Average Error: 35.6 → 28.5
Time: 13.8s
Precision: binary64
Cost: 64
\[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \]
↓
\[1 \]
(FPCore (x y)
 :precision binary64
 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))
↓
(FPCore (x y) :precision binary64 1.0)
double code(double x, double y) {
	return tan((x / (y * 2.0))) / sin((x / (y * 2.0)));
}
↓
double code(double x, double y) {
	return 1.0;
}

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = tan((x / (y * 2.0d0))) / sin((x / (y * 2.0d0)))
end function
↓
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

public static double code(double x, double y) {
	return Math.tan((x / (y * 2.0))) / Math.sin((x / (y * 2.0)));
}
↓
public static double code(double x, double y) {
	return 1.0;
}

def code(x, y):
	return math.tan((x / (y * 2.0))) / math.sin((x / (y * 2.0)))
↓
def code(x, y):
	return 1.0

function code(x, y)
	return Float64(tan(Float64(x / Float64(y * 2.0))) / sin(Float64(x / Float64(y * 2.0))))
end
↓
function code(x, y)
	return 1.0
end

function tmp = code(x, y)
	tmp = tan((x / (y * 2.0))) / sin((x / (y * 2.0)));
end
↓
function tmp = code(x, y)
	tmp = 1.0;
end

code[x_, y_] := N[(N[Tan[N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[Sin[N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := 1.0

\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}
↓
1

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original35.6
Target28.9
Herbie28.5
\[\begin{array}{l} \mathbf{if}\;y < -1.2303690911306994 \cdot 10^{+114}:\\ \;\;\;\;1\\ \mathbf{elif}\;y < -9.102852406811914 \cdot 10^{-222}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Derivation

  1. Initial program 35.6

    \[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \]

  2. Applied egg-rr28.5

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{1}{\cos \left(x \cdot \frac{0.5}{y}\right)}\right)\right)} \]

  3. Applied egg-rr28.4

    \[\leadsto \color{blue}{{\left(\frac{1}{\sqrt[3]{\cos \left(x \cdot \frac{0.5}{y}\right)}}\right)}^{3}} \]

  4. Applied egg-rr28.5

    \[\leadsto {\left(\frac{1}{\sqrt[3]{\cos \color{blue}{\left({\left(\sqrt[3]{x \cdot \frac{0.5}{y}}\right)}^{3}\right)}}}\right)}^{3} \]

  5. Taylor expanded in x around 0 28.5

    \[\leadsto \color{blue}{1} \]

  6. Final simplification28.5

    \[\leadsto 1 \]

Reproduce

herbie shell --seed 2022300 
(FPCore (x y)
  :name "Diagrams.TwoD.Layout.CirclePacking:approxRadius from diagrams-contrib-1.3.0.5"
  :precision binary64

  :herbie-target
  (if (< y -1.2303690911306994e+114) 1.0 (if (< y -9.102852406811914e-222) (/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (log (exp (cos (/ x (* y 2.0))))))) 1.0))

  (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))