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

Percentage Accurate: 99.7% → 99.7%

Time: 11.4s

Alternatives: 14

Speedup: N/A×

Specification

Math

\[\begin{array}{l} \\ \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))

C

double code(double x, double y) {
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * sqrt(x)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - (1.0d0 / (x * 9.0d0))) - (y / (3.0d0 * sqrt(x)))
end function

Java

public static double code(double x, double y) {
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * Math.sqrt(x)));
}

Python

def code(x, y):
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * math.sqrt(x)))

Julia

function code(x, y)
	return Float64(Float64(1.0 - Float64(1.0 / Float64(x * 9.0))) - Float64(y / Float64(3.0 * sqrt(x))))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * sqrt(x)));
end

Wolfram

code[x_, y_] := N[(N[(1.0 - N[(1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))

C

double code(double x, double y) {
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * sqrt(x)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - (1.0d0 / (x * 9.0d0))) - (y / (3.0d0 * sqrt(x)))
end function

Java

public static double code(double x, double y) {
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * Math.sqrt(x)));
}

Python

def code(x, y):
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * math.sqrt(x)))

Julia

function code(x, y)
	return Float64(Float64(1.0 - Float64(1.0 / Float64(x * 9.0))) - Float64(y / Float64(3.0 * sqrt(x))))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * sqrt(x)));
end

Wolfram

code[x_, y_] := N[(N[(1.0 - N[(1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 + \frac{-1}{x \cdot 9}\right) - \frac{y}{\sqrt{x \cdot 9}} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (- (+ 1.0 (/ -1.0 (* x 9.0))) (/ y (sqrt (* x 9.0)))))

C

double code(double x, double y) {
	return (1.0 + (-1.0 / (x * 9.0))) - (y / sqrt((x * 9.0)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 + ((-1.0d0) / (x * 9.0d0))) - (y / sqrt((x * 9.0d0)))
end function

Java

public static double code(double x, double y) {
	return (1.0 + (-1.0 / (x * 9.0))) - (y / Math.sqrt((x * 9.0)));
}

Python

def code(x, y):
	return (1.0 + (-1.0 / (x * 9.0))) - (y / math.sqrt((x * 9.0)))

Julia

function code(x, y)
	return Float64(Float64(1.0 + Float64(-1.0 / Float64(x * 9.0))) - Float64(y / sqrt(Float64(x * 9.0))))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 + (-1.0 / (x * 9.0))) - (y / sqrt((x * 9.0)));
end

Wolfram

code[x_, y_] := N[(N[(1.0 + N[(-1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. *-commutative 99.7%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x} \cdot 3}} \]

   2. metadata-eval 99.7%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\sqrt{x} \cdot \color{blue}{\sqrt{9}}} \]

   3. sqrt-prod 99.8%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   4. pow1/2 99.8%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]

4. Applied egg-rr 99.8%

   \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]
5. Step-by-step derivation

   1. unpow1/2 99.8%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

6. Simplified 99.8%

   \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

7. Final simplification 99.8%

   \[\leadsto \left(1 + \frac{-1}{x \cdot 9}\right) - \frac{y}{\sqrt{x \cdot 9}} \]
8. Add Preprocessing

Alternative 2: 94.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+82} \lor \neg \left(y \leq 1.9 \cdot 10^{+24}\right):\\ \;\;\;\;1 - \frac{y}{\sqrt{x}} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;1 - {\left(x \cdot 9\right)}^{-1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.05e+82) (not (<= y 1.9e+24)))
   (- 1.0 (* (/ y (sqrt x)) 0.3333333333333333))
   (- 1.0 (pow (* x 9.0) -1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.05e+82) || !(y <= 1.9e+24)) {
		tmp = 1.0 - ((y / sqrt(x)) * 0.3333333333333333);
	} else {
		tmp = 1.0 - pow((x * 9.0), -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.05d+82)) .or. (.not. (y <= 1.9d+24))) then
        tmp = 1.0d0 - ((y / sqrt(x)) * 0.3333333333333333d0)
    else
        tmp = 1.0d0 - ((x * 9.0d0) ** (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.05e+82) || !(y <= 1.9e+24)) {
		tmp = 1.0 - ((y / Math.sqrt(x)) * 0.3333333333333333);
	} else {
		tmp = 1.0 - Math.pow((x * 9.0), -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.05e+82) or not (y <= 1.9e+24):
		tmp = 1.0 - ((y / math.sqrt(x)) * 0.3333333333333333)
	else:
		tmp = 1.0 - math.pow((x * 9.0), -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.05e+82) || !(y <= 1.9e+24))
		tmp = Float64(1.0 - Float64(Float64(y / sqrt(x)) * 0.3333333333333333));
	else
		tmp = Float64(1.0 - (Float64(x * 9.0) ^ -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.05e+82) || ~((y <= 1.9e+24)))
		tmp = 1.0 - ((y / sqrt(x)) * 0.3333333333333333);
	else
		tmp = 1.0 - ((x * 9.0) ^ -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.05e+82], N[Not[LessEqual[y, 1.9e+24]], $MachinePrecision]], N[(1.0 - N[(N[(y / N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[Power[N[(x * 9.0), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e82 or 1.90000000000000008e24 < y

   1. Initial program 99.6%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 95.0%

      \[\leadsto \color{blue}{1 - 0.3333333333333333 \cdot \left(\sqrt{\frac{1}{x}} \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative 95.0%

         \[\leadsto 1 - 0.3333333333333333 \cdot \color{blue}{\left(y \cdot \sqrt{\frac{1}{x}}\right)} \]

      2. sqrt-div 94.9%

         \[\leadsto 1 - 0.3333333333333333 \cdot \left(y \cdot \color{blue}{\frac{\sqrt{1}}{\sqrt{x}}}\right) \]

      3. metadata-eval 94.9%

         \[\leadsto 1 - 0.3333333333333333 \cdot \left(y \cdot \frac{\color{blue}{1}}{\sqrt{x}}\right) \]

      4. un-div-inv 95.0%

         \[\leadsto 1 - 0.3333333333333333 \cdot \color{blue}{\frac{y}{\sqrt{x}}} \]

