ENA, Section 1.4, Mentioned, B

Percentage Accurate: 87.7% → 99.6%

Time: 11.0s

Alternatives: 13

Speedup: 1.0×

Specification

\[0.999 \leq x \land x \leq 1.001\]

Math

\[\begin{array}{l} \\ \frac{10}{1 - x \cdot x} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ 10.0 (- 1.0 (* x x))))

C

double code(double x) {
	return 10.0 / (1.0 - (x * x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 10.0d0 / (1.0d0 - (x * x))
end function

Java

public static double code(double x) {
	return 10.0 / (1.0 - (x * x));
}

Python

def code(x):
	return 10.0 / (1.0 - (x * x))

Julia

function code(x)
	return Float64(10.0 / Float64(1.0 - Float64(x * x)))
end

MATLAB

function tmp = code(x)
	tmp = 10.0 / (1.0 - (x * x));
end

Wolfram

code[x_] := N[(10.0 / N[(1.0 - N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 87.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{10}{1 - x \cdot x} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ 10.0 (- 1.0 (* x x))))

C

double code(double x) {
	return 10.0 / (1.0 - (x * x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 10.0d0 / (1.0d0 - (x * x))
end function

Java

public static double code(double x) {
	return 10.0 / (1.0 - (x * x));
}

Python

def code(x):
	return 10.0 / (1.0 - (x * x))

Julia

function code(x)
	return Float64(10.0 / Float64(1.0 - Float64(x * x)))
end

MATLAB

function tmp = code(x)
	tmp = 10.0 / (1.0 - (x * x));
end

Wolfram

code[x_] := N[(10.0 / N[(1.0 - N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \frac{10}{\mathsf{fma}\left(0 - x, x, 1\right)} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ 10.0 (fma (- 0.0 x) x 1.0)))

C

double code(double x) {
	return 10.0 / fma((0.0 - x), x, 1.0);
}

Julia

function code(x)
	return Float64(10.0 / fma(Float64(0.0 - x), x, 1.0))
end

Wolfram

code[x_] := N[(10.0 / N[(N[(0.0 - x), $MachinePrecision] * x + 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.9%

   \[\frac{10}{1 - x \cdot x} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto \mathsf{/.f64}\left(10, \left(1 + \color{blue}{\left(\mathsf{neg}\left(x \cdot x\right)\right)}\right)\right) \]

   2. +-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(10, \left(\left(\mathsf{neg}\left(x \cdot x\right)\right) + \color{blue}{1}\right)\right) \]

   3. distribute-lft-neg-in N/A

      \[\leadsto \mathsf{/.f64}\left(10, \left(\left(\mathsf{neg}\left(x\right)\right) \cdot x + 1\right)\right) \]

   4. fma-define N/A

      \[\leadsto \mathsf{/.f64}\left(10, \left(\mathsf{fma}\left(\mathsf{neg}\left(x\right), \color{blue}{x}, 1\right)\right)\right) \]

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

      \[\leadsto \mathsf{/.f64}\left(10, \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(x\right)\right), \color{blue}{x}, 1\right)\right) \]

   6. neg-sub0 N/A

      \[\leadsto \mathsf{/.f64}\left(10, \mathsf{fma.f64}\left(\left(0 - x\right), x, 1\right)\right) \]

   7. --lowering--.f64 99.6%

      \[\leadsto \mathsf{/.f64}\left(10, \mathsf{fma.f64}\left(\mathsf{\_.f64}\left(0, x\right), x, 1\right)\right) \]

4. Applied egg-rr 99.6%

   \[\leadsto \frac{10}{\color{blue}{\mathsf{fma}\left(0 - x, x, 1\right)}} \]
5. Step-by-step derivation

   1. sub0-neg N/A

      \[\leadsto \mathsf{/.f64}\left(10, \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(x\right)\right), x, 1\right)\right) \]

   2. neg-lowering-neg.f64 99.6%

      \[\leadsto \mathsf{/.f64}\left(10, \mathsf{fma.f64}\left(\mathsf{neg.f64}\left(x\right), x, 1\right)\right) \]

6. Applied egg-rr 99.6%

   \[\leadsto \frac{10}{\mathsf{fma}\left(\color{blue}{-x}, x, 1\right)} \]

7. Final simplification 99.6%

   \[\leadsto \frac{10}{\mathsf{fma}\left(0 - x, x, 1\right)} \]
8. Add Preprocessing

Alternative 2: 88.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{-1 + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)}{10}} \cdot \left(-1 - x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (/ 1.0 (/ (+ -1.0 (* x (* x (* x (* x (* x x)))))) 10.0))
  (- -1.0 (* x (* x (+ 1.0 (* x x)))))))

