tanhf (example 3.4)

Percentage Accurate: 52.8% → 100.0%

Time: 8.4s

Alternatives: 3

Speedup: 2.0×

Specification

Math

\[\begin{array}{l} \\ \frac{1 - \cos x}{\sin x} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ (- 1.0 (cos x)) (sin x)))

C

double code(double x) {
	return (1.0 - cos(x)) / sin(x);
}

Fortran

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

Java

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

Python

def code(x):
	return (1.0 - math.cos(x)) / math.sin(x)

Julia

function code(x)
	return Float64(Float64(1.0 - cos(x)) / sin(x))
end

MATLAB

function tmp = code(x)
	tmp = (1.0 - cos(x)) / sin(x);
end

Wolfram

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

Initial Program: 52.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1 - \cos x}{\sin x} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ (- 1.0 (cos x)) (sin x)))

C

double code(double x) {
	return (1.0 - cos(x)) / sin(x);
}

Fortran

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

Java

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

Python

def code(x):
	return (1.0 - math.cos(x)) / math.sin(x)

Julia

function code(x)
	return Float64(Float64(1.0 - cos(x)) / sin(x))
end

MATLAB

function tmp = code(x)
	tmp = (1.0 - cos(x)) / sin(x);
end

Wolfram

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

Alternative 1: 100.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \tan \left(\frac{x}{2}\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (tan (/ x 2.0)))

C

double code(double x) {
	return tan((x / 2.0));
}

Fortran

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

Java

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

Python

def code(x):
	return math.tan((x / 2.0))

Julia

function code(x)
	return tan(Float64(x / 2.0))
end

MATLAB

function tmp = code(x)
	tmp = tan((x / 2.0));
end

Wolfram

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

Derivation

1. Initial program 52.2%

   \[\frac{1 - \cos x}{\sin x} \]
2. Step-by-step derivation

   1. hang-p0-tan N/A

      \[\leadsto \tan \left(\frac{x}{2}\right) \]

   2. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{tan.f64}\left(\left(\frac{x}{2}\right)\right) \]

   3. /-lowering-/.f64 100.0%

      \[\leadsto \mathsf{tan.f64}\left(\mathsf{/.f64}\left(x, 2\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\tan \left(\frac{x}{2}\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 51.8% accurate, 15.8× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(0.25 \cdot \frac{1}{0.5 - x \cdot \left(x \cdot 0.041666666666666664\right)}\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (* x (* 0.25 (/ 1.0 (- 0.5 (* x (* x 0.041666666666666664)))))))

C

double code(double x) {
	return x * (0.25 * (1.0 / (0.5 - (x * (x * 0.041666666666666664)))));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x * (0.25d0 * (1.0d0 / (0.5d0 - (x * (x * 0.041666666666666664d0)))))
end function

Java

public static double code(double x) {
	return x * (0.25 * (1.0 / (0.5 - (x * (x * 0.041666666666666664)))));
}

Python

def code(x):
	return x * (0.25 * (1.0 / (0.5 - (x * (x * 0.041666666666666664)))))

Julia

function code(x)
	return Float64(x * Float64(0.25 * Float64(1.0 / Float64(0.5 - Float64(x * Float64(x * 0.041666666666666664))))))
end

MATLAB

function tmp = code(x)
	tmp = x * (0.25 * (1.0 / (0.5 - (x * (x * 0.041666666666666664)))));
end

Wolfram

code[x_] := N[(x * N[(0.25 * N[(1.0 / N[(0.5 - N[(x * N[(x * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 52.2%

   \[\frac{1 - \cos x}{\sin x} \]
2. Step-by-step derivation

   1. hang-p0-tan N/A

      \[\leadsto \tan \left(\frac{x}{2}\right) \]

   2. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{tan.f64}\left(\left(\frac{x}{2}\right)\right) \]