   5. Applied egg-rr 95.0%

      \[\leadsto 1 - 0.3333333333333333 \cdot \color{blue}{\frac{y}{\sqrt{x}}} \]

   if -1.05e82 < y < 1.90000000000000008e24

   1. Initial program 99.8%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Step-by-step derivation

      1. associate--l- 99.8%

         \[\leadsto \color{blue}{1 - \left(\frac{1}{x \cdot 9} + \frac{y}{3 \cdot \sqrt{x}}\right)} \]

      2. sub-neg 99.8%

         \[\leadsto \color{blue}{1 + \left(-\left(\frac{1}{x \cdot 9} + \frac{y}{3 \cdot \sqrt{x}}\right)\right)} \]

      3. +-commutative 99.8%

         \[\leadsto 1 + \left(-\color{blue}{\left(\frac{y}{3 \cdot \sqrt{x}} + \frac{1}{x \cdot 9}\right)}\right) \]

      4. distribute-neg-in 99.8%

         \[\leadsto 1 + \color{blue}{\left(\left(-\frac{y}{3 \cdot \sqrt{x}}\right) + \left(-\frac{1}{x \cdot 9}\right)\right)} \]

      5. distribute-frac-neg 99.8%

         \[\leadsto 1 + \left(\color{blue}{\frac{-y}{3 \cdot \sqrt{x}}} + \left(-\frac{1}{x \cdot 9}\right)\right) \]

      6. sub-neg 99.8%

         \[\leadsto 1 + \color{blue}{\left(\frac{-y}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right)} \]

      7. neg-mul-1 99.8%

         \[\leadsto 1 + \left(\frac{\color{blue}{-1 \cdot y}}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right) \]

      8. *-commutative 99.8%

         \[\leadsto 1 + \left(\frac{\color{blue}{y \cdot -1}}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right) \]

      9. associate-/l* 99.8%

         \[\leadsto 1 + \left(\color{blue}{y \cdot \frac{-1}{3 \cdot \sqrt{x}}} - \frac{1}{x \cdot 9}\right) \]

      10. fma-neg 99.8%

          \[\leadsto 1 + \color{blue}{\mathsf{fma}\left(y, \frac{-1}{3 \cdot \sqrt{x}}, -\frac{1}{x \cdot 9}\right)} \]

      11. associate-/r* 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \color{blue}{\frac{\frac{-1}{3}}{\sqrt{x}}}, -\frac{1}{x \cdot 9}\right) \]

      12. metadata-eval 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{\color{blue}{-0.3333333333333333}}{\sqrt{x}}, -\frac{1}{x \cdot 9}\right) \]

      13. *-commutative 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, -\frac{1}{\color{blue}{9 \cdot x}}\right) \]

      14. associate-/r* 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, -\color{blue}{\frac{\frac{1}{9}}{x}}\right) \]

      15. distribute-neg-frac 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \color{blue}{\frac{-\frac{1}{9}}{x}}\right) \]

      16. metadata-eval 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{-\color{blue}{0.1111111111111111}}{x}\right) \]

      17. metadata-eval 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{\color{blue}{-0.1111111111111111}}{x}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{-0.1111111111111111}{x}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 97.5%

      \[\leadsto 1 + \color{blue}{\frac{-0.1111111111111111}{x}} \]
   6. Step-by-step derivation

      1. metadata-eval 97.5%

         \[\leadsto 1 + \frac{\color{blue}{-0.1111111111111111}}{x} \]

      2. distribute-neg-frac 97.5%

         \[\leadsto 1 + \color{blue}{\left(-\frac{0.1111111111111111}{x}\right)} \]

      3. add-sqr-sqrt 97.3%

         \[\leadsto 1 + \left(-\color{blue}{\sqrt{\frac{0.1111111111111111}{x}} \cdot \sqrt{\frac{0.1111111111111111}{x}}}\right) \]

      4. sqrt-unprod 70.9%

         \[\leadsto 1 + \left(-\color{blue}{\sqrt{\frac{0.1111111111111111}{x} \cdot \frac{0.1111111111111111}{x}}}\right) \]

      5. frac-times 71.0%

         \[\leadsto 1 + \left(-\sqrt{\color{blue}{\frac{0.1111111111111111 \cdot 0.1111111111111111}{x \cdot x}}}\right) \]

      6. metadata-eval 71.0%

         \[\leadsto 1 + \left(-\sqrt{\frac{\color{blue}{0.012345679012345678}}{x \cdot x}}\right) \]

      7. metadata-eval 71.0%

         \[\leadsto 1 + \left(-\sqrt{\frac{\color{blue}{-0.1111111111111111 \cdot -0.1111111111111111}}{x \cdot x}}\right) \]

      8. frac-times 70.9%

         \[\leadsto 1 + \left(-\sqrt{\color{blue}{\frac{-0.1111111111111111}{x} \cdot \frac{-0.1111111111111111}{x}}}\right) \]

      9. sqrt-unprod 0.0%

         \[\leadsto 1 + \left(-\color{blue}{\sqrt{\frac{-0.1111111111111111}{x}} \cdot \sqrt{\frac{-0.1111111111111111}{x}}}\right) \]

      10. add-sqr-sqrt 45.5%

          \[\leadsto 1 + \left(-\color{blue}{\frac{-0.1111111111111111}{x}}\right) \]

   7. Applied egg-rr 45.5%

      \[\leadsto 1 + \color{blue}{\left(-\frac{-0.1111111111111111}{x}\right)} \]
   8. Step-by-step derivation

      1. add-sqr-sqrt 0.0%

         \[\leadsto 1 + \left(-\color{blue}{\sqrt{\frac{-0.1111111111111111}{x}} \cdot \sqrt{\frac{-0.1111111111111111}{x}}}\right) \]

      2. sqrt-unprod 70.9%

         \[\leadsto 1 + \left(-\color{blue}{\sqrt{\frac{-0.1111111111111111}{x} \cdot \frac{-0.1111111111111111}{x}}}\right) \]

      3. frac-times 71.0%

         \[\leadsto 1 + \left(-\sqrt{\color{blue}{\frac{-0.1111111111111111 \cdot -0.1111111111111111}{x \cdot x}}}\right) \]

      4. metadata-eval 71.0%

         \[\leadsto 1 + \left(-\sqrt{\frac{\color{blue}{0.012345679012345678}}{x \cdot x}}\right) \]

