Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C

Percentage Accurate: 100.0% → 100.0%

Time: 9.9s

Alternatives: 9

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))

C

double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((2.30753d0 + (x * 0.27061d0)) / (1.0d0 + (x * (0.99229d0 + (x * 0.04481d0))))) - x
end function

Java

public static double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
}

Python

def code(x):
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x

Julia

function code(x)
	return Float64(Float64(Float64(2.30753 + Float64(x * 0.27061)) / Float64(1.0 + Float64(x * Float64(0.99229 + Float64(x * 0.04481))))) - x)
end

MATLAB

function tmp = code(x)
	tmp = ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
end

Wolfram

code[x_] := N[(N[(N[(2.30753 + N[(x * 0.27061), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(x * N[(0.99229 + N[(x * 0.04481), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))

C

double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((2.30753d0 + (x * 0.27061d0)) / (1.0d0 + (x * (0.99229d0 + (x * 0.04481d0))))) - x
end function

Java

public static double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
}

Python

def code(x):
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x

Julia

function code(x)
	return Float64(Float64(Float64(2.30753 + Float64(x * 0.27061)) / Float64(1.0 + Float64(x * Float64(0.99229 + Float64(x * 0.04481))))) - x)
end

MATLAB

function tmp = code(x)
	tmp = ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
end

Wolfram

code[x_] := N[(N[(N[(2.30753 + N[(x * 0.27061), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(x * N[(0.99229 + N[(x * 0.04481), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \frac{2.30753 + x \cdot 0.27061}{1 + \frac{x}{\frac{1}{0.99229 + x \cdot 0.04481}}} - x \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (-
  (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (/ x (/ 1.0 (+ 0.99229 (* x 0.04481))))))
  x))

C

double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x / (1.0 / (0.99229 + (x * 0.04481)))))) - x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((2.30753d0 + (x * 0.27061d0)) / (1.0d0 + (x / (1.0d0 / (0.99229d0 + (x * 0.04481d0)))))) - x
end function

Java

public static double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x / (1.0 / (0.99229 + (x * 0.04481)))))) - x;
}

Python

def code(x):
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x / (1.0 / (0.99229 + (x * 0.04481)))))) - x

Julia

function code(x)
	return Float64(Float64(Float64(2.30753 + Float64(x * 0.27061)) / Float64(1.0 + Float64(x / Float64(1.0 / Float64(0.99229 + Float64(x * 0.04481)))))) - x)
end

MATLAB

function tmp = code(x)
	tmp = ((2.30753 + (x * 0.27061)) / (1.0 + (x / (1.0 / (0.99229 + (x * 0.04481)))))) - x;
end

Wolfram

code[x_] := N[(N[(N[(2.30753 + N[(x * 0.27061), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(x / N[(1.0 / N[(0.99229 + N[(x * 0.04481), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \]
2. Add Preprocessing
3. Step-by-step derivation

   1. flip3-+ N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \left(x \cdot \frac{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}\right)\right)\right), x\right) \]

   2. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \left(x \cdot \frac{1}{\frac{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}}\right)\right)\right), x\right) \]

   3. un-div-inv N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \left(\frac{x}{\frac{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}}\right)\right)\right), x\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \left(\frac{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}\right)\right)\right)\right), x\right) \]

   5. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}}\right)\right)\right)\right), x\right) \]

   6. flip3-+ N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{99229}{100000} + x \cdot \frac{4481}{100000}}\right)\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left(\frac{99229}{100000} + x \cdot \frac{4481}{100000}\right)\right)\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{99229}{100000}, \left(x \cdot \frac{4481}{100000}\right)\right)\right)\right)\right)\right), x\right) \]

   9. *-lowering-*.f64 100.0%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{99229}{100000}, \mathsf{*.f64}\left(x, \frac{4481}{100000}\right)\right)\right)\right)\right)\right), x\right) \]

4. Applied egg-rr 100.0%

   \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{\frac{x}{\frac{1}{0.99229 + x \cdot 0.04481}}}} - x \]
5. Add Preprocessing

Alternative 2: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))

C

double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((2.30753d0 + (x * 0.27061d0)) / (1.0d0 + (x * (0.99229d0 + (x * 0.04481d0))))) - x
end function