C

double code(double x) {
	return (1.0 / ((-1.0 + (x * (x * (x * (x * (x * x)))))) / 10.0)) * (-1.0 - (x * (x * (1.0 + (x * x)))));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (1.0d0 / (((-1.0d0) + (x * (x * (x * (x * (x * x)))))) / 10.0d0)) * ((-1.0d0) - (x * (x * (1.0d0 + (x * x)))))
end function

Java

public static double code(double x) {
	return (1.0 / ((-1.0 + (x * (x * (x * (x * (x * x)))))) / 10.0)) * (-1.0 - (x * (x * (1.0 + (x * x)))));
}

Python

def code(x):
	return (1.0 / ((-1.0 + (x * (x * (x * (x * (x * x)))))) / 10.0)) * (-1.0 - (x * (x * (1.0 + (x * x)))))

Julia

function code(x)
	return Float64(Float64(1.0 / Float64(Float64(-1.0 + Float64(x * Float64(x * Float64(x * Float64(x * Float64(x * x)))))) / 10.0)) * Float64(-1.0 - Float64(x * Float64(x * Float64(1.0 + Float64(x * x))))))
end

MATLAB

function tmp = code(x)
	tmp = (1.0 / ((-1.0 + (x * (x * (x * (x * (x * x)))))) / 10.0)) * (-1.0 - (x * (x * (1.0 + (x * x)))));
end

Wolfram

code[x_] := N[(N[(1.0 / N[(N[(-1.0 + N[(x * N[(x * N[(x * N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 10.0), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x * N[(x * N[(1.0 + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.9%

   \[\frac{10}{1 - x \cdot x} \]
2. Add Preprocessing

4. Applied egg-rr 88.4%

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

   1. clear-num N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{-1 + x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)}{10}}\right), \mathsf{+.f64}\left(\color{blue}{-1}, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{-1 + x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)}{10}\right)\right), \mathsf{+.f64}\left(\color{blue}{-1}, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(-1 + x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right), 10\right)\right), \mathsf{+.f64}\left(-1, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(-1, \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)\right), 10\right)\right), \mathsf{+.f64}\left(-1, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right) \]

   5. associate-*r* N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(-1, \left(\left(x \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right), 10\right)\right), \mathsf{+.f64}\left(-1, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(\left(x \cdot \left(x \cdot x\right)\right), \left(x \cdot \left(x \cdot x\right)\right)\right)\right), 10\right)\right), \mathsf{+.f64}\left(-1, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(x \cdot x\right)\right), \left(x \cdot \left(x \cdot x\right)\right)\right)\right), 10\right)\right), \mathsf{+.f64}\left(-1, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right), \left(x \cdot \left(x \cdot x\right)\right)\right)\right), 10\right)\right), \mathsf{+.f64}\left(-1, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right), \mathsf{*.f64}\left(x, \left(x \cdot x\right)\right)\right)\right), 10\right)\right), \mathsf{+.f64}\left(-1, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right) \]

   10. *-lowering-*.f64 88.2%

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), 10\right)\right), \mathsf{+.f64}\left(-1, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right) \]

6. Applied egg-rr 88.2%

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

   1. associate-*l* N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(-1, \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)\right), 10\right)\right), \mathsf{+.f64}\left(-1, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right) \]

   2. associate-*r* N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(-1, \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)\right)\right), 10\right)\right), \mathsf{+.f64}\left(-1, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right) \]

   3. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(-1, \left(\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right) \cdot x\right)\right), 10\right)\right), \mathsf{+.f64}\left(-1, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right), x\right)\right), 10\right)\right), \mathsf{+.f64}\left(-1, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right), x\right)\right), 10\right)\right), \mathsf{+.f64}\left(-1, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \left(x \cdot \left(x \cdot x\right)\right)\right)\right), x\right)\right), 10\right)\right), \mathsf{+.f64}\left(-1, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \left(x \cdot x\right)\right)\right)\right), x\right)\right), 10\right)\right), \mathsf{+.f64}\left(-1, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right) \]

   8. *-lowering-*.f64 88.9%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), x\right)\right), 10\right)\right), \mathsf{+.f64}\left(-1, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right) \]

8. Applied egg-rr 88.9%

   \[\leadsto \frac{1}{\frac{-1 + \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right) \cdot x}}{10}} \cdot \left(-1 + \left(-x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)\right) \]

9. Final simplification 88.9%

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

Alternative 3: 88.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot \left(x \cdot x\right)\right)\\ 10 \cdot \frac{-1 - \left(x \cdot x + t\_0\right)}{-1 + x \cdot \left(x \cdot t\_0\right)} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* x (* x (* x x)))))
   (* 10.0 (/ (- -1.0 (+ (* x x) t_0)) (+ -1.0 (* x (* x t_0)))))))

