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{{x}^{2} \cdot \left(1 + 0.08333333333333333 \cdot {x}^{2}\right)} \]
   9. Step-by-step derivation

      1. distribute-rgt-in 100.0%

         \[\leadsto \color{blue}{1 \cdot {x}^{2} + \left(0.08333333333333333 \cdot {x}^{2}\right) \cdot {x}^{2}} \]

      2. *-lft-identity 100.0%

         \[\leadsto \color{blue}{{x}^{2}} + \left(0.08333333333333333 \cdot {x}^{2}\right) \cdot {x}^{2} \]

      3. associate-*l* 100.0%

         \[\leadsto {x}^{2} + \color{blue}{0.08333333333333333 \cdot \left({x}^{2} \cdot {x}^{2}\right)} \]

      4. pow-sqr 100.0%

         \[\leadsto {x}^{2} + 0.08333333333333333 \cdot \color{blue}{{x}^{\left(2 \cdot 2\right)}} \]

      5. metadata-eval 100.0%

         \[\leadsto {x}^{2} + 0.08333333333333333 \cdot {x}^{\color{blue}{4}} \]

   10. Simplified 100.0%

       \[\leadsto \color{blue}{{x}^{2} + 0.08333333333333333 \cdot {x}^{4}} \]
   11. Step-by-step derivation

       1. unpow2 100.0%

          \[\leadsto \color{blue}{x \cdot x} + 0.08333333333333333 \cdot {x}^{4} \]

       2. fma-define 100.0%

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, 0.08333333333333333 \cdot {x}^{4}\right)} \]

   12. Applied egg-rr 100.0%

       \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, 0.08333333333333333 \cdot {x}^{4}\right)} \]

   if 1.00000000000000006e-9 < (+.f64 (-.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x)))

   1. Initial program 97.5%

      \[\left(e^{x} - 2\right) + e^{-x} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(e^{x} - 2\right) + e^{-x} \leq 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(x, x, 0.08333333333333333 \cdot {x}^{4}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(e^{x} - 2\right) + e^{-x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} \mathbf{if}\;x\_m \leq 0.00021:\\ \;\;\;\;x\_m \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;e^{x\_m} + \left(e^{-x\_m} + -2\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m)
 :precision binary64
 (if (<= x_m 0.00021) (* x_m x_m) (+ (exp x_m) (+ (exp (- x_m)) -2.0))))

C

x_m = fabs(x);
double code(double x_m) {
	double tmp;
	if (x_m <= 0.00021) {
		tmp = x_m * x_m;
	} else {
		tmp = exp(x_m) + (exp(-x_m) + -2.0);
	}
	return tmp;
}

Fortran

x_m = abs(x)
real(8) function code(x_m)
    real(8), intent (in) :: x_m
    real(8) :: tmp
    if (x_m <= 0.00021d0) then
        tmp = x_m * x_m
    else
        tmp = exp(x_m) + (exp(-x_m) + (-2.0d0))
    end if
    code = tmp
end function

Java

x_m = Math.abs(x);
public static double code(double x_m) {
	double tmp;
	if (x_m <= 0.00021) {
		tmp = x_m * x_m;
	} else {
		tmp = Math.exp(x_m) + (Math.exp(-x_m) + -2.0);
	}
	return tmp;
}

Python

x_m = math.fabs(x)
def code(x_m):
	tmp = 0
	if x_m <= 0.00021:
		tmp = x_m * x_m
	else:
		tmp = math.exp(x_m) + (math.exp(-x_m) + -2.0)
	return tmp

Julia

x_m = abs(x)
function code(x_m)
	tmp = 0.0
	if (x_m <= 0.00021)
		tmp = Float64(x_m * x_m);
	else
		tmp = Float64(exp(x_m) + Float64(exp(Float64(-x_m)) + -2.0));
	end
	return tmp
end