Java

public static double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
}

Python

def code(x):
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x

Julia

function code(x)
	return Float64(Float64(Float64(2.30753 + Float64(x * 0.27061)) / Float64(1.0 + Float64(x * Float64(0.99229 + Float64(x * 0.04481))))) - x)
end

MATLAB

function tmp = code(x)
	tmp = ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
end

Wolfram

code[x_] := N[(N[(N[(2.30753 + N[(x * 0.27061), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(x * N[(0.99229 + N[(x * 0.04481), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 3: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{0.4333638132548656 + x \cdot \left(0.37920088514346545 + x \cdot \left(-0.025050834237766436 + x \cdot 0.0029377759999141832\right)\right)} - x \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (-
  (/
   1.0
   (+
    0.4333638132548656
    (*
     x
     (+
      0.37920088514346545
      (* x (+ -0.025050834237766436 (* x 0.0029377759999141832)))))))
  x))

C

double code(double x) {
	return (1.0 / (0.4333638132548656 + (x * (0.37920088514346545 + (x * (-0.025050834237766436 + (x * 0.0029377759999141832))))))) - x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (1.0d0 / (0.4333638132548656d0 + (x * (0.37920088514346545d0 + (x * ((-0.025050834237766436d0) + (x * 0.0029377759999141832d0))))))) - x
end function

Java

public static double code(double x) {
	return (1.0 / (0.4333638132548656 + (x * (0.37920088514346545 + (x * (-0.025050834237766436 + (x * 0.0029377759999141832))))))) - x;
}

Python

def code(x):
	return (1.0 / (0.4333638132548656 + (x * (0.37920088514346545 + (x * (-0.025050834237766436 + (x * 0.0029377759999141832))))))) - x

Julia

function code(x)
	return Float64(Float64(1.0 / Float64(0.4333638132548656 + Float64(x * Float64(0.37920088514346545 + Float64(x * Float64(-0.025050834237766436 + Float64(x * 0.0029377759999141832))))))) - x)
end

MATLAB

function tmp = code(x)
	tmp = (1.0 / (0.4333638132548656 + (x * (0.37920088514346545 + (x * (-0.025050834237766436 + (x * 0.0029377759999141832))))))) - x;
end

Wolfram

code[x_] := N[(N[(1.0 / N[(0.4333638132548656 + N[(x * N[(0.37920088514346545 + N[(x * N[(-0.025050834237766436 + N[(x * 0.0029377759999141832), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \]
2. Add Preprocessing
3. Step-by-step derivation

   1. flip3-+ N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \left(x \cdot \frac{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}\right)\right)\right), x\right) \]

   2. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \left(x \cdot \frac{1}{\frac{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}}\right)\right)\right), x\right) \]

   3. un-div-inv N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \left(\frac{x}{\frac{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}}\right)\right)\right), x\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \left(\frac{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}\right)\right)\right)\right), x\right) \]

   5. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}}\right)\right)\right)\right), x\right) \]

   6. flip3-+ N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{99229}{100000} + x \cdot \frac{4481}{100000}}\right)\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left(\frac{99229}{100000} + x \cdot \frac{4481}{100000}\right)\right)\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{99229}{100000}, \left(x \cdot \frac{4481}{100000}\right)\right)\right)\right)\right)\right), x\right) \]

   9. *-lowering-*.f64 100.0%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{99229}{100000}, \mathsf{*.f64}\left(x, \frac{4481}{100000}\right)\right)\right)\right)\right)\right), x\right) \]

4. Applied egg-rr 100.0%

   \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{\frac{x}{\frac{1}{0.99229 + x \cdot 0.04481}}}} - x \]

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\frac{1}{\frac{1}{2.30753 + x \cdot 0.27061} \cdot \left(1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)\right)}} - x \]

7. Taylor expanded in x around 0

   \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \color{blue}{\left(\frac{100000}{230753} + x \cdot \left(\frac{20191289437}{53246947009} + x \cdot \left(\frac{8329292287246203008}{2835237365779254046081} \cdot x - \frac{307796913907328}{12286892763167777}\right)\right)\right)}\right), x\right) \]
8. Step-by-step derivation