      5. metadata-eval 71.0%

         \[\leadsto 1 + \left(-\sqrt{\frac{\color{blue}{0.1111111111111111 \cdot 0.1111111111111111}}{x \cdot x}}\right) \]

      6. frac-times 70.9%

         \[\leadsto 1 + \left(-\sqrt{\color{blue}{\frac{0.1111111111111111}{x} \cdot \frac{0.1111111111111111}{x}}}\right) \]

      7. sqrt-unprod 97.3%

         \[\leadsto 1 + \left(-\color{blue}{\sqrt{\frac{0.1111111111111111}{x}} \cdot \sqrt{\frac{0.1111111111111111}{x}}}\right) \]

      8. add-sqr-sqrt 97.5%

         \[\leadsto 1 + \left(-\color{blue}{\frac{0.1111111111111111}{x}}\right) \]

      9. clear-num 97.5%

         \[\leadsto 1 + \left(-\color{blue}{\frac{1}{\frac{x}{0.1111111111111111}}}\right) \]

      10. div-inv 97.6%

          \[\leadsto 1 + \left(-\frac{1}{\color{blue}{x \cdot \frac{1}{0.1111111111111111}}}\right) \]

      11. metadata-eval 97.6%

          \[\leadsto 1 + \left(-\frac{1}{x \cdot \color{blue}{9}}\right) \]

      12. inv-pow 97.6%

          \[\leadsto 1 + \left(-\color{blue}{{\left(x \cdot 9\right)}^{-1}}\right) \]

   9. Applied egg-rr 97.6%

      \[\leadsto 1 + \left(-\color{blue}{{\left(x \cdot 9\right)}^{-1}}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+82} \lor \neg \left(y \leq 1.9 \cdot 10^{+24}\right):\\ \;\;\;\;1 - \frac{y}{\sqrt{x}} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;1 - {\left(x \cdot 9\right)}^{-1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+82} \lor \neg \left(y \leq 1.75 \cdot 10^{+24}\right):\\ \;\;\;\;1 - \frac{y}{\sqrt{x \cdot 9}}\\ \mathbf{else}:\\ \;\;\;\;1 - {\left(x \cdot 9\right)}^{-1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.95e+82) (not (<= y 1.75e+24)))
   (- 1.0 (/ y (sqrt (* x 9.0))))
   (- 1.0 (pow (* x 9.0) -1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.95e+82) || !(y <= 1.75e+24)) {
		tmp = 1.0 - (y / sqrt((x * 9.0)));
	} else {
		tmp = 1.0 - pow((x * 9.0), -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.95d+82)) .or. (.not. (y <= 1.75d+24))) then
        tmp = 1.0d0 - (y / sqrt((x * 9.0d0)))
    else
        tmp = 1.0d0 - ((x * 9.0d0) ** (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.95e+82) || !(y <= 1.75e+24)) {
		tmp = 1.0 - (y / Math.sqrt((x * 9.0)));
	} else {
		tmp = 1.0 - Math.pow((x * 9.0), -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.95e+82) or not (y <= 1.75e+24):
		tmp = 1.0 - (y / math.sqrt((x * 9.0)))
	else:
		tmp = 1.0 - math.pow((x * 9.0), -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.95e+82) || !(y <= 1.75e+24))
		tmp = Float64(1.0 - Float64(y / sqrt(Float64(x * 9.0))));
	else
		tmp = Float64(1.0 - (Float64(x * 9.0) ^ -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.95e+82) || ~((y <= 1.75e+24)))
		tmp = 1.0 - (y / sqrt((x * 9.0)));
	else
		tmp = 1.0 - ((x * 9.0) ^ -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.95e+82], N[Not[LessEqual[y, 1.75e+24]], $MachinePrecision]], N[(1.0 - N[(y / N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[Power[N[(x * 9.0), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.94999999999999988e82 or 1.7500000000000001e24 < y

   1. Initial program 99.6%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 95.0%

      \[\leadsto \color{blue}{1 - 0.3333333333333333 \cdot \left(\sqrt{\frac{1}{x}} \cdot y\right)} \]
   4. Step-by-step derivation

      1. metadata-eval 95.0%

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

      2. *-commutative 95.0%

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

      3. sqrt-div 94.9%

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

      4. metadata-eval 94.9%

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

      5. un-div-inv 95.0%

         \[\leadsto 1 - \frac{1}{3} \cdot \color{blue}{\frac{y}{\sqrt{x}}} \]

      6. times-frac 95.9%

         \[\leadsto 1 - \color{blue}{\frac{1 \cdot y}{3 \cdot \sqrt{x}}} \]

      7. *-un-lft-identity 95.9%

         \[\leadsto 1 - \frac{\color{blue}{y}}{3 \cdot \sqrt{x}} \]

   5. Applied egg-rr 95.9%

      \[\leadsto 1 - \color{blue}{\frac{y}{3 \cdot \sqrt{x}}} \]
   6. Step-by-step derivation

      1. *-commutative 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x} \cdot 3}} \]

      2. metadata-eval 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\sqrt{x} \cdot \color{blue}{\sqrt{9}}} \]

      3. sqrt-prod 99.7%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

      4. pow1/2 99.7%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]

   7. Applied egg-rr 96.0%

      \[\leadsto 1 - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]
   8. Step-by-step derivation

      1. unpow1/2 99.7%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   9. Simplified 96.0%

      \[\leadsto 1 - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   if -1.94999999999999988e82 < y < 1.7500000000000001e24

   1. Initial program 99.8%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Step-by-step derivation

      1. associate--l- 99.8%

         \[\leadsto \color{blue}{1 - \left(\frac{1}{x \cdot 9} + \frac{y}{3 \cdot \sqrt{x}}\right)} \]

      2. sub-neg 99.8%

         \[\leadsto \color{blue}{1 + \left(-\left(\frac{1}{x \cdot 9} + \frac{y}{3 \cdot \sqrt{x}}\right)\right)} \]

      3. +-commutative 99.8%

         \[\leadsto 1 + \left(-\color{blue}{\left(\frac{y}{3 \cdot \sqrt{x}} + \frac{1}{x \cdot 9}\right)}\right) \]