MATLAB

x_m = abs(x);
function tmp_2 = code(x_m)
	tmp = 0.0;
	if (x_m <= 0.00021)
		tmp = x_m * x_m;
	else
		tmp = exp(x_m) + (exp(-x_m) + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_] := If[LessEqual[x$95$m, 0.00021], N[(x$95$m * x$95$m), $MachinePrecision], N[(N[Exp[x$95$m], $MachinePrecision] + N[(N[Exp[(-x$95$m)], $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.1000000000000001e-4

   1. Initial program 57.0%

      \[\left(e^{x} - 2\right) + e^{-x} \]
   2. Step-by-step derivation

      1. associate-+l- 57.0%

         \[\leadsto \color{blue}{e^{x} - \left(2 - e^{-x}\right)} \]

      2. sub-neg 57.0%

         \[\leadsto \color{blue}{e^{x} + \left(-\left(2 - e^{-x}\right)\right)} \]

      3. sub-neg 57.0%

         \[\leadsto e^{x} + \left(-\color{blue}{\left(2 + \left(-e^{-x}\right)\right)}\right) \]

      4. distribute-neg-in 57.0%

         \[\leadsto e^{x} + \color{blue}{\left(\left(-2\right) + \left(-\left(-e^{-x}\right)\right)\right)} \]

      5. remove-double-neg 57.0%

         \[\leadsto e^{x} + \left(\left(-2\right) + \color{blue}{e^{-x}}\right) \]

      6. +-commutative 57.0%

         \[\leadsto e^{x} + \color{blue}{\left(e^{-x} + \left(-2\right)\right)} \]

      7. metadata-eval 57.0%

         \[\leadsto e^{x} + \left(e^{-x} + \color{blue}{-2}\right) \]

   3. Simplified 57.0%

      \[\leadsto \color{blue}{e^{x} + \left(e^{-x} + -2\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cbrt-cube 56.2%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(e^{x} + \left(e^{-x} + -2\right)\right) \cdot \left(e^{x} + \left(e^{-x} + -2\right)\right)\right) \cdot \left(e^{x} + \left(e^{-x} + -2\right)\right)}} \]

      2. pow1/3 56.2%

         \[\leadsto \color{blue}{{\left(\left(\left(e^{x} + \left(e^{-x} + -2\right)\right) \cdot \left(e^{x} + \left(e^{-x} + -2\right)\right)\right) \cdot \left(e^{x} + \left(e^{-x} + -2\right)\right)\right)}^{0.3333333333333333}} \]

      3. pow3 56.2%

         \[\leadsto {\color{blue}{\left({\left(e^{x} + \left(e^{-x} + -2\right)\right)}^{3}\right)}}^{0.3333333333333333} \]

      4. associate-+r+ 56.1%

         \[\leadsto {\left({\color{blue}{\left(\left(e^{x} + e^{-x}\right) + -2\right)}}^{3}\right)}^{0.3333333333333333} \]

      5. +-commutative 56.1%

         \[\leadsto {\left({\color{blue}{\left(-2 + \left(e^{x} + e^{-x}\right)\right)}}^{3}\right)}^{0.3333333333333333} \]

      6. cosh-undef 56.1%

         \[\leadsto {\left({\left(-2 + \color{blue}{2 \cdot \cosh x}\right)}^{3}\right)}^{0.3333333333333333} \]

   6. Applied egg-rr 56.1%

      \[\leadsto \color{blue}{{\left({\left(-2 + 2 \cdot \cosh x\right)}^{3}\right)}^{0.3333333333333333}} \]

   7. Taylor expanded in x around 0 68.7%

      \[\leadsto {\color{blue}{\left({x}^{6}\right)}}^{0.3333333333333333} \]
   8. Step-by-step derivation

      1. pow-pow 98.4%

         \[\leadsto \color{blue}{{x}^{\left(6 \cdot 0.3333333333333333\right)}} \]

      2. metadata-eval 98.4%

         \[\leadsto {x}^{\color{blue}{2}} \]