C

double code(double x) {
	double t_0 = x * (x * (x * x));
	return 10.0 * ((-1.0 - ((x * x) + t_0)) / (-1.0 + (x * (x * t_0))));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    t_0 = x * (x * (x * x))
    code = 10.0d0 * (((-1.0d0) - ((x * x) + t_0)) / ((-1.0d0) + (x * (x * t_0))))
end function

Java

public static double code(double x) {
	double t_0 = x * (x * (x * x));
	return 10.0 * ((-1.0 - ((x * x) + t_0)) / (-1.0 + (x * (x * t_0))));
}

Python

def code(x):
	t_0 = x * (x * (x * x))
	return 10.0 * ((-1.0 - ((x * x) + t_0)) / (-1.0 + (x * (x * t_0))))

Julia

function code(x)
	t_0 = Float64(x * Float64(x * Float64(x * x)))
	return Float64(10.0 * Float64(Float64(-1.0 - Float64(Float64(x * x) + t_0)) / Float64(-1.0 + Float64(x * Float64(x * t_0)))))
end

MATLAB

function tmp = code(x)
	t_0 = x * (x * (x * x));
	tmp = 10.0 * ((-1.0 - ((x * x) + t_0)) / (-1.0 + (x * (x * t_0))));
end

Wolfram

code[x_] := Block[{t$95$0 = N[(x * N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(10.0 * N[(N[(-1.0 - N[(N[(x * x), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] / N[(-1.0 + N[(x * N[(x * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 87.9%

   \[\frac{10}{1 - x \cdot x} \]
2. Add Preprocessing

4. Applied egg-rr 88.4%

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

   1. clear-num N/A

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1 + x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)}{-1 + \left(\mathsf{neg}\left(x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)\right)}}{10}}} \]

   2. associate-/r/ N/A

      \[\leadsto \frac{1}{\frac{-1 + x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)}{-1 + \left(\mathsf{neg}\left(x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)\right)}} \cdot \color{blue}{10} \]

   3. clear-num N/A

      \[\leadsto \frac{-1 + \left(\mathsf{neg}\left(x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)\right)}{-1 + x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)} \cdot 10 \]

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

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{-1 + \left(\mathsf{neg}\left(x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)\right)}{-1 + x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)}\right), \color{blue}{10}\right) \]

6. Applied egg-rr 88.9%

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

   1. +-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(-1, \left(x \cdot \left(x \cdot \left(x \cdot x + 1\right)\right)\right)\right), \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right), 10\right) \]

   2. distribute-lft-in N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(-1, \left(x \cdot \left(x \cdot \left(x \cdot x\right) + x \cdot 1\right)\right)\right), \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right), 10\right) \]

   3. *-rgt-identity N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(-1, \left(x \cdot \left(x \cdot \left(x \cdot x\right) + x\right)\right)\right), \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right), 10\right) \]

   4. distribute-lft-in N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(-1, \left(x \cdot \left(x \cdot \left(x \cdot x\right)\right) + x \cdot x\right)\right), \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right), 10\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(-1, \mathsf{+.f64}\left(\left(x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right), \left(x \cdot x\right)\right)\right), \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right), 10\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(-1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(x \cdot \left(x \cdot x\right)\right)\right), \left(x \cdot x\right)\right)\right), \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right), 10\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(-1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \left(x \cdot x\right)\right)\right), \left(x \cdot x\right)\right)\right), \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right), 10\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(-1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right), \left(x \cdot x\right)\right)\right), \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right), 10\right) \]

   9. *-lowering-*.f64 88.9%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(-1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right), \mathsf{*.f64}\left(x, x\right)\right)\right), \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right), 10\right) \]

8. Applied egg-rr 88.9%

   \[\leadsto \frac{-1 - \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot x\right)\right) + x \cdot x\right)}}{-1 + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)} \cdot 10 \]

9. Final simplification 88.9%

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

Alternative 4: 88.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ 10 \cdot \frac{-1 - x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)}{-1 + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  10.0
  (/
   (- -1.0 (* x (* x (+ 1.0 (* x x)))))
   (+ -1.0 (* x (* x (* x (* x (* x x)))))))))

C

double code(double x) {
	return 10.0 * ((-1.0 - (x * (x * (1.0 + (x * x))))) / (-1.0 + (x * (x * (x * (x * (x * x)))))));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 10.0d0 * (((-1.0d0) - (x * (x * (1.0d0 + (x * x))))) / ((-1.0d0) + (x * (x * (x * (x * (x * x)))))))
end function

Java

public static double code(double x) {
	return 10.0 * ((-1.0 - (x * (x * (1.0 + (x * x))))) / (-1.0 + (x * (x * (x * (x * (x * x)))))));
}

Python

def code(x):
	return 10.0 * ((-1.0 - (x * (x * (1.0 + (x * x))))) / (-1.0 + (x * (x * (x * (x * (x * x)))))))