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \left(x \cdot \left(\frac{20191289437}{53246947009} + x \cdot \left(\frac{8329292287246203008}{2835237365779254046081} \cdot x - \frac{307796913907328}{12286892763167777}\right)\right)\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \left(\frac{20191289437}{53246947009} + x \cdot \left(\frac{8329292287246203008}{2835237365779254046081} \cdot x - \frac{307796913907328}{12286892763167777}\right)\right)\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{20191289437}{53246947009}, \left(x \cdot \left(\frac{8329292287246203008}{2835237365779254046081} \cdot x - \frac{307796913907328}{12286892763167777}\right)\right)\right)\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{20191289437}{53246947009}, \mathsf{*.f64}\left(x, \left(\frac{8329292287246203008}{2835237365779254046081} \cdot x - \frac{307796913907328}{12286892763167777}\right)\right)\right)\right)\right)\right), x\right) \]

   5. sub-neg N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{20191289437}{53246947009}, \mathsf{*.f64}\left(x, \left(\frac{8329292287246203008}{2835237365779254046081} \cdot x + \left(\mathsf{neg}\left(\frac{307796913907328}{12286892763167777}\right)\right)\right)\right)\right)\right)\right)\right), x\right) \]

   6. metadata-eval N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{20191289437}{53246947009}, \mathsf{*.f64}\left(x, \left(\frac{8329292287246203008}{2835237365779254046081} \cdot x + \frac{-307796913907328}{12286892763167777}\right)\right)\right)\right)\right)\right), x\right) \]

   7. +-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{20191289437}{53246947009}, \mathsf{*.f64}\left(x, \left(\frac{-307796913907328}{12286892763167777} + \frac{8329292287246203008}{2835237365779254046081} \cdot x\right)\right)\right)\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{20191289437}{53246947009}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{-307796913907328}{12286892763167777}, \left(\frac{8329292287246203008}{2835237365779254046081} \cdot x\right)\right)\right)\right)\right)\right)\right), x\right) \]

   9. *-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{20191289437}{53246947009}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{-307796913907328}{12286892763167777}, \left(x \cdot \frac{8329292287246203008}{2835237365779254046081}\right)\right)\right)\right)\right)\right)\right), x\right) \]

   10. *-lowering-*.f64 99.2%

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{20191289437}{53246947009}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{-307796913907328}{12286892763167777}, \mathsf{*.f64}\left(x, \frac{8329292287246203008}{2835237365779254046081}\right)\right)\right)\right)\right)\right)\right), x\right) \]

9. Simplified 99.2%

   \[\leadsto \frac{1}{\color{blue}{0.4333638132548656 + x \cdot \left(0.37920088514346545 + x \cdot \left(-0.025050834237766436 + x \cdot 0.0029377759999141832\right)\right)}} - x \]
10. Add Preprocessing

Alternative 4: 99.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\left(0.4333638132548656 + x \cdot 0.37920088514346545\right) + -0.025050834237766436 \cdot \left(x \cdot x\right)} - x \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (-
  (/
   1.0
   (+
    (+ 0.4333638132548656 (* x 0.37920088514346545))
    (* -0.025050834237766436 (* x x))))
  x))

C

double code(double x) {
	return (1.0 / ((0.4333638132548656 + (x * 0.37920088514346545)) + (-0.025050834237766436 * (x * x)))) - x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (1.0d0 / ((0.4333638132548656d0 + (x * 0.37920088514346545d0)) + ((-0.025050834237766436d0) * (x * x)))) - x
end function

Java

public static double code(double x) {
	return (1.0 / ((0.4333638132548656 + (x * 0.37920088514346545)) + (-0.025050834237766436 * (x * x)))) - x;
}

Python

def code(x):
	return (1.0 / ((0.4333638132548656 + (x * 0.37920088514346545)) + (-0.025050834237766436 * (x * x)))) - x

Julia

function code(x)
	return Float64(Float64(1.0 / Float64(Float64(0.4333638132548656 + Float64(x * 0.37920088514346545)) + Float64(-0.025050834237766436 * Float64(x * x)))) - x)
end

MATLAB

function tmp = code(x)
	tmp = (1.0 / ((0.4333638132548656 + (x * 0.37920088514346545)) + (-0.025050834237766436 * (x * x)))) - x;
end