      3. unpow2 98.4%

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

   9. Applied egg-rr 98.4%

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

   if 2.1000000000000001e-4 < x

   1. Initial program 96.0%

      \[\left(e^{x} - 2\right) + e^{-x} \]
   2. Step-by-step derivation

      1. associate-+l- 96.0%

         \[\leadsto \color{blue}{e^{x} - \left(2 - e^{-x}\right)} \]

      2. sub-neg 96.0%

         \[\leadsto \color{blue}{e^{x} + \left(-\left(2 - e^{-x}\right)\right)} \]

      3. sub-neg 96.0%

         \[\leadsto e^{x} + \left(-\color{blue}{\left(2 + \left(-e^{-x}\right)\right)}\right) \]

      4. distribute-neg-in 96.0%

         \[\leadsto e^{x} + \color{blue}{\left(\left(-2\right) + \left(-\left(-e^{-x}\right)\right)\right)} \]

      5. remove-double-neg 96.0%

         \[\leadsto e^{x} + \left(\left(-2\right) + \color{blue}{e^{-x}}\right) \]

      6. +-commutative 96.0%

         \[\leadsto e^{x} + \color{blue}{\left(e^{-x} + \left(-2\right)\right)} \]

      7. metadata-eval 96.0%

         \[\leadsto e^{x} + \left(e^{-x} + \color{blue}{-2}\right) \]

   3. Simplified 96.0%

      \[\leadsto \color{blue}{e^{x} + \left(e^{-x} + -2\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.00021:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;e^{x} + \left(e^{-x} + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} \mathbf{if}\;x\_m \leq 0.000185:\\ \;\;\;\;x\_m \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \cosh x\_m - 2\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m)
 :precision binary64
 (if (<= x_m 0.000185) (* x_m x_m) (- (* 2.0 (cosh x_m)) 2.0)))

C

x_m = fabs(x);
double code(double x_m) {
	double tmp;
	if (x_m <= 0.000185) {
		tmp = x_m * x_m;
	} else {
		tmp = (2.0 * cosh(x_m)) - 2.0;
	}
	return tmp;
}

Fortran

x_m = abs(x)
real(8) function code(x_m)
    real(8), intent (in) :: x_m
    real(8) :: tmp
    if (x_m <= 0.000185d0) then
        tmp = x_m * x_m
    else
        tmp = (2.0d0 * cosh(x_m)) - 2.0d0
    end if
    code = tmp
end function

Java

x_m = Math.abs(x);
public static double code(double x_m) {
	double tmp;
	if (x_m <= 0.000185) {
		tmp = x_m * x_m;
	} else {
		tmp = (2.0 * Math.cosh(x_m)) - 2.0;
	}
	return tmp;
}

Python

x_m = math.fabs(x)
def code(x_m):
	tmp = 0
	if x_m <= 0.000185:
		tmp = x_m * x_m
	else:
		tmp = (2.0 * math.cosh(x_m)) - 2.0
	return tmp

Julia

x_m = abs(x)
function code(x_m)
	tmp = 0.0
	if (x_m <= 0.000185)
		tmp = Float64(x_m * x_m);
	else
		tmp = Float64(Float64(2.0 * cosh(x_m)) - 2.0);
	end
	return tmp
end

MATLAB

x_m = abs(x);
function tmp_2 = code(x_m)
	tmp = 0.0;
	if (x_m <= 0.000185)
		tmp = x_m * x_m;
	else
		tmp = (2.0 * cosh(x_m)) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_] := If[LessEqual[x$95$m, 0.000185], N[(x$95$m * x$95$m), $MachinePrecision], N[(N[(2.0 * N[Cosh[x$95$m], $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.85e-4

   1. Initial program 57.0%

      \[\left(e^{x} - 2\right) + e^{-x} \]
   2. Step-by-step derivation

      1. associate-+l- 57.0%

         \[\leadsto \color{blue}{e^{x} - \left(2 - e^{-x}\right)} \]