Julia

function code(x)
	return Float64(10.0 * Float64(Float64(-1.0 - Float64(x * Float64(x * Float64(1.0 + Float64(x * x))))) / Float64(-1.0 + Float64(x * Float64(x * Float64(x * Float64(x * Float64(x * x))))))))
end

MATLAB

function tmp = code(x)
	tmp = 10.0 * ((-1.0 - (x * (x * (1.0 + (x * x))))) / (-1.0 + (x * (x * (x * (x * (x * x)))))));
end

Wolfram

code[x_] := N[(10.0 * N[(N[(-1.0 - N[(x * N[(x * N[(1.0 + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-1.0 + N[(x * N[(x * N[(x * N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.9%

   \[\frac{10}{1 - x \cdot x} \]
2. Add Preprocessing

4. Applied egg-rr 88.4%

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

   1. clear-num N/A

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1 + x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)}{-1 + \left(\mathsf{neg}\left(x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)\right)}}{10}}} \]

   2. associate-/r/ N/A

      \[\leadsto \frac{1}{\frac{-1 + x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)}{-1 + \left(\mathsf{neg}\left(x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)\right)}} \cdot \color{blue}{10} \]

   3. clear-num N/A

      \[\leadsto \frac{-1 + \left(\mathsf{neg}\left(x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)\right)}{-1 + x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)} \cdot 10 \]

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

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{-1 + \left(\mathsf{neg}\left(x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)\right)}{-1 + x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)}\right), \color{blue}{10}\right) \]

6. Applied egg-rr 88.9%

   \[\leadsto \color{blue}{\frac{-1 - x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)}{-1 + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)} \cdot 10} \]

7. Final simplification 88.9%

   \[\leadsto 10 \cdot \frac{-1 - x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)}{-1 + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)} \]
8. Add Preprocessing

Alternative 5: 88.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \left(-1 - x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right) \cdot \frac{10}{-1 + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (- -1.0 (* x (* x (+ 1.0 (* x x)))))
  (/ 10.0 (+ -1.0 (* x (* x (* x (* x (* x x)))))))))

C

double code(double x) {
	return (-1.0 - (x * (x * (1.0 + (x * x))))) * (10.0 / (-1.0 + (x * (x * (x * (x * (x * x)))))));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((-1.0d0) - (x * (x * (1.0d0 + (x * x))))) * (10.0d0 / ((-1.0d0) + (x * (x * (x * (x * (x * x)))))))
end function

Java

public static double code(double x) {
	return (-1.0 - (x * (x * (1.0 + (x * x))))) * (10.0 / (-1.0 + (x * (x * (x * (x * (x * x)))))));
}

Python

def code(x):
	return (-1.0 - (x * (x * (1.0 + (x * x))))) * (10.0 / (-1.0 + (x * (x * (x * (x * (x * x)))))))

Julia

function code(x)
	return Float64(Float64(-1.0 - Float64(x * Float64(x * Float64(1.0 + Float64(x * x))))) * Float64(10.0 / Float64(-1.0 + Float64(x * Float64(x * Float64(x * Float64(x * Float64(x * x))))))))
end

MATLAB

function tmp = code(x)
	tmp = (-1.0 - (x * (x * (1.0 + (x * x))))) * (10.0 / (-1.0 + (x * (x * (x * (x * (x * x)))))));
end

Wolfram

code[x_] := N[(N[(-1.0 - N[(x * N[(x * N[(1.0 + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(10.0 / N[(-1.0 + N[(x * N[(x * N[(x * N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.9%

   \[\frac{10}{1 - x \cdot x} \]
2. Add Preprocessing

4. Applied egg-rr 88.4%

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

   1. associate-/r/ N/A

      \[\leadsto \frac{10}{-1 + x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)} \cdot \color{blue}{\left(-1 + \left(\mathsf{neg}\left(x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)\right)\right)} \]

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

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{10}{-1 + x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)}\right), \color{blue}{\left(-1 + \left(\mathsf{neg}\left(x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)\right)\right)}\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(10, \left(-1 + x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)\right), \left(\color{blue}{-1} + \left(\mathsf{neg}\left(x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(10, \mathsf{+.f64}\left(-1, \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)\right)\right), \left(-1 + \left(\mathsf{neg}\left(x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(10, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(x, \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)\right)\right), \left(-1 + \left(\mathsf{neg}\left(x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)\right)\right)\right) \]

   6. associate-*l* N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(10, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(x, \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)\right)\right)\right), \left(-1 + \left(\mathsf{neg}\left(x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(10, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \left(x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)\right)\right)\right), \left(-1 + \left(\mathsf{neg}\left(x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(10, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \left(x \cdot \left(x \cdot x\right)\right)\right)\right)\right)\right)\right), \left(-1 + \left(\mathsf{neg}\left(x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(10, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \left(x \cdot x\right)\right)\right)\right)\right)\right)\right), \left(-1 + \left(\mathsf{neg}\left(x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)\right)\right)\right) \]

