sintan (problem 3.4.5)

Average Accuracy: 51.9% → 100.0%

Time: 19.2s

Precision: binary64

Cost: 13636

Math

\[\frac{x - \sin x}{x - \tan x} \]

↓

\[\begin{array}{l} \mathbf{if}\;x \leq -0.086:\\ \;\;\;\;\frac{\frac{1}{\tan x - x}}{\frac{1}{\sin x - x}}\\ \mathbf{elif}\;x \leq 0.086:\\ \;\;\;\;\left(\left(x \cdot x\right) \cdot 0.225 + {x}^{4} \cdot \left(\left(x \cdot x\right) \cdot 0.00024107142857142857 + -0.009642857142857142\right)\right) + -0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \sin x}{x - \tan x}\\ \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ (- x (sin x)) (- x (tan x))))

↓

(FPCore (x)
 :precision binary64
 (if (<= x -0.086)
   (/ (/ 1.0 (- (tan x) x)) (/ 1.0 (- (sin x) x)))
   (if (<= x 0.086)
     (+
      (+
       (* (* x x) 0.225)
       (*
        (pow x 4.0)
        (+ (* (* x x) 0.00024107142857142857) -0.009642857142857142)))
      -0.5)
     (/ (- x (sin x)) (- x (tan x))))))

C

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

↓

double code(double x) {
	double tmp;
	if (x <= -0.086) {
		tmp = (1.0 / (tan(x) - x)) / (1.0 / (sin(x) - x));
	} else if (x <= 0.086) {
		tmp = (((x * x) * 0.225) + (pow(x, 4.0) * (((x * x) * 0.00024107142857142857) + -0.009642857142857142))) + -0.5;
	} else {
		tmp = (x - sin(x)) / (x - tan(x));
	}
	return tmp;
}

Fortran

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

↓

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-0.086d0)) then
        tmp = (1.0d0 / (tan(x) - x)) / (1.0d0 / (sin(x) - x))
    else if (x <= 0.086d0) then
        tmp = (((x * x) * 0.225d0) + ((x ** 4.0d0) * (((x * x) * 0.00024107142857142857d0) + (-0.009642857142857142d0)))) + (-0.5d0)
    else
        tmp = (x - sin(x)) / (x - tan(x))
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x) {
	double tmp;
	if (x <= -0.086) {
		tmp = (1.0 / (Math.tan(x) - x)) / (1.0 / (Math.sin(x) - x));
	} else if (x <= 0.086) {
		tmp = (((x * x) * 0.225) + (Math.pow(x, 4.0) * (((x * x) * 0.00024107142857142857) + -0.009642857142857142))) + -0.5;
	} else {
		tmp = (x - Math.sin(x)) / (x - Math.tan(x));
	}
	return tmp;
}

Python

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

↓

def code(x):
	tmp = 0
	if x <= -0.086:
		tmp = (1.0 / (math.tan(x) - x)) / (1.0 / (math.sin(x) - x))
	elif x <= 0.086:
		tmp = (((x * x) * 0.225) + (math.pow(x, 4.0) * (((x * x) * 0.00024107142857142857) + -0.009642857142857142))) + -0.5
	else:
		tmp = (x - math.sin(x)) / (x - math.tan(x))
	return tmp