   3. /-lowering-/.f64 100.0%

      \[\leadsto \mathsf{tan.f64}\left(\mathsf{/.f64}\left(x, 2\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\tan \left(\frac{x}{2}\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around 0

   \[\leadsto \color{blue}{x \cdot \left(\frac{1}{2} + {x}^{2} \cdot \left(\frac{1}{24} + {x}^{2} \cdot \left(\frac{1}{240} + \frac{17}{40320} \cdot {x}^{2}\right)\right)\right)} \]
6. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} + {x}^{2} \cdot \left(\frac{1}{24} + {x}^{2} \cdot \left(\frac{1}{240} + \frac{17}{40320} \cdot {x}^{2}\right)\right)\right)}\right) \]

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left({x}^{2} \cdot \left(\frac{1}{24} + {x}^{2} \cdot \left(\frac{1}{240} + \frac{17}{40320} \cdot {x}^{2}\right)\right)\right)}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left({x}^{2}\right), \color{blue}{\left(\frac{1}{24} + {x}^{2} \cdot \left(\frac{1}{240} + \frac{17}{40320} \cdot {x}^{2}\right)\right)}\right)\right)\right) \]

   4. unpow2 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(x \cdot x\right), \left(\color{blue}{\frac{1}{24}} + {x}^{2} \cdot \left(\frac{1}{240} + \frac{17}{40320} \cdot {x}^{2}\right)\right)\right)\right)\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \left(\color{blue}{\frac{1}{24}} + {x}^{2} \cdot \left(\frac{1}{240} + \frac{17}{40320} \cdot {x}^{2}\right)\right)\right)\right)\right) \]

   6. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \mathsf{+.f64}\left(\frac{1}{24}, \color{blue}{\left({x}^{2} \cdot \left(\frac{1}{240} + \frac{17}{40320} \cdot {x}^{2}\right)\right)}\right)\right)\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \mathsf{+.f64}\left(\frac{1}{24}, \mathsf{*.f64}\left(\left({x}^{2}\right), \color{blue}{\left(\frac{1}{240} + \frac{17}{40320} \cdot {x}^{2}\right)}\right)\right)\right)\right)\right) \]

   8. unpow2 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \mathsf{+.f64}\left(\frac{1}{24}, \mathsf{*.f64}\left(\left(x \cdot x\right), \left(\color{blue}{\frac{1}{240}} + \frac{17}{40320} \cdot {x}^{2}\right)\right)\right)\right)\right)\right) \]

   9. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \mathsf{+.f64}\left(\frac{1}{24}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \left(\color{blue}{\frac{1}{240}} + \frac{17}{40320} \cdot {x}^{2}\right)\right)\right)\right)\right)\right) \]

   10. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \mathsf{+.f64}\left(\frac{1}{24}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \mathsf{+.f64}\left(\frac{1}{240}, \color{blue}{\left(\frac{17}{40320} \cdot {x}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

   11. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \mathsf{+.f64}\left(\frac{1}{24}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \mathsf{+.f64}\left(\frac{1}{240}, \left({x}^{2} \cdot \color{blue}{\frac{17}{40320}}\right)\right)\right)\right)\right)\right)\right) \]

   12. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \mathsf{+.f64}\left(\frac{1}{24}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \mathsf{+.f64}\left(\frac{1}{240}, \mathsf{*.f64}\left(\left({x}^{2}\right), \color{blue}{\frac{17}{40320}}\right)\right)\right)\right)\right)\right)\right) \]

   13. unpow2 N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \mathsf{+.f64}\left(\frac{1}{24}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \mathsf{+.f64}\left(\frac{1}{240}, \mathsf{*.f64}\left(\left(x \cdot x\right), \frac{17}{40320}\right)\right)\right)\right)\right)\right)\right) \]

   14. *-lowering-*.f64 52.1%

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \mathsf{+.f64}\left(\frac{1}{24}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \mathsf{+.f64}\left(\frac{1}{240}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \frac{17}{40320}\right)\right)\right)\right)\right)\right)\right) \]