      4. distribute-neg-in 99.8%

         \[\leadsto 1 + \color{blue}{\left(\left(-\frac{y}{3 \cdot \sqrt{x}}\right) + \left(-\frac{1}{x \cdot 9}\right)\right)} \]

      5. distribute-frac-neg 99.8%

         \[\leadsto 1 + \left(\color{blue}{\frac{-y}{3 \cdot \sqrt{x}}} + \left(-\frac{1}{x \cdot 9}\right)\right) \]

      6. sub-neg 99.8%

         \[\leadsto 1 + \color{blue}{\left(\frac{-y}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right)} \]

      7. neg-mul-1 99.8%

         \[\leadsto 1 + \left(\frac{\color{blue}{-1 \cdot y}}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right) \]

      8. *-commutative 99.8%

         \[\leadsto 1 + \left(\frac{\color{blue}{y \cdot -1}}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right) \]

      9. associate-/l* 99.8%

         \[\leadsto 1 + \left(\color{blue}{y \cdot \frac{-1}{3 \cdot \sqrt{x}}} - \frac{1}{x \cdot 9}\right) \]

      10. fma-neg 99.8%

          \[\leadsto 1 + \color{blue}{\mathsf{fma}\left(y, \frac{-1}{3 \cdot \sqrt{x}}, -\frac{1}{x \cdot 9}\right)} \]

      11. associate-/r* 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \color{blue}{\frac{\frac{-1}{3}}{\sqrt{x}}}, -\frac{1}{x \cdot 9}\right) \]

      12. metadata-eval 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{\color{blue}{-0.3333333333333333}}{\sqrt{x}}, -\frac{1}{x \cdot 9}\right) \]

      13. *-commutative 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, -\frac{1}{\color{blue}{9 \cdot x}}\right) \]

      14. associate-/r* 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, -\color{blue}{\frac{\frac{1}{9}}{x}}\right) \]

      15. distribute-neg-frac 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \color{blue}{\frac{-\frac{1}{9}}{x}}\right) \]

      16. metadata-eval 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{-\color{blue}{0.1111111111111111}}{x}\right) \]

      17. metadata-eval 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{\color{blue}{-0.1111111111111111}}{x}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{-0.1111111111111111}{x}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 97.5%

      \[\leadsto 1 + \color{blue}{\frac{-0.1111111111111111}{x}} \]
   6. Step-by-step derivation

      1. metadata-eval 97.5%

         \[\leadsto 1 + \frac{\color{blue}{-0.1111111111111111}}{x} \]

      2. distribute-neg-frac 97.5%

         \[\leadsto 1 + \color{blue}{\left(-\frac{0.1111111111111111}{x}\right)} \]

      3. add-sqr-sqrt 97.3%

         \[\leadsto 1 + \left(-\color{blue}{\sqrt{\frac{0.1111111111111111}{x}} \cdot \sqrt{\frac{0.1111111111111111}{x}}}\right) \]

      4. sqrt-unprod 70.9%

         \[\leadsto 1 + \left(-\color{blue}{\sqrt{\frac{0.1111111111111111}{x} \cdot \frac{0.1111111111111111}{x}}}\right) \]

      5. frac-times 71.0%

         \[\leadsto 1 + \left(-\sqrt{\color{blue}{\frac{0.1111111111111111 \cdot 0.1111111111111111}{x \cdot x}}}\right) \]

      6. metadata-eval 71.0%

         \[\leadsto 1 + \left(-\sqrt{\frac{\color{blue}{0.012345679012345678}}{x \cdot x}}\right) \]

      7. metadata-eval 71.0%

         \[\leadsto 1 + \left(-\sqrt{\frac{\color{blue}{-0.1111111111111111 \cdot -0.1111111111111111}}{x \cdot x}}\right) \]

      8. frac-times 70.9%

         \[\leadsto 1 + \left(-\sqrt{\color{blue}{\frac{-0.1111111111111111}{x} \cdot \frac{-0.1111111111111111}{x}}}\right) \]

      9. sqrt-unprod 0.0%

         \[\leadsto 1 + \left(-\color{blue}{\sqrt{\frac{-0.1111111111111111}{x}} \cdot \sqrt{\frac{-0.1111111111111111}{x}}}\right) \]

      10. add-sqr-sqrt 45.5%

          \[\leadsto 1 + \left(-\color{blue}{\frac{-0.1111111111111111}{x}}\right) \]

   7. Applied egg-rr 45.5%

      \[\leadsto 1 + \color{blue}{\left(-\frac{-0.1111111111111111}{x}\right)} \]
   8. Step-by-step derivation

      1. add-sqr-sqrt 0.0%

         \[\leadsto 1 + \left(-\color{blue}{\sqrt{\frac{-0.1111111111111111}{x}} \cdot \sqrt{\frac{-0.1111111111111111}{x}}}\right) \]

      2. sqrt-unprod 70.9%

         \[\leadsto 1 + \left(-\color{blue}{\sqrt{\frac{-0.1111111111111111}{x} \cdot \frac{-0.1111111111111111}{x}}}\right) \]

      3. frac-times 71.0%

         \[\leadsto 1 + \left(-\sqrt{\color{blue}{\frac{-0.1111111111111111 \cdot -0.1111111111111111}{x \cdot x}}}\right) \]

      4. metadata-eval 71.0%

         \[\leadsto 1 + \left(-\sqrt{\frac{\color{blue}{0.012345679012345678}}{x \cdot x}}\right) \]

      5. metadata-eval 71.0%

         \[\leadsto 1 + \left(-\sqrt{\frac{\color{blue}{0.1111111111111111 \cdot 0.1111111111111111}}{x \cdot x}}\right) \]

      6. frac-times 70.9%

         \[\leadsto 1 + \left(-\sqrt{\color{blue}{\frac{0.1111111111111111}{x} \cdot \frac{0.1111111111111111}{x}}}\right) \]

      7. sqrt-unprod 97.3%

         \[\leadsto 1 + \left(-\color{blue}{\sqrt{\frac{0.1111111111111111}{x}} \cdot \sqrt{\frac{0.1111111111111111}{x}}}\right) \]