Julia

function code(x)
	return Float64(Float64(x - sin(x)) / Float64(x - tan(x)))
end

↓

function code(x)
	tmp = 0.0
	if (x <= -0.086)
		tmp = Float64(Float64(1.0 / Float64(tan(x) - x)) / Float64(1.0 / Float64(sin(x) - x)));
	elseif (x <= 0.086)
		tmp = Float64(Float64(Float64(Float64(x * x) * 0.225) + Float64((x ^ 4.0) * Float64(Float64(Float64(x * x) * 0.00024107142857142857) + -0.009642857142857142))) + -0.5);
	else
		tmp = Float64(Float64(x - sin(x)) / Float64(x - tan(x)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -0.086)
		tmp = (1.0 / (tan(x) - x)) / (1.0 / (sin(x) - x));
	elseif (x <= 0.086)
		tmp = (((x * x) * 0.225) + ((x ^ 4.0) * (((x * x) * 0.00024107142857142857) + -0.009642857142857142))) + -0.5;
	else
		tmp = (x - sin(x)) / (x - tan(x));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_] := If[LessEqual[x, -0.086], N[(N[(1.0 / N[(N[Tan[x], $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[(N[Sin[x], $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.086], N[(N[(N[(N[(x * x), $MachinePrecision] * 0.225), $MachinePrecision] + N[(N[Power[x, 4.0], $MachinePrecision] * N[(N[(N[(x * x), $MachinePrecision] * 0.00024107142857142857), $MachinePrecision] + -0.009642857142857142), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -0.5), $MachinePrecision], N[(N[(x - N[Sin[x], $MachinePrecision]), $MachinePrecision] / N[(x - N[Tan[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.085999999999999993

   1. Initial program 99.9%

      \[\frac{x - \sin x}{x - \tan x} \]

   2. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{\sin x - x}{\tan x - x}} \]
      Proof

      [Start] 99.9	\[ \frac{x - \sin x}{x - \tan x} \]
      sub-neg [=>] 99.9	\[ \frac{\color{blue}{x + \left(-\sin x\right)}}{x - \tan x} \]
      +-commutative [=>] 99.9	\[ \frac{\color{blue}{\left(-\sin x\right) + x}}{x - \tan x} \]
      neg-sub0 [=>] 99.9	\[ \frac{\color{blue}{\left(0 - \sin x\right)} + x}{x - \tan x} \]
      associate-+l- [=>] 99.9	\[ \frac{\color{blue}{0 - \left(\sin x - x\right)}}{x - \tan x} \]
      sub0-neg [=>] 99.9	\[ \frac{\color{blue}{-\left(\sin x - x\right)}}{x - \tan x} \]
      neg-mul-1 [=>] 99.9	\[ \frac{\color{blue}{-1 \cdot \left(\sin x - x\right)}}{x - \tan x} \]
      sub-neg [=>] 99.9	\[ \frac{-1 \cdot \left(\sin x - x\right)}{\color{blue}{x + \left(-\tan x\right)}} \]
      +-commutative [=>] 99.9	\[ \frac{-1 \cdot \left(\sin x - x\right)}{\color{blue}{\left(-\tan x\right) + x}} \]
      neg-sub0 [=>] 99.9	\[ \frac{-1 \cdot \left(\sin x - x\right)}{\color{blue}{\left(0 - \tan x\right)} + x} \]
      associate-+l- [=>] 99.9	\[ \frac{-1 \cdot \left(\sin x - x\right)}{\color{blue}{0 - \left(\tan x - x\right)}} \]
      sub0-neg [=>] 99.9	\[ \frac{-1 \cdot \left(\sin x - x\right)}{\color{blue}{-\left(\tan x - x\right)}} \]
      neg-mul-1 [=>] 99.9	\[ \frac{-1 \cdot \left(\sin x - x\right)}{\color{blue}{-1 \cdot \left(\tan x - x\right)}} \]
      times-frac [=>] 99.9	\[ \color{blue}{\frac{-1}{-1} \cdot \frac{\sin x - x}{\tan x - x}} \]
      metadata-eval [=>] 99.9	\[ \color{blue}{1} \cdot \frac{\sin x - x}{\tan x - x} \]
      *-lft-identity [=>] 99.9	\[ \color{blue}{\frac{\sin x - x}{\tan x - x}} \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{1}{\tan x - x} \cdot \left(\sin x - x\right)} \]
      Proof

      [Start] 99.9	\[ \frac{\sin x - x}{\tan x - x} \]
      div-inv [=>] 99.7	\[ \color{blue}{\left(\sin x - x\right) \cdot \frac{1}{\tan x - x}} \]
      *-commutative [=>] 99.7	\[ \color{blue}{\frac{1}{\tan x - x} \cdot \left(\sin x - x\right)} \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{\frac{1}{\tan x - x}}{\frac{1}{\sin x - x}}} \]
      Proof