7. Simplified 52.1%

   \[\leadsto \color{blue}{x \cdot \left(0.5 + \left(x \cdot x\right) \cdot \left(0.041666666666666664 + \left(x \cdot x\right) \cdot \left(0.004166666666666667 + \left(x \cdot x\right) \cdot 0.00042162698412698415\right)\right)\right)} \]
8. Step-by-step derivation

   1. flip-+ N/A

      \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{\frac{1}{2} \cdot \frac{1}{2} - \left(\left(x \cdot x\right) \cdot \left(\frac{1}{24} + \left(x \cdot x\right) \cdot \left(\frac{1}{240} + \left(x \cdot x\right) \cdot \frac{17}{40320}\right)\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(\frac{1}{24} + \left(x \cdot x\right) \cdot \left(\frac{1}{240} + \left(x \cdot x\right) \cdot \frac{17}{40320}\right)\right)\right)}{\color{blue}{\frac{1}{2} - \left(x \cdot x\right) \cdot \left(\frac{1}{24} + \left(x \cdot x\right) \cdot \left(\frac{1}{240} + \left(x \cdot x\right) \cdot \frac{17}{40320}\right)\right)}}\right)\right) \]

   2. div-inv N/A

      \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot \frac{1}{2} - \left(\left(x \cdot x\right) \cdot \left(\frac{1}{24} + \left(x \cdot x\right) \cdot \left(\frac{1}{240} + \left(x \cdot x\right) \cdot \frac{17}{40320}\right)\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(\frac{1}{24} + \left(x \cdot x\right) \cdot \left(\frac{1}{240} + \left(x \cdot x\right) \cdot \frac{17}{40320}\right)\right)\right)\right) \cdot \color{blue}{\frac{1}{\frac{1}{2} - \left(x \cdot x\right) \cdot \left(\frac{1}{24} + \left(x \cdot x\right) \cdot \left(\frac{1}{240} + \left(x \cdot x\right) \cdot \frac{17}{40320}\right)\right)}}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot \frac{1}{2} - \left(\left(x \cdot x\right) \cdot \left(\frac{1}{24} + \left(x \cdot x\right) \cdot \left(\frac{1}{240} + \left(x \cdot x\right) \cdot \frac{17}{40320}\right)\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(\frac{1}{24} + \left(x \cdot x\right) \cdot \left(\frac{1}{240} + \left(x \cdot x\right) \cdot \frac{17}{40320}\right)\right)\right)\right), \color{blue}{\left(\frac{1}{\frac{1}{2} - \left(x \cdot x\right) \cdot \left(\frac{1}{24} + \left(x \cdot x\right) \cdot \left(\frac{1}{240} + \left(x \cdot x\right) \cdot \frac{17}{40320}\right)\right)}\right)}\right)\right) \]

9. Applied egg-rr 51.4%

   \[\leadsto x \cdot \color{blue}{\left(\left(0.25 - \left(\left(x \cdot x\right) \cdot \left(0.041666666666666664 + \left(x \cdot x\right) \cdot \left(0.004166666666666667 + x \cdot \left(x \cdot 0.00042162698412698415\right)\right)\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(0.041666666666666664 + \left(x \cdot x\right) \cdot \left(0.004166666666666667 + x \cdot \left(x \cdot 0.00042162698412698415\right)\right)\right)\right)\right) \cdot \frac{1}{0.5 - \left(x \cdot x\right) \cdot \left(0.041666666666666664 + \left(x \cdot x\right) \cdot \left(0.004166666666666667 + x \cdot \left(x \cdot 0.00042162698412698415\right)\right)\right)}\right)} \]

10. Taylor expanded in x around 0

    \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{\frac{1}{4}}, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \mathsf{+.f64}\left(\frac{1}{24}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \mathsf{+.f64}\left(\frac{1}{240}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \frac{17}{40320}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
11. Step-by-step derivation