Wolfram

code[x_] := N[(N[(1.0 / N[(N[(0.4333638132548656 + N[(x * 0.37920088514346545), $MachinePrecision]), $MachinePrecision] + N[(-0.025050834237766436 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \]
2. Add Preprocessing
3. Step-by-step derivation

   1. flip3-+ N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \left(x \cdot \frac{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}\right)\right)\right), x\right) \]

   2. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \left(x \cdot \frac{1}{\frac{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}}\right)\right)\right), x\right) \]

   3. un-div-inv N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \left(\frac{x}{\frac{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}}\right)\right)\right), x\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \left(\frac{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}\right)\right)\right)\right), x\right) \]

   5. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}}\right)\right)\right)\right), x\right) \]

   6. flip3-+ N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{99229}{100000} + x \cdot \frac{4481}{100000}}\right)\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left(\frac{99229}{100000} + x \cdot \frac{4481}{100000}\right)\right)\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{99229}{100000}, \left(x \cdot \frac{4481}{100000}\right)\right)\right)\right)\right)\right), x\right) \]

   9. *-lowering-*.f64 100.0%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{99229}{100000}, \mathsf{*.f64}\left(x, \frac{4481}{100000}\right)\right)\right)\right)\right)\right), x\right) \]

4. Applied egg-rr 100.0%

   \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{\frac{x}{\frac{1}{0.99229 + x \cdot 0.04481}}}} - x \]

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\frac{1}{\frac{1}{2.30753 + x \cdot 0.27061} \cdot \left(1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)\right)}} - x \]

7. Taylor expanded in x around 0

   \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \color{blue}{\left(\frac{100000}{230753} + x \cdot \left(\frac{20191289437}{53246947009} + \frac{-307796913907328}{12286892763167777} \cdot x\right)\right)}\right), x\right) \]
8. Step-by-step derivation

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \left(x \cdot \left(\frac{20191289437}{53246947009} + \frac{-307796913907328}{12286892763167777} \cdot x\right)\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \left(\frac{20191289437}{53246947009} + \frac{-307796913907328}{12286892763167777} \cdot x\right)\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{20191289437}{53246947009}, \left(\frac{-307796913907328}{12286892763167777} \cdot x\right)\right)\right)\right)\right), x\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{20191289437}{53246947009}, \left(x \cdot \frac{-307796913907328}{12286892763167777}\right)\right)\right)\right)\right), x\right) \]

   5. *-lowering-*.f64 98.9%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{20191289437}{53246947009}, \mathsf{*.f64}\left(x, \frac{-307796913907328}{12286892763167777}\right)\right)\right)\right)\right), x\right) \]

9. Simplified 98.9%

   \[\leadsto \frac{1}{\color{blue}{0.4333638132548656 + x \cdot \left(0.37920088514346545 + x \cdot -0.025050834237766436\right)}} - x \]
10. Step-by-step derivation

    1. distribute-lft-in N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{100000}{230753} + \left(x \cdot \frac{20191289437}{53246947009} + x \cdot \left(x \cdot \frac{-307796913907328}{12286892763167777}\right)\right)\right)\right), x\right) \]

    2. associate-+r+ N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\left(\frac{100000}{230753} + x \cdot \frac{20191289437}{53246947009}\right) + x \cdot \left(x \cdot \frac{-307796913907328}{12286892763167777}\right)\right)\right), x\right) \]

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

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(\frac{100000}{230753} + x \cdot \frac{20191289437}{53246947009}\right), \left(x \cdot \left(x \cdot \frac{-307796913907328}{12286892763167777}\right)\right)\right)\right), x\right) \]

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

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{100000}{230753}, \left(x \cdot \frac{20191289437}{53246947009}\right)\right), \left(x \cdot \left(x \cdot \frac{-307796913907328}{12286892763167777}\right)\right)\right)\right), x\right) \]

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

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \frac{20191289437}{53246947009}\right)\right), \left(x \cdot \left(x \cdot \frac{-307796913907328}{12286892763167777}\right)\right)\right)\right), x\right) \]

    6. *-commutative N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \frac{20191289437}{53246947009}\right)\right), \left(\left(x \cdot \frac{-307796913907328}{12286892763167777}\right) \cdot x\right)\right)\right), x\right) \]

    7. *-commutative N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \frac{20191289437}{53246947009}\right)\right), \left(\left(\frac{-307796913907328}{12286892763167777} \cdot x\right) \cdot x\right)\right)\right), x\right) \]