      [Start] 99.7	\[ \frac{1}{\tan x - x} \cdot \left(\sin x - x\right) \]
      flip-- [=>] 51.7	\[ \frac{1}{\tan x - x} \cdot \color{blue}{\frac{\sin x \cdot \sin x - x \cdot x}{\sin x + x}} \]
      associate-*r/ [=>] 51.7	\[ \color{blue}{\frac{\frac{1}{\tan x - x} \cdot \left(\sin x \cdot \sin x - x \cdot x\right)}{\sin x + x}} \]
      associate-/l* [=>] 51.7	\[ \color{blue}{\frac{\frac{1}{\tan x - x}}{\frac{\sin x + x}{\sin x \cdot \sin x - x \cdot x}}} \]
      *-un-lft-identity [=>] 51.7	\[ \frac{\frac{1}{\tan x - x}}{\frac{\color{blue}{1 \cdot \left(\sin x + x\right)}}{\sin x \cdot \sin x - x \cdot x}} \]
      associate-/l* [=>] 51.8	\[ \frac{\frac{1}{\tan x - x}}{\color{blue}{\frac{1}{\frac{\sin x \cdot \sin x - x \cdot x}{\sin x + x}}}} \]
      flip-- [<=] 99.9	\[ \frac{\frac{1}{\tan x - x}}{\frac{1}{\color{blue}{\sin x - x}}} \]

   if -0.085999999999999993 < x < 0.085999999999999993

   1. Initial program 1.1%

      \[\frac{x - \sin x}{x - \tan x} \]

   2. Simplified 1.1%

      \[\leadsto \color{blue}{\frac{\sin x - x}{\tan x - x}} \]
      Proof

      [Start] 1.1	\[ \frac{x - \sin x}{x - \tan x} \]
      sub-neg [=>] 1.1	\[ \frac{\color{blue}{x + \left(-\sin x\right)}}{x - \tan x} \]
      +-commutative [=>] 1.1	\[ \frac{\color{blue}{\left(-\sin x\right) + x}}{x - \tan x} \]
      neg-sub0 [=>] 1.1	\[ \frac{\color{blue}{\left(0 - \sin x\right)} + x}{x - \tan x} \]
      associate-+l- [=>] 1.1	\[ \frac{\color{blue}{0 - \left(\sin x - x\right)}}{x - \tan x} \]
      sub0-neg [=>] 1.1	\[ \frac{\color{blue}{-\left(\sin x - x\right)}}{x - \tan x} \]
      neg-mul-1 [=>] 1.1	\[ \frac{\color{blue}{-1 \cdot \left(\sin x - x\right)}}{x - \tan x} \]
      sub-neg [=>] 1.1	\[ \frac{-1 \cdot \left(\sin x - x\right)}{\color{blue}{x + \left(-\tan x\right)}} \]
      +-commutative [=>] 1.1	\[ \frac{-1 \cdot \left(\sin x - x\right)}{\color{blue}{\left(-\tan x\right) + x}} \]
      neg-sub0 [=>] 1.1	\[ \frac{-1 \cdot \left(\sin x - x\right)}{\color{blue}{\left(0 - \tan x\right)} + x} \]
      associate-+l- [=>] 1.1	\[ \frac{-1 \cdot \left(\sin x - x\right)}{\color{blue}{0 - \left(\tan x - x\right)}} \]
      sub0-neg [=>] 1.1	\[ \frac{-1 \cdot \left(\sin x - x\right)}{\color{blue}{-\left(\tan x - x\right)}} \]
      neg-mul-1 [=>] 1.1	\[ \frac{-1 \cdot \left(\sin x - x\right)}{\color{blue}{-1 \cdot \left(\tan x - x\right)}} \]
      times-frac [=>] 1.1	\[ \color{blue}{\frac{-1}{-1} \cdot \frac{\sin x - x}{\tan x - x}} \]
      metadata-eval [=>] 1.1	\[ \color{blue}{1} \cdot \frac{\sin x - x}{\tan x - x} \]
      *-lft-identity [=>] 1.1	\[ \color{blue}{\frac{\sin x - x}{\tan x - x}} \]