12. Simplified 52.5%

    \[\leadsto x \cdot \left(\color{blue}{0.25} \cdot \frac{1}{0.5 - \left(x \cdot x\right) \cdot \left(0.041666666666666664 + \left(x \cdot x\right) \cdot \left(0.004166666666666667 + x \cdot \left(x \cdot 0.00042162698412698415\right)\right)\right)}\right) \]

13. Taylor expanded in x around 0

    \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{4}, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{1}{24} \cdot {x}^{2}\right)}\right)\right)\right)\right) \]
14. Step-by-step derivation

    1. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{4}, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\frac{1}{2}, \left({x}^{2} \cdot \color{blue}{\frac{1}{24}}\right)\right)\right)\right)\right) \]

    2. unpow2 N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{4}, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\frac{1}{2}, \left(\left(x \cdot x\right) \cdot \frac{1}{24}\right)\right)\right)\right)\right) \]

    3. associate-*l* N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{4}, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\frac{1}{2}, \left(x \cdot \color{blue}{\left(x \cdot \frac{1}{24}\right)}\right)\right)\right)\right)\right) \]

    4. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{4}, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\frac{1}{2}, \left(x \cdot \left(\frac{1}{24} \cdot \color{blue}{x}\right)\right)\right)\right)\right)\right) \]

    5. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{4}, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{24} \cdot x\right)}\right)\right)\right)\right)\right) \]

    6. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{4}, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \left(x \cdot \color{blue}{\frac{1}{24}}\right)\right)\right)\right)\right)\right) \]

    7. *-lowering-*.f64 52.7%

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{4}, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{\frac{1}{24}}\right)\right)\right)\right)\right)\right) \]

15. Simplified 52.7%

    \[\leadsto x \cdot \left(0.25 \cdot \frac{1}{0.5 - \color{blue}{x \cdot \left(x \cdot 0.041666666666666664\right)}}\right) \]
16. Add Preprocessing

Alternative 3: 51.2% accurate, 68.3× speedup

Math

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

FPCore

(FPCore (x) :precision binary64 (* x 0.5))

C

double code(double x) {
	return x * 0.5;
}

Fortran

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

Java

public static double code(double x) {
	return x * 0.5;
}

Python

def code(x):
	return x * 0.5

Julia

function code(x)
	return Float64(x * 0.5)
end

MATLAB

function tmp = code(x)
	tmp = x * 0.5;
end

Wolfram

code[x_] := N[(x * 0.5), $MachinePrecision]

Derivation

1. Initial program 52.2%

   \[\frac{1 - \cos x}{\sin x} \]
2. Step-by-step derivation

   1. hang-p0-tan N/A

      \[\leadsto \tan \left(\frac{x}{2}\right) \]

   2. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{tan.f64}\left(\left(\frac{x}{2}\right)\right) \]

   3. /-lowering-/.f64 100.0%

      \[\leadsto \mathsf{tan.f64}\left(\mathsf{/.f64}\left(x, 2\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\tan \left(\frac{x}{2}\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{1}{2} \cdot x} \]
6. Step-by-step derivation

   1. *-lowering-*.f64 52.0%

      \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{x}\right) \]

7. Simplified 52.0%

   \[\leadsto \color{blue}{0.5 \cdot x} \]

8. Final simplification 52.0%

   \[\leadsto x \cdot 0.5 \]
9. Add Preprocessing

Developer Target 1: 100.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \tan \left(\frac{x}{2}\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (tan (/ x 2.0)))

C

double code(double x) {
	return tan((x / 2.0));
}

Fortran

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

Java

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

Python

def code(x):
	return math.tan((x / 2.0))

Julia

function code(x)
	return tan(Float64(x / 2.0))
end

MATLAB

function tmp = code(x)
	tmp = tan((x / 2.0));
end

Wolfram

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

Reproduce

herbie shell --seed 2024139 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :precision binary64

  :alt
  (! :herbie-platform default (tan (/ x 2)))

  (/ (- 1.0 (cos x)) (sin x)))