      2. sub-neg 57.0%

         \[\leadsto \color{blue}{e^{x} + \left(-\left(2 - e^{-x}\right)\right)} \]

      3. sub-neg 57.0%

         \[\leadsto e^{x} + \left(-\color{blue}{\left(2 + \left(-e^{-x}\right)\right)}\right) \]

      4. distribute-neg-in 57.0%

         \[\leadsto e^{x} + \color{blue}{\left(\left(-2\right) + \left(-\left(-e^{-x}\right)\right)\right)} \]

      5. remove-double-neg 57.0%

         \[\leadsto e^{x} + \left(\left(-2\right) + \color{blue}{e^{-x}}\right) \]

      6. +-commutative 57.0%

         \[\leadsto e^{x} + \color{blue}{\left(e^{-x} + \left(-2\right)\right)} \]

      7. metadata-eval 57.0%

         \[\leadsto e^{x} + \left(e^{-x} + \color{blue}{-2}\right) \]

   3. Simplified 57.0%

      \[\leadsto \color{blue}{e^{x} + \left(e^{-x} + -2\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cbrt-cube 56.2%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(e^{x} + \left(e^{-x} + -2\right)\right) \cdot \left(e^{x} + \left(e^{-x} + -2\right)\right)\right) \cdot \left(e^{x} + \left(e^{-x} + -2\right)\right)}} \]

      2. pow1/3 56.2%

         \[\leadsto \color{blue}{{\left(\left(\left(e^{x} + \left(e^{-x} + -2\right)\right) \cdot \left(e^{x} + \left(e^{-x} + -2\right)\right)\right) \cdot \left(e^{x} + \left(e^{-x} + -2\right)\right)\right)}^{0.3333333333333333}} \]

      3. pow3 56.2%

         \[\leadsto {\color{blue}{\left({\left(e^{x} + \left(e^{-x} + -2\right)\right)}^{3}\right)}}^{0.3333333333333333} \]

      4. associate-+r+ 56.1%

         \[\leadsto {\left({\color{blue}{\left(\left(e^{x} + e^{-x}\right) + -2\right)}}^{3}\right)}^{0.3333333333333333} \]

      5. +-commutative 56.1%

         \[\leadsto {\left({\color{blue}{\left(-2 + \left(e^{x} + e^{-x}\right)\right)}}^{3}\right)}^{0.3333333333333333} \]

      6. cosh-undef 56.1%

         \[\leadsto {\left({\left(-2 + \color{blue}{2 \cdot \cosh x}\right)}^{3}\right)}^{0.3333333333333333} \]

   6. Applied egg-rr 56.1%

      \[\leadsto \color{blue}{{\left({\left(-2 + 2 \cdot \cosh x\right)}^{3}\right)}^{0.3333333333333333}} \]

   7. Taylor expanded in x around 0 68.7%

      \[\leadsto {\color{blue}{\left({x}^{6}\right)}}^{0.3333333333333333} \]
   8. Step-by-step derivation

      1. pow-pow 98.4%

         \[\leadsto \color{blue}{{x}^{\left(6 \cdot 0.3333333333333333\right)}} \]

      2. metadata-eval 98.4%

         \[\leadsto {x}^{\color{blue}{2}} \]

      3. unpow2 98.4%

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

   9. Applied egg-rr 98.4%

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

   if 1.85e-4 < x

   1. Initial program 96.0%

      \[\left(e^{x} - 2\right) + e^{-x} \]
   2. Step-by-step derivation

      1. associate-+l- 96.0%

         \[\leadsto \color{blue}{e^{x} - \left(2 - e^{-x}\right)} \]

      2. sub-neg 96.0%

         \[\leadsto \color{blue}{e^{x} + \left(-\left(2 - e^{-x}\right)\right)} \]

      3. sub-neg 96.0%

         \[\leadsto e^{x} + \left(-\color{blue}{\left(2 + \left(-e^{-x}\right)\right)}\right) \]