      8. add-sqr-sqrt 97.5%

         \[\leadsto 1 + \left(-\color{blue}{\frac{0.1111111111111111}{x}}\right) \]

      9. clear-num 97.5%

         \[\leadsto 1 + \left(-\color{blue}{\frac{1}{\frac{x}{0.1111111111111111}}}\right) \]

      10. div-inv 97.6%

          \[\leadsto 1 + \left(-\frac{1}{\color{blue}{x \cdot \frac{1}{0.1111111111111111}}}\right) \]

      11. metadata-eval 97.6%

          \[\leadsto 1 + \left(-\frac{1}{x \cdot \color{blue}{9}}\right) \]

      12. inv-pow 97.6%

          \[\leadsto 1 + \left(-\color{blue}{{\left(x \cdot 9\right)}^{-1}}\right) \]

   9. Applied egg-rr 97.6%

      \[\leadsto 1 + \left(-\color{blue}{{\left(x \cdot 9\right)}^{-1}}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+82} \lor \neg \left(y \leq 1.75 \cdot 10^{+24}\right):\\ \;\;\;\;1 - \frac{y}{\sqrt{x \cdot 9}}\\ \mathbf{else}:\\ \;\;\;\;1 - {\left(x \cdot 9\right)}^{-1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+92}:\\ \;\;\;\;\frac{y}{\sqrt{x} \cdot -3}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+93}:\\ \;\;\;\;1 + \frac{-0.1111111111111111}{x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{x}} \cdot \left(y \cdot -0.3333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5e+92)
   (/ y (* (sqrt x) -3.0))
   (if (<= y 5.5e+93)
     (+ 1.0 (/ -0.1111111111111111 x))
     (* (sqrt (/ 1.0 x)) (* y -0.3333333333333333)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5e+92) {
		tmp = y / (sqrt(x) * -3.0);
	} else if (y <= 5.5e+93) {
		tmp = 1.0 + (-0.1111111111111111 / x);
	} else {
		tmp = sqrt((1.0 / x)) * (y * -0.3333333333333333);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-5d+92)) then
        tmp = y / (sqrt(x) * (-3.0d0))
    else if (y <= 5.5d+93) then
        tmp = 1.0d0 + ((-0.1111111111111111d0) / x)
    else
        tmp = sqrt((1.0d0 / x)) * (y * (-0.3333333333333333d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5e+92) {
		tmp = y / (Math.sqrt(x) * -3.0);
	} else if (y <= 5.5e+93) {
		tmp = 1.0 + (-0.1111111111111111 / x);
	} else {
		tmp = Math.sqrt((1.0 / x)) * (y * -0.3333333333333333);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5e+92:
		tmp = y / (math.sqrt(x) * -3.0)
	elif y <= 5.5e+93:
		tmp = 1.0 + (-0.1111111111111111 / x)
	else:
		tmp = math.sqrt((1.0 / x)) * (y * -0.3333333333333333)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5e+92)
		tmp = Float64(y / Float64(sqrt(x) * -3.0));
	elseif (y <= 5.5e+93)
		tmp = Float64(1.0 + Float64(-0.1111111111111111 / x));
	else
		tmp = Float64(sqrt(Float64(1.0 / x)) * Float64(y * -0.3333333333333333));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5e+92)
		tmp = y / (sqrt(x) * -3.0);
	elseif (y <= 5.5e+93)
		tmp = 1.0 + (-0.1111111111111111 / x);
	else
		tmp = sqrt((1.0 / x)) * (y * -0.3333333333333333);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5e+92], N[(y / N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+93], N[(1.0 + N[(-0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(1.0 / x), $MachinePrecision]], $MachinePrecision] * N[(y * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.00000000000000022e92

   1. Initial program 99.5%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.5%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x} \cdot 3}} \]

      2. metadata-eval 99.5%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\sqrt{x} \cdot \color{blue}{\sqrt{9}}} \]

      3. sqrt-prod 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

      4. pow1/2 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]

   4. Applied egg-rr 99.6%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]
   5. Step-by-step derivation

      1. unpow1/2 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   6. Simplified 99.6%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   7. Taylor expanded in y around inf 94.7%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \left(\sqrt{\frac{1}{x}} \cdot y\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 94.7%

         \[\leadsto \color{blue}{\left(-0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\right) \cdot y} \]

      2. *-commutative 94.7%

         \[\leadsto \color{blue}{y \cdot \left(-0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\right)} \]

      3. *-commutative 94.7%

         \[\leadsto y \cdot \color{blue}{\left(\sqrt{\frac{1}{x}} \cdot -0.3333333333333333\right)} \]

      4. unpow1/2 94.7%

         \[\leadsto y \cdot \left(\color{blue}{{\left(\frac{1}{x}\right)}^{0.5}} \cdot -0.3333333333333333\right) \]

      5. unpow-1 94.7%

         \[\leadsto y \cdot \left({\color{blue}{\left({x}^{-1}\right)}}^{0.5} \cdot -0.3333333333333333\right) \]

      6. exp-to-pow 89.4%

         \[\leadsto y \cdot \left({\color{blue}{\left(e^{\log x \cdot -1}\right)}}^{0.5} \cdot -0.3333333333333333\right) \]

      7. *-commutative 89.4%

         \[\leadsto y \cdot \left({\left(e^{\color{blue}{-1 \cdot \log x}}\right)}^{0.5} \cdot -0.3333333333333333\right) \]

      8. neg-mul-1 89.4%

         \[\leadsto y \cdot \left({\left(e^{\color{blue}{-\log x}}\right)}^{0.5} \cdot -0.3333333333333333\right) \]

      9. exp-prod 89.4%

         \[\leadsto y \cdot \left(\color{blue}{e^{\left(-\log x\right) \cdot 0.5}} \cdot -0.3333333333333333\right) \]

      10. distribute-lft-neg-out 89.4%

          \[\leadsto y \cdot \left(e^{\color{blue}{-\log x \cdot 0.5}} \cdot -0.3333333333333333\right) \]

      11. exp-neg 89.4%

          \[\leadsto y \cdot \left(\color{blue}{\frac{1}{e^{\log x \cdot 0.5}}} \cdot -0.3333333333333333\right) \]

      12. exp-to-pow 94.5%

          \[\leadsto y \cdot \left(\frac{1}{\color{blue}{{x}^{0.5}}} \cdot -0.3333333333333333\right) \]