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

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(10, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right), \left(-1 + \left(\mathsf{neg}\left(x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)\right)\right)\right) \]

   11. unsub-neg N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(10, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right), \left(-1 - \color{blue}{x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)}\right)\right) \]

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

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(10, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right), \mathsf{\_.f64}\left(-1, \color{blue}{\left(x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)}\right)\right) \]

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

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(10, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right), \mathsf{\_.f64}\left(-1, \mathsf{*.f64}\left(x, \color{blue}{\left(x \cdot \left(1 + x \cdot x\right)\right)}\right)\right)\right) \]

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

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(10, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right), \mathsf{\_.f64}\left(-1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{\left(1 + x \cdot x\right)}\right)\right)\right)\right) \]

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

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(10, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right)\right)\right)\right)\right), \mathsf{\_.f64}\left(-1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot x\right)}\right)\right)\right)\right)\right) \]

6. Applied egg-rr 88.9%

   \[\leadsto \color{blue}{\frac{10}{-1 + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)} \cdot \left(-1 - x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right)} \]

7. Final simplification 88.9%

   \[\leadsto \left(-1 - x \cdot \left(x \cdot \left(1 + x \cdot x\right)\right)\right) \cdot \frac{10}{-1 + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)} \]
8. Add Preprocessing

Alternative 6: 88.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{\frac{1}{1 + x \cdot x} \cdot \left(1 - x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)}{10}} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (/ 1.0 (/ (* (/ 1.0 (+ 1.0 (* x x))) (- 1.0 (* x (* x (* x x))))) 10.0)))

C

double code(double x) {
	return 1.0 / (((1.0 / (1.0 + (x * x))) * (1.0 - (x * (x * (x * x))))) / 10.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 / (((1.0d0 / (1.0d0 + (x * x))) * (1.0d0 - (x * (x * (x * x))))) / 10.0d0)
end function

Java

public static double code(double x) {
	return 1.0 / (((1.0 / (1.0 + (x * x))) * (1.0 - (x * (x * (x * x))))) / 10.0);
}

Python

def code(x):
	return 1.0 / (((1.0 / (1.0 + (x * x))) * (1.0 - (x * (x * (x * x))))) / 10.0)

Julia

function code(x)
	return Float64(1.0 / Float64(Float64(Float64(1.0 / Float64(1.0 + Float64(x * x))) * Float64(1.0 - Float64(x * Float64(x * Float64(x * x))))) / 10.0))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 / (((1.0 / (1.0 + (x * x))) * (1.0 - (x * (x * (x * x))))) / 10.0);
end

Wolfram

code[x_] := N[(1.0 / N[(N[(N[(1.0 / N[(1.0 + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 - N[(x * N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 10.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.9%

   \[\frac{10}{1 - x \cdot x} \]
2. Add Preprocessing

4. Applied egg-rr 88.3%

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

   1. clear-num N/A

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{\left(1 - \left(x \cdot x\right) \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)\right) \cdot \frac{1}{1 + x \cdot x}}{1 + x \cdot \left(x \cdot \left(x \cdot x\right)\right)}}{10}}} \]

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

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\frac{\left(1 - \left(x \cdot x\right) \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)\right) \cdot \frac{1}{1 + x \cdot x}}{1 + x \cdot \left(x \cdot \left(x \cdot x\right)\right)}}{10}\right)}\right) \]

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

      \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{\left(1 - \left(x \cdot x\right) \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)\right) \cdot \frac{1}{1 + x \cdot x}}{1 + x \cdot \left(x \cdot \left(x \cdot x\right)\right)}\right), \color{blue}{10}\right)\right) \]

6. Applied egg-rr 88.6%

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

Alternative 7: 88.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \frac{10}{\frac{1}{1 + x \cdot x} \cdot \left(1 - x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (/ 10.0 (* (/ 1.0 (+ 1.0 (* x x))) (- 1.0 (* x (* x (* x x)))))))

C

double code(double x) {
	return 10.0 / ((1.0 / (1.0 + (x * x))) * (1.0 - (x * (x * (x * x)))));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 10.0d0 / ((1.0d0 / (1.0d0 + (x * x))) * (1.0d0 - (x * (x * (x * x)))))
end function

Java

public static double code(double x) {
	return 10.0 / ((1.0 / (1.0 + (x * x))) * (1.0 - (x * (x * (x * x)))));
}

Python

def code(x):
	return 10.0 / ((1.0 / (1.0 + (x * x))) * (1.0 - (x * (x * (x * x)))))

Julia

function code(x)
	return Float64(10.0 / Float64(Float64(1.0 / Float64(1.0 + Float64(x * x))) * Float64(1.0 - Float64(x * Float64(x * Float64(x * x))))))
end