      4. distribute-neg-in 96.0%

         \[\leadsto e^{x} + \color{blue}{\left(\left(-2\right) + \left(-\left(-e^{-x}\right)\right)\right)} \]

      5. remove-double-neg 96.0%

         \[\leadsto e^{x} + \left(\left(-2\right) + \color{blue}{e^{-x}}\right) \]

      6. +-commutative 96.0%

         \[\leadsto e^{x} + \color{blue}{\left(e^{-x} + \left(-2\right)\right)} \]

      7. metadata-eval 96.0%

         \[\leadsto e^{x} + \left(e^{-x} + \color{blue}{-2}\right) \]

   3. Simplified 96.0%

      \[\leadsto \color{blue}{e^{x} + \left(e^{-x} + -2\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 96.0%

         \[\leadsto e^{x} + \color{blue}{\left(-2 + e^{-x}\right)} \]

      2. associate-+r+ 96.0%

         \[\leadsto \color{blue}{\left(e^{x} + -2\right) + e^{-x}} \]

      3. metadata-eval 96.0%

         \[\leadsto \left(e^{x} + \color{blue}{\left(-2\right)}\right) + e^{-x} \]

      4. sub-neg 96.0%

         \[\leadsto \color{blue}{\left(e^{x} - 2\right)} + e^{-x} \]

      5. +-commutative 96.0%

         \[\leadsto \color{blue}{e^{-x} + \left(e^{x} - 2\right)} \]

      6. associate-+r- 95.2%

         \[\leadsto \color{blue}{\left(e^{-x} + e^{x}\right) - 2} \]

      7. +-commutative 95.2%

         \[\leadsto \color{blue}{\left(e^{x} + e^{-x}\right)} - 2 \]

      8. cosh-undef 95.2%

         \[\leadsto \color{blue}{2 \cdot \cosh x} - 2 \]

   6. Applied egg-rr 95.2%

      \[\leadsto \color{blue}{2 \cdot \cosh x - 2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.000185:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \cosh x - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.3% accurate, 68.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x\_m \cdot x\_m \end{array} \]

FPCore

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

C

x_m = fabs(x);
double code(double x_m) {
	return x_m * x_m;
}

Fortran

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

Java

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

Python

x_m = math.fabs(x)
def code(x_m):
	return x_m * x_m

Julia

x_m = abs(x)
function code(x_m)
	return Float64(x_m * x_m)
end

MATLAB

x_m = abs(x);
function tmp = code(x_m)
	tmp = x_m * x_m;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_] := N[(x$95$m * x$95$m), $MachinePrecision]

Derivation

1. Initial program 57.5%

   \[\left(e^{x} - 2\right) + e^{-x} \]
2. Step-by-step derivation

   1. associate-+l- 57.4%

      \[\leadsto \color{blue}{e^{x} - \left(2 - e^{-x}\right)} \]

   2. sub-neg 57.4%

      \[\leadsto \color{blue}{e^{x} + \left(-\left(2 - e^{-x}\right)\right)} \]

   3. sub-neg 57.4%

      \[\leadsto e^{x} + \left(-\color{blue}{\left(2 + \left(-e^{-x}\right)\right)}\right) \]

   4. distribute-neg-in 57.4%

      \[\leadsto e^{x} + \color{blue}{\left(\left(-2\right) + \left(-\left(-e^{-x}\right)\right)\right)} \]

   5. remove-double-neg 57.4%

      \[\leadsto e^{x} + \left(\left(-2\right) + \color{blue}{e^{-x}}\right) \]

   6. +-commutative 57.4%

      \[\leadsto e^{x} + \color{blue}{\left(e^{-x} + \left(-2\right)\right)} \]

   7. metadata-eval 57.4%

      \[\leadsto e^{x} + \left(e^{-x} + \color{blue}{-2}\right) \]