      13. unpow1/2 94.5%

          \[\leadsto y \cdot \left(\frac{1}{\color{blue}{\sqrt{x}}} \cdot -0.3333333333333333\right) \]

      14. unpow-1 94.5%

          \[\leadsto y \cdot \left(\color{blue}{{\left(\sqrt{x}\right)}^{-1}} \cdot -0.3333333333333333\right) \]

      15. metadata-eval 94.5%

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

      16. associate-/l* 94.7%

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

      17. *-rgt-identity 94.7%

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

      18. unpow-1 94.7%

          \[\leadsto y \cdot \frac{\color{blue}{\frac{1}{\sqrt{x}}}}{-3} \]

      19. associate-/r* 94.8%

          \[\leadsto y \cdot \color{blue}{\frac{1}{\sqrt{x} \cdot -3}} \]

      20. *-commutative 94.8%

          \[\leadsto y \cdot \frac{1}{\color{blue}{-3 \cdot \sqrt{x}}} \]

      21. associate-/r* 94.6%

          \[\leadsto y \cdot \color{blue}{\frac{\frac{1}{-3}}{\sqrt{x}}} \]

      22. metadata-eval 94.6%

          \[\leadsto y \cdot \frac{\color{blue}{-0.3333333333333333}}{\sqrt{x}} \]

   9. Simplified 94.6%

      \[\leadsto \color{blue}{y \cdot \frac{-0.3333333333333333}{\sqrt{x}}} \]
   10. Step-by-step derivation

       1. clear-num 94.7%

          \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{\sqrt{x}}{-0.3333333333333333}}} \]

       2. un-div-inv 94.7%

          \[\leadsto \color{blue}{\frac{y}{\frac{\sqrt{x}}{-0.3333333333333333}}} \]

       3. div-inv 94.8%

          \[\leadsto \frac{y}{\color{blue}{\sqrt{x} \cdot \frac{1}{-0.3333333333333333}}} \]

       4. metadata-eval 94.8%

          \[\leadsto \frac{y}{\sqrt{x} \cdot \color{blue}{-3}} \]

   11. Applied egg-rr 94.8%

       \[\leadsto \color{blue}{\frac{y}{\sqrt{x} \cdot -3}} \]

   if -5.00000000000000022e92 < y < 5.5000000000000003e93

   1. Initial program 99.8%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Step-by-step derivation

      1. associate--l- 99.8%

         \[\leadsto \color{blue}{1 - \left(\frac{1}{x \cdot 9} + \frac{y}{3 \cdot \sqrt{x}}\right)} \]

      2. sub-neg 99.8%

         \[\leadsto \color{blue}{1 + \left(-\left(\frac{1}{x \cdot 9} + \frac{y}{3 \cdot \sqrt{x}}\right)\right)} \]

      3. +-commutative 99.8%

         \[\leadsto 1 + \left(-\color{blue}{\left(\frac{y}{3 \cdot \sqrt{x}} + \frac{1}{x \cdot 9}\right)}\right) \]

      4. distribute-neg-in 99.8%

         \[\leadsto 1 + \color{blue}{\left(\left(-\frac{y}{3 \cdot \sqrt{x}}\right) + \left(-\frac{1}{x \cdot 9}\right)\right)} \]

      5. distribute-frac-neg 99.8%

         \[\leadsto 1 + \left(\color{blue}{\frac{-y}{3 \cdot \sqrt{x}}} + \left(-\frac{1}{x \cdot 9}\right)\right) \]

      6. sub-neg 99.8%

         \[\leadsto 1 + \color{blue}{\left(\frac{-y}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right)} \]

      7. neg-mul-1 99.8%

         \[\leadsto 1 + \left(\frac{\color{blue}{-1 \cdot y}}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right) \]

      8. *-commutative 99.8%

         \[\leadsto 1 + \left(\frac{\color{blue}{y \cdot -1}}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right) \]

      9. associate-/l* 99.8%

         \[\leadsto 1 + \left(\color{blue}{y \cdot \frac{-1}{3 \cdot \sqrt{x}}} - \frac{1}{x \cdot 9}\right) \]

      10. fma-neg 99.8%

          \[\leadsto 1 + \color{blue}{\mathsf{fma}\left(y, \frac{-1}{3 \cdot \sqrt{x}}, -\frac{1}{x \cdot 9}\right)} \]

      11. associate-/r* 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \color{blue}{\frac{\frac{-1}{3}}{\sqrt{x}}}, -\frac{1}{x \cdot 9}\right) \]

      12. metadata-eval 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{\color{blue}{-0.3333333333333333}}{\sqrt{x}}, -\frac{1}{x \cdot 9}\right) \]

      13. *-commutative 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, -\frac{1}{\color{blue}{9 \cdot x}}\right) \]

      14. associate-/r* 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, -\color{blue}{\frac{\frac{1}{9}}{x}}\right) \]

      15. distribute-neg-frac 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \color{blue}{\frac{-\frac{1}{9}}{x}}\right) \]

      16. metadata-eval 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{-\color{blue}{0.1111111111111111}}{x}\right) \]

      17. metadata-eval 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{\color{blue}{-0.1111111111111111}}{x}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{-0.1111111111111111}{x}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 94.0%

      \[\leadsto 1 + \color{blue}{\frac{-0.1111111111111111}{x}} \]

   if 5.5000000000000003e93 < y

   1. Initial program 99.6%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x} \cdot 3}} \]

      2. metadata-eval 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\sqrt{x} \cdot \color{blue}{\sqrt{9}}} \]

      3. sqrt-prod 99.8%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

      4. pow1/2 99.8%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]

   4. Applied egg-rr 99.8%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]
   5. Step-by-step derivation

      1. unpow1/2 99.8%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   6. Simplified 99.8%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   7. Taylor expanded in y around inf 94.9%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \left(\sqrt{\frac{1}{x}} \cdot y\right)} \]
   8. Step-by-step derivation

      1. *-commutative 94.9%

         \[\leadsto \color{blue}{\left(\sqrt{\frac{1}{x}} \cdot y\right) \cdot -0.3333333333333333} \]