MATLAB

function tmp = code(x)
	tmp = 10.0 / ((1.0 / (1.0 + (x * x))) * (1.0 - (x * (x * (x * x)))));
end

Wolfram

code[x_] := N[(10.0 / N[(N[(1.0 / N[(1.0 + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 - N[(x * N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.9%

   \[\frac{10}{1 - x \cdot x} \]
2. Add Preprocessing

4. Applied egg-rr 88.3%

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

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

      \[\leadsto \mathsf{/.f64}\left(10, \color{blue}{\left(\frac{\left(1 - \left(x \cdot x\right) \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)\right) \cdot \frac{1}{1 + x \cdot x}}{1 + x \cdot \left(x \cdot \left(x \cdot x\right)\right)}\right)}\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(10, \left(\frac{\frac{1}{1 + x \cdot x} \cdot \left(1 - \left(x \cdot x\right) \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)\right)}{\color{blue}{1} + x \cdot \left(x \cdot \left(x \cdot x\right)\right)}\right)\right) \]

   3. associate-/l* N/A

      \[\leadsto \mathsf{/.f64}\left(10, \left(\frac{1}{1 + x \cdot x} \cdot \color{blue}{\frac{1 - \left(x \cdot x\right) \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)}{1 + x \cdot \left(x \cdot \left(x \cdot x\right)\right)}}\right)\right) \]

   4. metadata-eval N/A

      \[\leadsto \mathsf{/.f64}\left(10, \left(\frac{1}{1 + x \cdot x} \cdot \frac{1 \cdot 1 - \left(x \cdot x\right) \cdot \left(x \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right)}{1 + x \cdot \left(x \cdot \left(x \cdot x\right)\right)}\right)\right) \]

   5. associate-*r* N/A

      \[\leadsto \mathsf{/.f64}\left(10, \left(\frac{1}{1 + x \cdot x} \cdot \frac{1 \cdot 1 - \left(x \cdot x\right) \cdot \left(\left(x \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)}{1 + x \cdot \left(x \cdot \left(x \cdot x\right)\right)}\right)\right) \]

   6. swap-sqr N/A

      \[\leadsto \mathsf{/.f64}\left(10, \left(\frac{1}{1 + x \cdot x} \cdot \frac{1 \cdot 1 - \left(x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)}{1 + x \cdot \left(x \cdot \left(x \cdot x\right)\right)}\right)\right) \]

   7. flip-- N/A

      \[\leadsto \mathsf{/.f64}\left(10, \left(\frac{1}{1 + x \cdot x} \cdot \left(1 - \color{blue}{x \cdot \left(x \cdot \left(x \cdot x\right)\right)}\right)\right)\right) \]

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

      \[\leadsto \mathsf{/.f64}\left(10, \mathsf{*.f64}\left(\left(\frac{1}{1 + x \cdot x}\right), \color{blue}{\left(1 - x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)}\right)\right) \]

6. Applied egg-rr 88.6%

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

Alternative 8: 88.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \frac{10}{\frac{1 - x \cdot \left(x \cdot \left(x \cdot x\right)\right)}{1 + x \cdot x}} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (/ 10.0 (/ (- 1.0 (* x (* x (* x x)))) (+ 1.0 (* x x)))))

C

double code(double x) {
	return 10.0 / ((1.0 - (x * (x * (x * x)))) / (1.0 + (x * x)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 10.0d0 / ((1.0d0 - (x * (x * (x * x)))) / (1.0d0 + (x * x)))
end function

Java

public static double code(double x) {
	return 10.0 / ((1.0 - (x * (x * (x * x)))) / (1.0 + (x * x)));
}

Python

def code(x):
	return 10.0 / ((1.0 - (x * (x * (x * x)))) / (1.0 + (x * x)))

Julia

function code(x)
	return Float64(10.0 / Float64(Float64(1.0 - Float64(x * Float64(x * Float64(x * x)))) / Float64(1.0 + Float64(x * x))))
end

MATLAB

function tmp = code(x)
	tmp = 10.0 / ((1.0 - (x * (x * (x * x)))) / (1.0 + (x * x)));
end

Wolfram

code[x_] := N[(10.0 / N[(N[(1.0 - N[(x * N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.9%

   \[\frac{10}{1 - x \cdot x} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto \mathsf{/.f64}\left(10, \left(1 + \color{blue}{\left(\mathsf{neg}\left(x \cdot x\right)\right)}\right)\right) \]

   2. +-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(10, \left(\left(\mathsf{neg}\left(x \cdot x\right)\right) + \color{blue}{1}\right)\right) \]

   3. distribute-lft-neg-in N/A

      \[\leadsto \mathsf{/.f64}\left(10, \left(\left(\mathsf{neg}\left(x\right)\right) \cdot x + 1\right)\right) \]