    8. associate-*l* N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \frac{20191289437}{53246947009}\right)\right), \left(\frac{-307796913907328}{12286892763167777} \cdot \left(x \cdot x\right)\right)\right)\right), x\right) \]

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

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \frac{20191289437}{53246947009}\right)\right), \mathsf{*.f64}\left(\frac{-307796913907328}{12286892763167777}, \left(x \cdot x\right)\right)\right)\right), x\right) \]

    10. *-lowering-*.f64 98.9%

        \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \frac{20191289437}{53246947009}\right)\right), \mathsf{*.f64}\left(\frac{-307796913907328}{12286892763167777}, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), x\right) \]

11. Applied egg-rr 98.9%

    \[\leadsto \frac{1}{\color{blue}{\left(0.4333638132548656 + x \cdot 0.37920088514346545\right) + -0.025050834237766436 \cdot \left(x \cdot x\right)}} - x \]
12. Add Preprocessing

Alternative 5: 98.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05:\\ \;\;\;\;0 - x\\ \mathbf{elif}\;x \leq 1.16:\\ \;\;\;\;2.30753\\ \mathbf{else}:\\ \;\;\;\;0 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -1.05) (- 0.0 x) (if (<= x 1.16) 2.30753 (- 0.0 x))))

C

double code(double x) {
	double tmp;
	if (x <= -1.05) {
		tmp = 0.0 - x;
	} else if (x <= 1.16) {
		tmp = 2.30753;
	} else {
		tmp = 0.0 - x;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-1.05d0)) then
        tmp = 0.0d0 - x
    else if (x <= 1.16d0) then
        tmp = 2.30753d0
    else
        tmp = 0.0d0 - x
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -1.05) {
		tmp = 0.0 - x;
	} else if (x <= 1.16) {
		tmp = 2.30753;
	} else {
		tmp = 0.0 - x;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -1.05:
		tmp = 0.0 - x
	elif x <= 1.16:
		tmp = 2.30753
	else:
		tmp = 0.0 - x
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -1.05)
		tmp = Float64(0.0 - x);
	elseif (x <= 1.16)
		tmp = 2.30753;
	else
		tmp = Float64(0.0 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -1.05)
		tmp = 0.0 - x;
	elseif (x <= 1.16)
		tmp = 2.30753;
	else
		tmp = 0.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -1.05], N[(0.0 - x), $MachinePrecision], If[LessEqual[x, 1.16], 2.30753, N[(0.0 - x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05000000000000004 or 1.15999999999999992 < x

   1. Initial program 100.0%

      \[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{x} \]

      3. --lowering--.f64 99.1%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{x}\right) \]

   5. Simplified 99.1%

      \[\leadsto \color{blue}{0 - x} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(x\right) \]

      2. neg-lowering-neg.f64 99.1%

         \[\leadsto \mathsf{neg.f64}\left(x\right) \]

   7. Applied egg-rr 99.1%

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

   if -1.05000000000000004 < x < 1.15999999999999992

   1. Initial program 99.9%

      \[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{230753}{100000}} \]
   4. Step-by-step derivation

   5. Simplified 95.5%

      \[\leadsto \color{blue}{2.30753} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05:\\ \;\;\;\;0 - x\\ \mathbf{elif}\;x \leq 1.16:\\ \;\;\;\;2.30753\\ \mathbf{else}:\\ \;\;\;\;0 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \frac{1}{0.4333638132548656 + x \cdot \left(0.37920088514346545 + x \cdot -0.025050834237766436\right)} - x \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (-
  (/
   1.0
   (+
    0.4333638132548656
    (* x (+ 0.37920088514346545 (* x -0.025050834237766436)))))
  x))

C

double code(double x) {
	return (1.0 / (0.4333638132548656 + (x * (0.37920088514346545 + (x * -0.025050834237766436))))) - x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (1.0d0 / (0.4333638132548656d0 + (x * (0.37920088514346545d0 + (x * (-0.025050834237766436d0)))))) - x
end function

Java

public static double code(double x) {
	return (1.0 / (0.4333638132548656 + (x * (0.37920088514346545 + (x * -0.025050834237766436))))) - x;
}