   3. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{\left(0.225 \cdot {x}^{2} + \left(-0.009642857142857142 \cdot {x}^{4} + 0.00024107142857142857 \cdot {x}^{6}\right)\right) - 0.5} \]

   4. Applied egg-rr 100.0%

      \[\leadsto \left(\color{blue}{\left(e^{\mathsf{log1p}\left(0.225 \cdot \left(x \cdot x\right)\right)} - 1\right)} + \left(-0.009642857142857142 \cdot {x}^{4} + 0.00024107142857142857 \cdot {x}^{6}\right)\right) - 0.5 \]
      Proof

      [Start] 100.0	\[ \left(0.225 \cdot {x}^{2} + \left(-0.009642857142857142 \cdot {x}^{4} + 0.00024107142857142857 \cdot {x}^{6}\right)\right) - 0.5 \]
      expm1-log1p-u [=>] 100.0	\[ \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.225 \cdot {x}^{2}\right)\right)} + \left(-0.009642857142857142 \cdot {x}^{4} + 0.00024107142857142857 \cdot {x}^{6}\right)\right) - 0.5 \]
      expm1-udef [=>] 100.0	\[ \left(\color{blue}{\left(e^{\mathsf{log1p}\left(0.225 \cdot {x}^{2}\right)} - 1\right)} + \left(-0.009642857142857142 \cdot {x}^{4} + 0.00024107142857142857 \cdot {x}^{6}\right)\right) - 0.5 \]
      unpow2 [=>] 100.0	\[ \left(\left(e^{\mathsf{log1p}\left(0.225 \cdot \color{blue}{\left(x \cdot x\right)}\right)} - 1\right) + \left(-0.009642857142857142 \cdot {x}^{4} + 0.00024107142857142857 \cdot {x}^{6}\right)\right) - 0.5 \]

   5. Simplified 100.0%

      \[\leadsto \left(\color{blue}{\left(x \cdot x\right) \cdot 0.225} + \left(-0.009642857142857142 \cdot {x}^{4} + 0.00024107142857142857 \cdot {x}^{6}\right)\right) - 0.5 \]
      Proof

      [Start] 100.0	\[ \left(\left(e^{\mathsf{log1p}\left(0.225 \cdot \left(x \cdot x\right)\right)} - 1\right) + \left(-0.009642857142857142 \cdot {x}^{4} + 0.00024107142857142857 \cdot {x}^{6}\right)\right) - 0.5 \]
      expm1-def [=>] 100.0	\[ \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.225 \cdot \left(x \cdot x\right)\right)\right)} + \left(-0.009642857142857142 \cdot {x}^{4} + 0.00024107142857142857 \cdot {x}^{6}\right)\right) - 0.5 \]
      expm1-log1p [=>] 100.0	\[ \left(\color{blue}{0.225 \cdot \left(x \cdot x\right)} + \left(-0.009642857142857142 \cdot {x}^{4} + 0.00024107142857142857 \cdot {x}^{6}\right)\right) - 0.5 \]
      *-commutative [=>] 100.0	\[ \left(\color{blue}{\left(x \cdot x\right) \cdot 0.225} + \left(-0.009642857142857142 \cdot {x}^{4} + 0.00024107142857142857 \cdot {x}^{6}\right)\right) - 0.5 \]

   6. Applied egg-rr 100.0%

      \[\leadsto \left(\left(x \cdot x\right) \cdot 0.225 + \color{blue}{{x}^{4} \cdot \left(\left(x \cdot x\right) \cdot 0.00024107142857142857 + -0.009642857142857142\right)}\right) - 0.5 \]
      Proof