   4. fma-define N/A

      \[\leadsto \mathsf{/.f64}\left(10, \left(\mathsf{fma}\left(\mathsf{neg}\left(x\right), \color{blue}{x}, 1\right)\right)\right) \]

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

      \[\leadsto \mathsf{/.f64}\left(10, \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(x\right)\right), \color{blue}{x}, 1\right)\right) \]

   6. neg-sub0 N/A

      \[\leadsto \mathsf{/.f64}\left(10, \mathsf{fma.f64}\left(\left(0 - x\right), x, 1\right)\right) \]

   7. --lowering--.f64 99.6%

      \[\leadsto \mathsf{/.f64}\left(10, \mathsf{fma.f64}\left(\mathsf{\_.f64}\left(0, x\right), x, 1\right)\right) \]

4. Applied egg-rr 99.6%

   \[\leadsto \frac{10}{\color{blue}{\mathsf{fma}\left(0 - x, x, 1\right)}} \]
5. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(10, \left(1 + \color{blue}{\left(0 - x\right) \cdot x}\right)\right) \]

   2. sub0-neg N/A

      \[\leadsto \mathsf{/.f64}\left(10, \left(1 + \left(\mathsf{neg}\left(x\right)\right) \cdot x\right)\right) \]

   3. cancel-sign-sub-inv N/A

      \[\leadsto \mathsf{/.f64}\left(10, \left(1 - \color{blue}{x \cdot x}\right)\right) \]

   4. flip-- N/A

      \[\leadsto \mathsf{/.f64}\left(10, \left(\frac{1 \cdot 1 - \left(x \cdot x\right) \cdot \left(x \cdot x\right)}{\color{blue}{1 + x \cdot x}}\right)\right) \]

   5. metadata-eval N/A

      \[\leadsto \mathsf{/.f64}\left(10, \left(\frac{1 - \left(x \cdot x\right) \cdot \left(x \cdot x\right)}{1 + x \cdot x}\right)\right) \]

   6. associate-*r* N/A

      \[\leadsto \mathsf{/.f64}\left(10, \left(\frac{1 - x \cdot \left(x \cdot \left(x \cdot x\right)\right)}{1 + x \cdot x}\right)\right) \]

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

      \[\leadsto \mathsf{/.f64}\left(10, \mathsf{/.f64}\left(\left(1 - x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right), \color{blue}{\left(1 + x \cdot x\right)}\right)\right) \]

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

      \[\leadsto \mathsf{/.f64}\left(10, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(1, \left(x \cdot \left(x \cdot \left(x \cdot x\right)\right)\right)\right), \left(\color{blue}{1} + x \cdot x\right)\right)\right) \]

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

      \[\leadsto \mathsf{/.f64}\left(10, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(x, \left(x \cdot \left(x \cdot x\right)\right)\right)\right), \left(1 + x \cdot x\right)\right)\right) \]

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

       \[\leadsto \mathsf{/.f64}\left(10, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \left(x \cdot x\right)\right)\right)\right), \left(1 + x \cdot x\right)\right)\right) \]

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

       \[\leadsto \mathsf{/.f64}\left(10, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), \left(1 + x \cdot x\right)\right)\right) \]

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

       \[\leadsto \mathsf{/.f64}\left(10, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot x\right)}\right)\right)\right) \]

   13. *-lowering-*.f64 88.6%

       \[\leadsto \mathsf{/.f64}\left(10, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right)\right) \]

6. Applied egg-rr 88.6%

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

Alternative 9: 13.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 1:\\ \;\;\;\;10\\ \mathbf{else}:\\ \;\;\;\;\frac{-10}{x \cdot x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= (* x x) 1.0) 10.0 (/ -10.0 (* x x))))

C

double code(double x) {
	double tmp;
	if ((x * x) <= 1.0) {
		tmp = 10.0;
	} else {
		tmp = -10.0 / (x * x);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x * x) <= 1.0d0) then
        tmp = 10.0d0
    else
        tmp = (-10.0d0) / (x * x)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x * x) <= 1.0) {
		tmp = 10.0;
	} else {
		tmp = -10.0 / (x * x);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x * x) <= 1.0:
		tmp = 10.0
	else:
		tmp = -10.0 / (x * x)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(x * x) <= 1.0)
		tmp = 10.0;
	else
		tmp = Float64(-10.0 / Float64(x * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x * x) <= 1.0)
		tmp = 10.0;
	else
		tmp = -10.0 / (x * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(x * x), $MachinePrecision], 1.0], 10.0, N[(-10.0 / N[(x * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 1

   1. Initial program 88.5%

      \[\frac{10}{1 - x \cdot x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{10} \]
   4. Step-by-step derivation

   5. Simplified 13.5%

      \[\leadsto \color{blue}{10} \]

   if 1 < (*.f64 x x)