Python

def code(x):
	return (1.0 / (0.4333638132548656 + (x * (0.37920088514346545 + (x * -0.025050834237766436))))) - x

Julia

function code(x)
	return Float64(Float64(1.0 / Float64(0.4333638132548656 + Float64(x * Float64(0.37920088514346545 + Float64(x * -0.025050834237766436))))) - x)
end

MATLAB

function tmp = code(x)
	tmp = (1.0 / (0.4333638132548656 + (x * (0.37920088514346545 + (x * -0.025050834237766436))))) - x;
end

Wolfram

code[x_] := N[(N[(1.0 / N[(0.4333638132548656 + N[(x * N[(0.37920088514346545 + N[(x * -0.025050834237766436), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \]
2. Add Preprocessing
3. Step-by-step derivation

   1. flip3-+ N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \left(x \cdot \frac{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}\right)\right)\right), x\right) \]

   2. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \left(x \cdot \frac{1}{\frac{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}}\right)\right)\right), x\right) \]

   3. un-div-inv N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \left(\frac{x}{\frac{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}}\right)\right)\right), x\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \left(\frac{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}\right)\right)\right)\right), x\right) \]

   5. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}}\right)\right)\right)\right), x\right) \]

   6. flip3-+ N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{99229}{100000} + x \cdot \frac{4481}{100000}}\right)\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left(\frac{99229}{100000} + x \cdot \frac{4481}{100000}\right)\right)\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{99229}{100000}, \left(x \cdot \frac{4481}{100000}\right)\right)\right)\right)\right)\right), x\right) \]

   9. *-lowering-*.f64 100.0%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{99229}{100000}, \mathsf{*.f64}\left(x, \frac{4481}{100000}\right)\right)\right)\right)\right)\right), x\right) \]

4. Applied egg-rr 100.0%

   \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{\frac{x}{\frac{1}{0.99229 + x \cdot 0.04481}}}} - x \]

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\frac{1}{\frac{1}{2.30753 + x \cdot 0.27061} \cdot \left(1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)\right)}} - x \]

7. Taylor expanded in x around 0

   \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \color{blue}{\left(\frac{100000}{230753} + x \cdot \left(\frac{20191289437}{53246947009} + \frac{-307796913907328}{12286892763167777} \cdot x\right)\right)}\right), x\right) \]
8. Step-by-step derivation

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \left(x \cdot \left(\frac{20191289437}{53246947009} + \frac{-307796913907328}{12286892763167777} \cdot x\right)\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \left(\frac{20191289437}{53246947009} + \frac{-307796913907328}{12286892763167777} \cdot x\right)\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{20191289437}{53246947009}, \left(\frac{-307796913907328}{12286892763167777} \cdot x\right)\right)\right)\right)\right), x\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{20191289437}{53246947009}, \left(x \cdot \frac{-307796913907328}{12286892763167777}\right)\right)\right)\right)\right), x\right) \]

   5. *-lowering-*.f64 98.9%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{20191289437}{53246947009}, \mathsf{*.f64}\left(x, \frac{-307796913907328}{12286892763167777}\right)\right)\right)\right)\right), x\right) \]

9. Simplified 98.9%

   \[\leadsto \frac{1}{\color{blue}{0.4333638132548656 + x \cdot \left(0.37920088514346545 + x \cdot -0.025050834237766436\right)}} - x \]
10. Add Preprocessing

Alternative 7: 98.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \frac{1}{0.4333638132548656 + x \cdot 0.37920088514346545} - x \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (- (/ 1.0 (+ 0.4333638132548656 (* x 0.37920088514346545))) x))

C

double code(double x) {
	return (1.0 / (0.4333638132548656 + (x * 0.37920088514346545))) - x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (1.0d0 / (0.4333638132548656d0 + (x * 0.37920088514346545d0))) - x
end function

Java

public static double code(double x) {
	return (1.0 / (0.4333638132548656 + (x * 0.37920088514346545))) - x;
}

Python

def code(x):
	return (1.0 / (0.4333638132548656 + (x * 0.37920088514346545))) - x

Julia

function code(x)
	return Float64(Float64(1.0 / Float64(0.4333638132548656 + Float64(x * 0.37920088514346545))) - x)
end

MATLAB

function tmp = code(x)
	tmp = (1.0 / (0.4333638132548656 + (x * 0.37920088514346545))) - x;
end