      2. associate-*l* 97.1%

         \[\leadsto \color{blue}{\sqrt{\frac{1}{x}} \cdot \left(y \cdot -0.3333333333333333\right)} \]

   9. Simplified 97.1%

      \[\leadsto \color{blue}{\sqrt{\frac{1}{x}} \cdot \left(y \cdot -0.3333333333333333\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+92}:\\ \;\;\;\;\frac{y}{\sqrt{x} \cdot -3}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+93}:\\ \;\;\;\;1 + \frac{-0.1111111111111111}{x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{x}} \cdot \left(y \cdot -0.3333333333333333\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+92}:\\ \;\;\;\;\frac{y}{\sqrt{x} \cdot -3}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+93}:\\ \;\;\;\;1 - {\left(x \cdot 9\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{x}} \cdot \left(y \cdot -0.3333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5e+92)
   (/ y (* (sqrt x) -3.0))
   (if (<= y 1.05e+93)
     (- 1.0 (pow (* x 9.0) -1.0))
     (* (sqrt (/ 1.0 x)) (* y -0.3333333333333333)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5e+92) {
		tmp = y / (sqrt(x) * -3.0);
	} else if (y <= 1.05e+93) {
		tmp = 1.0 - pow((x * 9.0), -1.0);
	} else {
		tmp = sqrt((1.0 / x)) * (y * -0.3333333333333333);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-5d+92)) then
        tmp = y / (sqrt(x) * (-3.0d0))
    else if (y <= 1.05d+93) then
        tmp = 1.0d0 - ((x * 9.0d0) ** (-1.0d0))
    else
        tmp = sqrt((1.0d0 / x)) * (y * (-0.3333333333333333d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5e+92) {
		tmp = y / (Math.sqrt(x) * -3.0);
	} else if (y <= 1.05e+93) {
		tmp = 1.0 - Math.pow((x * 9.0), -1.0);
	} else {
		tmp = Math.sqrt((1.0 / x)) * (y * -0.3333333333333333);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5e+92:
		tmp = y / (math.sqrt(x) * -3.0)
	elif y <= 1.05e+93:
		tmp = 1.0 - math.pow((x * 9.0), -1.0)
	else:
		tmp = math.sqrt((1.0 / x)) * (y * -0.3333333333333333)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5e+92)
		tmp = Float64(y / Float64(sqrt(x) * -3.0));
	elseif (y <= 1.05e+93)
		tmp = Float64(1.0 - (Float64(x * 9.0) ^ -1.0));
	else
		tmp = Float64(sqrt(Float64(1.0 / x)) * Float64(y * -0.3333333333333333));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5e+92)
		tmp = y / (sqrt(x) * -3.0);
	elseif (y <= 1.05e+93)
		tmp = 1.0 - ((x * 9.0) ^ -1.0);
	else
		tmp = sqrt((1.0 / x)) * (y * -0.3333333333333333);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5e+92], N[(y / N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+93], N[(1.0 - N[Power[N[(x * 9.0), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(1.0 / x), $MachinePrecision]], $MachinePrecision] * N[(y * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.00000000000000022e92

   1. Initial program 99.5%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.5%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x} \cdot 3}} \]

      2. metadata-eval 99.5%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\sqrt{x} \cdot \color{blue}{\sqrt{9}}} \]

      3. sqrt-prod 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

      4. pow1/2 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]

   4. Applied egg-rr 99.6%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]
   5. Step-by-step derivation

      1. unpow1/2 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   6. Simplified 99.6%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   7. Taylor expanded in y around inf 94.7%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \left(\sqrt{\frac{1}{x}} \cdot y\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 94.7%

         \[\leadsto \color{blue}{\left(-0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\right) \cdot y} \]

      2. *-commutative 94.7%

         \[\leadsto \color{blue}{y \cdot \left(-0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\right)} \]

      3. *-commutative 94.7%

         \[\leadsto y \cdot \color{blue}{\left(\sqrt{\frac{1}{x}} \cdot -0.3333333333333333\right)} \]

      4. unpow1/2 94.7%

         \[\leadsto y \cdot \left(\color{blue}{{\left(\frac{1}{x}\right)}^{0.5}} \cdot -0.3333333333333333\right) \]

      5. unpow-1 94.7%

         \[\leadsto y \cdot \left({\color{blue}{\left({x}^{-1}\right)}}^{0.5} \cdot -0.3333333333333333\right) \]

      6. exp-to-pow 89.4%

         \[\leadsto y \cdot \left({\color{blue}{\left(e^{\log x \cdot -1}\right)}}^{0.5} \cdot -0.3333333333333333\right) \]

      7. *-commutative 89.4%

         \[\leadsto y \cdot \left({\left(e^{\color{blue}{-1 \cdot \log x}}\right)}^{0.5} \cdot -0.3333333333333333\right) \]

      8. neg-mul-1 89.4%

         \[\leadsto y \cdot \left({\left(e^{\color{blue}{-\log x}}\right)}^{0.5} \cdot -0.3333333333333333\right) \]

      9. exp-prod 89.4%

         \[\leadsto y \cdot \left(\color{blue}{e^{\left(-\log x\right) \cdot 0.5}} \cdot -0.3333333333333333\right) \]

      10. distribute-lft-neg-out 89.4%

          \[\leadsto y \cdot \left(e^{\color{blue}{-\log x \cdot 0.5}} \cdot -0.3333333333333333\right) \]

      11. exp-neg 89.4%

          \[\leadsto y \cdot \left(\color{blue}{\frac{1}{e^{\log x \cdot 0.5}}} \cdot -0.3333333333333333\right) \]

      12. exp-to-pow 94.5%

          \[\leadsto y \cdot \left(\frac{1}{\color{blue}{{x}^{0.5}}} \cdot -0.3333333333333333\right) \]

      13. unpow1/2 94.5%

          \[\leadsto y \cdot \left(\frac{1}{\color{blue}{\sqrt{x}}} \cdot -0.3333333333333333\right) \]

      14. unpow-1 94.5%

          \[\leadsto y \cdot \left(\color{blue}{{\left(\sqrt{x}\right)}^{-1}} \cdot -0.3333333333333333\right) \]