   1. Initial program 86.7%

      \[\frac{10}{1 - x \cdot x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{-10}{{x}^{2}}} \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(-10, \color{blue}{\left({x}^{2}\right)}\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(-10, \left(x \cdot \color{blue}{x}\right)\right) \]

      3. *-lowering-*.f64 13.5%

         \[\leadsto \mathsf{/.f64}\left(-10, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right) \]

   5. Simplified 13.5%

      \[\leadsto \color{blue}{\frac{-10}{x \cdot x}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 87.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{1}{-1 + x \cdot x}}{-0.1} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ (/ 1.0 (+ -1.0 (* x x))) -0.1))

C

double code(double x) {
	return (1.0 / (-1.0 + (x * x))) / -0.1;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (1.0d0 / ((-1.0d0) + (x * x))) / (-0.1d0)
end function

Java

public static double code(double x) {
	return (1.0 / (-1.0 + (x * x))) / -0.1;
}

Python

def code(x):
	return (1.0 / (-1.0 + (x * x))) / -0.1

Julia

function code(x)
	return Float64(Float64(1.0 / Float64(-1.0 + Float64(x * x))) / -0.1)
end

MATLAB

function tmp = code(x)
	tmp = (1.0 / (-1.0 + (x * x))) / -0.1;
end

Wolfram

code[x_] := N[(N[(1.0 / N[(-1.0 + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / -0.1), $MachinePrecision]

Derivation

1. Initial program 87.9%

   \[\frac{10}{1 - x \cdot x} \]
2. Add Preprocessing

4. Applied egg-rr 87.9%

   \[\leadsto \color{blue}{\frac{\frac{1}{x \cdot x + -1}}{-0.1}} \]

5. Final simplification 87.9%

   \[\leadsto \frac{\frac{1}{-1 + x \cdot x}}{-0.1} \]
6. Add Preprocessing

Alternative 11: 87.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{1}{-1 + x \cdot x} \cdot -10 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (/ 1.0 (+ -1.0 (* x x))) -10.0))

C

double code(double x) {
	return (1.0 / (-1.0 + (x * x))) * -10.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (1.0d0 / ((-1.0d0) + (x * x))) * (-10.0d0)
end function

Java

public static double code(double x) {
	return (1.0 / (-1.0 + (x * x))) * -10.0;
}

Python

def code(x):
	return (1.0 / (-1.0 + (x * x))) * -10.0

Julia

function code(x)
	return Float64(Float64(1.0 / Float64(-1.0 + Float64(x * x))) * -10.0)
end

MATLAB

function tmp = code(x)
	tmp = (1.0 / (-1.0 + (x * x))) * -10.0;
end

Wolfram

code[x_] := N[(N[(1.0 / N[(-1.0 + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -10.0), $MachinePrecision]

Derivation

1. Initial program 87.9%

   \[\frac{10}{1 - x \cdot x} \]
2. Add Preprocessing

4. Applied egg-rr 87.9%

   \[\leadsto \color{blue}{\frac{1}{x \cdot x + -1} \cdot -10} \]

5. Final simplification 87.9%

   \[\leadsto \frac{1}{-1 + x \cdot x} \cdot -10 \]
6. Add Preprocessing

Alternative 12: 87.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{10}{1 - x \cdot x} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ 10.0 (- 1.0 (* x x))))

C

double code(double x) {
	return 10.0 / (1.0 - (x * x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 10.0d0 / (1.0d0 - (x * x))
end function

Java

public static double code(double x) {
	return 10.0 / (1.0 - (x * x));
}

Python

def code(x):
	return 10.0 / (1.0 - (x * x))

Julia

function code(x)
	return Float64(10.0 / Float64(1.0 - Float64(x * x)))
end

MATLAB

function tmp = code(x)
	tmp = 10.0 / (1.0 - (x * x));
end

Wolfram

code[x_] := N[(10.0 / N[(1.0 - N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.9%

   \[\frac{10}{1 - x \cdot x} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 13: 9.5% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ 10 \end{array} \]

FPCore

(FPCore (x) :precision binary64 10.0)

C

double code(double x) {
	return 10.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 10.0d0
end function

Java

public static double code(double x) {
	return 10.0;
}

Python

def code(x):
	return 10.0

Julia

function code(x)
	return 10.0
end

MATLAB

function tmp = code(x)
	tmp = 10.0;
end

Wolfram

code[x_] := 10.0

Derivation

1. Initial program 87.9%

   \[\frac{10}{1 - x \cdot x} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{10} \]
4. Step-by-step derivation

5. Simplified 9.4%

   \[\leadsto \color{blue}{10} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024139 
(FPCore (x)
  :name "ENA, Section 1.4, Mentioned, B"
  :precision binary64
  :pre (and (<= 0.999 x) (<= x 1.001))
  (/ 10.0 (- 1.0 (* x x))))