Wolfram

code[x_] := N[(N[(1.0 / N[(0.4333638132548656 + N[(x * 0.37920088514346545), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \]
2. Add Preprocessing
3. Step-by-step derivation

   1. flip3-+ N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \left(x \cdot \frac{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}\right)\right)\right), x\right) \]

   2. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \left(x \cdot \frac{1}{\frac{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}}\right)\right)\right), x\right) \]

   3. un-div-inv N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \left(\frac{x}{\frac{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}}\right)\right)\right), x\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \left(\frac{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}\right)\right)\right)\right), x\right) \]

   5. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{{\frac{99229}{100000}}^{3} + {\left(x \cdot \frac{4481}{100000}\right)}^{3}}{\frac{99229}{100000} \cdot \frac{99229}{100000} + \left(\left(x \cdot \frac{4481}{100000}\right) \cdot \left(x \cdot \frac{4481}{100000}\right) - \frac{99229}{100000} \cdot \left(x \cdot \frac{4481}{100000}\right)\right)}}\right)\right)\right)\right), x\right) \]

   6. flip3-+ N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{99229}{100000} + x \cdot \frac{4481}{100000}}\right)\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left(\frac{99229}{100000} + x \cdot \frac{4481}{100000}\right)\right)\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{99229}{100000}, \left(x \cdot \frac{4481}{100000}\right)\right)\right)\right)\right)\right), x\right) \]

   9. *-lowering-*.f64 100.0%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{230753}{100000}, \mathsf{*.f64}\left(x, \frac{27061}{100000}\right)\right), \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{99229}{100000}, \mathsf{*.f64}\left(x, \frac{4481}{100000}\right)\right)\right)\right)\right)\right), x\right) \]

4. Applied egg-rr 100.0%

   \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{\frac{x}{\frac{1}{0.99229 + x \cdot 0.04481}}}} - x \]

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\frac{1}{\frac{1}{2.30753 + x \cdot 0.27061} \cdot \left(1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)\right)}} - x \]

7. Taylor expanded in x around 0

   \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \color{blue}{\left(\frac{100000}{230753} + \frac{20191289437}{53246947009} \cdot x\right)}\right), x\right) \]
8. Step-by-step derivation

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \left(\frac{20191289437}{53246947009} \cdot x\right)\right)\right), x\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \left(x \cdot \frac{20191289437}{53246947009}\right)\right)\right), x\right) \]

   3. *-lowering-*.f64 98.4%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\frac{100000}{230753}, \mathsf{*.f64}\left(x, \frac{20191289437}{53246947009}\right)\right)\right), x\right) \]

9. Simplified 98.4%

   \[\leadsto \frac{1}{\color{blue}{0.4333638132548656 + x \cdot 0.37920088514346545}} - x \]
10. Add Preprocessing

Alternative 8: 97.6% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ 2.30753 - x \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- 2.30753 x))

C

double code(double x) {
	return 2.30753 - x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 2.30753d0 - x
end function

Java

public static double code(double x) {
	return 2.30753 - x;
}

Python

def code(x):
	return 2.30753 - x

Julia

function code(x)
	return Float64(2.30753 - x)
end

MATLAB

function tmp = code(x)
	tmp = 2.30753 - x;
end

Wolfram

code[x_] := N[(2.30753 - x), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\frac{230753}{100000}}, x\right) \]
4. Step-by-step derivation

5. Simplified 97.1%

   \[\leadsto \color{blue}{2.30753} - x \]
6. Add Preprocessing

Alternative 9: 50.0% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ 2.30753 \end{array} \]

FPCore

(FPCore (x) :precision binary64 2.30753)

C

double code(double x) {
	return 2.30753;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 2.30753d0
end function

Java

public static double code(double x) {
	return 2.30753;
}

Python

def code(x):
	return 2.30753

Julia

function code(x)
	return 2.30753
end

MATLAB

function tmp = code(x)
	tmp = 2.30753;
end

Wolfram

code[x_] := 2.30753

Derivation

1. Initial program 99.9%

   \[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{230753}{100000}} \]
4. Step-by-step derivation

5. Simplified 47.6%

   \[\leadsto \color{blue}{2.30753} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024158 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  :precision binary64
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))