3. Simplified 57.4%

   \[\leadsto \color{blue}{e^{x} + \left(e^{-x} + -2\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. add-cbrt-cube 56.7%

      \[\leadsto \color{blue}{\sqrt[3]{\left(\left(e^{x} + \left(e^{-x} + -2\right)\right) \cdot \left(e^{x} + \left(e^{-x} + -2\right)\right)\right) \cdot \left(e^{x} + \left(e^{-x} + -2\right)\right)}} \]

   2. pow1/3 56.6%

      \[\leadsto \color{blue}{{\left(\left(\left(e^{x} + \left(e^{-x} + -2\right)\right) \cdot \left(e^{x} + \left(e^{-x} + -2\right)\right)\right) \cdot \left(e^{x} + \left(e^{-x} + -2\right)\right)\right)}^{0.3333333333333333}} \]

   3. pow3 56.6%

      \[\leadsto {\color{blue}{\left({\left(e^{x} + \left(e^{-x} + -2\right)\right)}^{3}\right)}}^{0.3333333333333333} \]

   4. associate-+r+ 56.6%

      \[\leadsto {\left({\color{blue}{\left(\left(e^{x} + e^{-x}\right) + -2\right)}}^{3}\right)}^{0.3333333333333333} \]

   5. +-commutative 56.6%

      \[\leadsto {\left({\color{blue}{\left(-2 + \left(e^{x} + e^{-x}\right)\right)}}^{3}\right)}^{0.3333333333333333} \]

   6. cosh-undef 56.6%

      \[\leadsto {\left({\left(-2 + \color{blue}{2 \cdot \cosh x}\right)}^{3}\right)}^{0.3333333333333333} \]

6. Applied egg-rr 56.6%

   \[\leadsto \color{blue}{{\left({\left(-2 + 2 \cdot \cosh x\right)}^{3}\right)}^{0.3333333333333333}} \]

7. Taylor expanded in x around 0 68.2%

   \[\leadsto {\color{blue}{\left({x}^{6}\right)}}^{0.3333333333333333} \]
8. Step-by-step derivation

   1. pow-pow 97.5%

      \[\leadsto \color{blue}{{x}^{\left(6 \cdot 0.3333333333333333\right)}} \]

   2. metadata-eval 97.5%

      \[\leadsto {x}^{\color{blue}{2}} \]

   3. unpow2 97.5%

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

9. Applied egg-rr 97.5%

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

10. Final simplification 97.5%

    \[\leadsto x \cdot x \]
11. Add Preprocessing

Developer target: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sinh \left(\frac{x}{2}\right)\\ 4 \cdot \left(t\_0 \cdot t\_0\right) \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (sinh (/ x 2.0)))) (* 4.0 (* t_0 t_0))))

C

double code(double x) {
	double t_0 = sinh((x / 2.0));
	return 4.0 * (t_0 * t_0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    t_0 = sinh((x / 2.0d0))
    code = 4.0d0 * (t_0 * t_0)
end function

Java

public static double code(double x) {
	double t_0 = Math.sinh((x / 2.0));
	return 4.0 * (t_0 * t_0);
}

Python

def code(x):
	t_0 = math.sinh((x / 2.0))
	return 4.0 * (t_0 * t_0)

Julia

function code(x)
	t_0 = sinh(Float64(x / 2.0))
	return Float64(4.0 * Float64(t_0 * t_0))
end

MATLAB

function tmp = code(x)
	t_0 = sinh((x / 2.0));
	tmp = 4.0 * (t_0 * t_0);
end

Wolfram

code[x_] := Block[{t$95$0 = N[Sinh[N[(x / 2.0), $MachinePrecision]], $MachinePrecision]}, N[(4.0 * N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024095 
(FPCore (x)
  :name "exp2 (problem 3.3.7)"
  :precision binary64
  :pre (<= (fabs x) 710.0)

  :alt
  (* 4.0 (* (sinh (/ x 2.0)) (sinh (/ x 2.0))))

  (+ (- (exp x) 2.0) (exp (- x))))