      [Start] 100.0	\[ \left(\left(x \cdot x\right) \cdot 0.225 + \left(-0.009642857142857142 \cdot {x}^{4} + 0.00024107142857142857 \cdot {x}^{6}\right)\right) - 0.5 \]
      +-commutative [=>] 100.0	\[ \left(\left(x \cdot x\right) \cdot 0.225 + \color{blue}{\left(0.00024107142857142857 \cdot {x}^{6} + -0.009642857142857142 \cdot {x}^{4}\right)}\right) - 0.5 \]
      *-commutative [=>] 100.0	\[ \left(\left(x \cdot x\right) \cdot 0.225 + \left(\color{blue}{{x}^{6} \cdot 0.00024107142857142857} + -0.009642857142857142 \cdot {x}^{4}\right)\right) - 0.5 \]
      add-cube-cbrt [=>] 100.0	\[ \left(\left(x \cdot x\right) \cdot 0.225 + \left(\color{blue}{\left(\left(\sqrt[3]{{x}^{6}} \cdot \sqrt[3]{{x}^{6}}\right) \cdot \sqrt[3]{{x}^{6}}\right)} \cdot 0.00024107142857142857 + -0.009642857142857142 \cdot {x}^{4}\right)\right) - 0.5 \]
      associate-*l* [=>] 100.0	\[ \left(\left(x \cdot x\right) \cdot 0.225 + \left(\color{blue}{\left(\sqrt[3]{{x}^{6}} \cdot \sqrt[3]{{x}^{6}}\right) \cdot \left(\sqrt[3]{{x}^{6}} \cdot 0.00024107142857142857\right)} + -0.009642857142857142 \cdot {x}^{4}\right)\right) - 0.5 \]
      pow2 [=>] 100.0	\[ \left(\left(x \cdot x\right) \cdot 0.225 + \left(\color{blue}{{\left(\sqrt[3]{{x}^{6}}\right)}^{2}} \cdot \left(\sqrt[3]{{x}^{6}} \cdot 0.00024107142857142857\right) + -0.009642857142857142 \cdot {x}^{4}\right)\right) - 0.5 \]
      metadata-eval [<=] 100.0	\[ \left(\left(x \cdot x\right) \cdot 0.225 + \left({\left(\sqrt[3]{{x}^{\color{blue}{\left(4 + 2\right)}}}\right)}^{2} \cdot \left(\sqrt[3]{{x}^{6}} \cdot 0.00024107142857142857\right) + -0.009642857142857142 \cdot {x}^{4}\right)\right) - 0.5 \]
      pow-prod-up [<=] 100.0	\[ \left(\left(x \cdot x\right) \cdot 0.225 + \left({\left(\sqrt[3]{\color{blue}{{x}^{4} \cdot {x}^{2}}}\right)}^{2} \cdot \left(\sqrt[3]{{x}^{6}} \cdot 0.00024107142857142857\right) + -0.009642857142857142 \cdot {x}^{4}\right)\right) - 0.5 \]
      metadata-eval [<=] 100.0	\[ \left(\left(x \cdot x\right) \cdot 0.225 + \left({\left(\sqrt[3]{{x}^{\color{blue}{\left(2 + 2\right)}} \cdot {x}^{2}}\right)}^{2} \cdot \left(\sqrt[3]{{x}^{6}} \cdot 0.00024107142857142857\right) + -0.009642857142857142 \cdot {x}^{4}\right)\right) - 0.5 \]
      pow-prod-up [<=] 100.0	\[ \left(\left(x \cdot x\right) \cdot 0.225 + \left({\left(\sqrt[3]{\color{blue}{\left({x}^{2} \cdot {x}^{2}\right)} \cdot {x}^{2}}\right)}^{2} \cdot \left(\sqrt[3]{{x}^{6}} \cdot 0.00024107142857142857\right) + -0.009642857142857142 \cdot {x}^{4}\right)\right) - 0.5 \]
      add-cbrt-cube [<=] 100.0	\[ \left(\left(x \cdot x\right) \cdot 0.225 + \left({\color{blue}{\left({x}^{2}\right)}}^{2} \cdot \left(\sqrt[3]{{x}^{6}} \cdot 0.00024107142857142857\right) + -0.009642857142857142 \cdot {x}^{4}\right)\right) - 0.5 \]
      pow2 [<=] 100.0	\[ \left(\left(x \cdot x\right) \cdot 0.225 + \left(\color{blue}{\left({x}^{2} \cdot {x}^{2}\right)} \cdot \left(\sqrt[3]{{x}^{6}} \cdot 0.00024107142857142857\right) + -0.009642857142857142 \cdot {x}^{4}\right)\right) - 0.5 \]
      pow-prod-up [=>] 100.0	\[ \left(\left(x \cdot x\right) \cdot 0.225 + \left(\color{blue}{{x}^{\left(2 + 2\right)}} \cdot \left(\sqrt[3]{{x}^{6}} \cdot 0.00024107142857142857\right) + -0.009642857142857142 \cdot {x}^{4}\right)\right) - 0.5 \]
      metadata-eval [=>] 100.0	\[ \left(\left(x \cdot x\right) \cdot 0.225 + \left({x}^{\color{blue}{4}} \cdot \left(\sqrt[3]{{x}^{6}} \cdot 0.00024107142857142857\right) + -0.009642857142857142 \cdot {x}^{4}\right)\right) - 0.5 \]
      *-commutative [=>] 100.0	\[ \left(\left(x \cdot x\right) \cdot 0.225 + \left({x}^{4} \cdot \left(\sqrt[3]{{x}^{6}} \cdot 0.00024107142857142857\right) + \color{blue}{{x}^{4} \cdot -0.009642857142857142}\right)\right) - 0.5 \]
      distribute-lft-out [=>] 100.0	\[ \left(\left(x \cdot x\right) \cdot 0.225 + \color{blue}{{x}^{4} \cdot \left(\sqrt[3]{{x}^{6}} \cdot 0.00024107142857142857 + -0.009642857142857142\right)}\right) - 0.5 \]

   if 0.085999999999999993 < x

   1. Initial program 99.9%

      \[\frac{x - \sin x}{x - \tan x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.086:\\ \;\;\;\;\frac{\frac{1}{\tan x - x}}{\frac{1}{\sin x - x}}\\ \mathbf{elif}\;x \leq 0.086:\\ \;\;\;\;\left(\left(x \cdot x\right) \cdot 0.225 + {x}^{4} \cdot \left(\left(x \cdot x\right) \cdot 0.00024107142857142857 + -0.009642857142857142\right)\right) + -0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \sin x}{x - \tan x}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	100.0%
Cost	13513

\[\begin{array}{l} \mathbf{if}\;x \leq -0.086 \lor \neg \left(x \leq 0.086\right):\\ \;\;\;\;\frac{x - \sin x}{x - \tan x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot x\right) \cdot 0.225 + {x}^{4} \cdot \left(\left(x \cdot x\right) \cdot 0.00024107142857142857 + -0.009642857142857142\right)\right) + -0.5\\ \end{array} \]

Alternative 2
Accuracy	99.0%
Cost	7816

\[\begin{array}{l} \mathbf{if}\;x \leq -4.5:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.5:\\ \;\;\;\;\left(\left(x \cdot x\right) \cdot 0.225 + {x}^{4} \cdot \left(\left(x \cdot x\right) \cdot 0.00024107142857142857 + -0.009642857142857142\right)\right) + -0.5\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Accuracy	98.9%
Cost	1096

\[\begin{array}{l} \mathbf{if}\;x \leq -2.9:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(0.225 + \left(x \cdot x\right) \cdot -0.009642857142857142\right) + -0.5\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Accuracy	98.8%
Cost	712

\[\begin{array}{l} \mathbf{if}\;x \leq -2.6:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.5:\\ \;\;\;\;x \cdot \left(x \cdot 0.225\right) + -0.5\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Accuracy	98.6%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -1.55:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.6:\\ \;\;\;\;-0.5\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Accuracy	49.2%
Cost	64

\[-0.5 \]

Reproduce

herbie shell --seed 2023126 
(FPCore (x)
  :name "sintan (problem 3.4.5)"
  :precision binary64
  (/ (- x (sin x)) (- x (tan x))))