      15. metadata-eval 94.5%

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

      16. associate-/l* 94.7%

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

      17. *-rgt-identity 94.7%

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

      18. unpow-1 94.7%

          \[\leadsto y \cdot \frac{\color{blue}{\frac{1}{\sqrt{x}}}}{-3} \]

      19. associate-/r* 94.8%

          \[\leadsto y \cdot \color{blue}{\frac{1}{\sqrt{x} \cdot -3}} \]

      20. *-commutative 94.8%

          \[\leadsto y \cdot \frac{1}{\color{blue}{-3 \cdot \sqrt{x}}} \]

      21. associate-/r* 94.6%

          \[\leadsto y \cdot \color{blue}{\frac{\frac{1}{-3}}{\sqrt{x}}} \]

      22. metadata-eval 94.6%

          \[\leadsto y \cdot \frac{\color{blue}{-0.3333333333333333}}{\sqrt{x}} \]

   9. Simplified 94.6%

      \[\leadsto \color{blue}{y \cdot \frac{-0.3333333333333333}{\sqrt{x}}} \]
   10. Step-by-step derivation

       1. clear-num 94.7%

          \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{\sqrt{x}}{-0.3333333333333333}}} \]

       2. un-div-inv 94.7%

          \[\leadsto \color{blue}{\frac{y}{\frac{\sqrt{x}}{-0.3333333333333333}}} \]

       3. div-inv 94.8%

          \[\leadsto \frac{y}{\color{blue}{\sqrt{x} \cdot \frac{1}{-0.3333333333333333}}} \]

       4. metadata-eval 94.8%

          \[\leadsto \frac{y}{\sqrt{x} \cdot \color{blue}{-3}} \]

   11. Applied egg-rr 94.8%

       \[\leadsto \color{blue}{\frac{y}{\sqrt{x} \cdot -3}} \]

   if -5.00000000000000022e92 < y < 1.0499999999999999e93

   1. Initial program 99.8%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Step-by-step derivation

      1. associate--l- 99.8%

         \[\leadsto \color{blue}{1 - \left(\frac{1}{x \cdot 9} + \frac{y}{3 \cdot \sqrt{x}}\right)} \]

      2. sub-neg 99.8%

         \[\leadsto \color{blue}{1 + \left(-\left(\frac{1}{x \cdot 9} + \frac{y}{3 \cdot \sqrt{x}}\right)\right)} \]

      3. +-commutative 99.8%

         \[\leadsto 1 + \left(-\color{blue}{\left(\frac{y}{3 \cdot \sqrt{x}} + \frac{1}{x \cdot 9}\right)}\right) \]

      4. distribute-neg-in 99.8%

         \[\leadsto 1 + \color{blue}{\left(\left(-\frac{y}{3 \cdot \sqrt{x}}\right) + \left(-\frac{1}{x \cdot 9}\right)\right)} \]

      5. distribute-frac-neg 99.8%

         \[\leadsto 1 + \left(\color{blue}{\frac{-y}{3 \cdot \sqrt{x}}} + \left(-\frac{1}{x \cdot 9}\right)\right) \]

      6. sub-neg 99.8%

         \[\leadsto 1 + \color{blue}{\left(\frac{-y}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right)} \]

      7. neg-mul-1 99.8%

         \[\leadsto 1 + \left(\frac{\color{blue}{-1 \cdot y}}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right) \]

      8. *-commutative 99.8%

         \[\leadsto 1 + \left(\frac{\color{blue}{y \cdot -1}}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right) \]

      9. associate-/l* 99.8%

         \[\leadsto 1 + \left(\color{blue}{y \cdot \frac{-1}{3 \cdot \sqrt{x}}} - \frac{1}{x \cdot 9}\right) \]

      10. fma-neg 99.8%

          \[\leadsto 1 + \color{blue}{\mathsf{fma}\left(y, \frac{-1}{3 \cdot \sqrt{x}}, -\frac{1}{x \cdot 9}\right)} \]

      11. associate-/r* 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \color{blue}{\frac{\frac{-1}{3}}{\sqrt{x}}}, -\frac{1}{x \cdot 9}\right) \]

      12. metadata-eval 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{\color{blue}{-0.3333333333333333}}{\sqrt{x}}, -\frac{1}{x \cdot 9}\right) \]

      13. *-commutative 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, -\frac{1}{\color{blue}{9 \cdot x}}\right) \]

      14. associate-/r* 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, -\color{blue}{\frac{\frac{1}{9}}{x}}\right) \]

      15. distribute-neg-frac 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \color{blue}{\frac{-\frac{1}{9}}{x}}\right) \]

      16. metadata-eval 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{-\color{blue}{0.1111111111111111}}{x}\right) \]

      17. metadata-eval 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{\color{blue}{-0.1111111111111111}}{x}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{-0.1111111111111111}{x}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 94.0%

      \[\leadsto 1 + \color{blue}{\frac{-0.1111111111111111}{x}} \]
   6. Step-by-step derivation

      1. metadata-eval 94.0%

         \[\leadsto 1 + \frac{\color{blue}{-0.1111111111111111}}{x} \]

      2. distribute-neg-frac 94.0%

         \[\leadsto 1 + \color{blue}{\left(-\frac{0.1111111111111111}{x}\right)} \]

      3. add-sqr-sqrt 93.9%

         \[\leadsto 1 + \left(-\color{blue}{\sqrt{\frac{0.1111111111111111}{x}} \cdot \sqrt{\frac{0.1111111111111111}{x}}}\right) \]

      4. sqrt-unprod 69.9%

         \[\leadsto 1 + \left(-\color{blue}{\sqrt{\frac{0.1111111111111111}{x} \cdot \frac{0.1111111111111111}{x}}}\right) \]

      5. frac-times 70.0%

         \[\leadsto 1 + \left(-\sqrt{\color{blue}{\frac{0.1111111111111111 \cdot 0.1111111111111111}{x \cdot x}}}\right) \]

      6. metadata-eval 70.0%

         \[\leadsto 1 + \left(-\sqrt{\frac{\color{blue}{0.012345679012345678}}{x \cdot x}}\right) \]

      7. metadata-eval 70.0%

         \[\leadsto 1 + \left(-\sqrt{\frac{\color{blue}{-0.1111111111111111 \cdot -0.1111111111111111}}{x \cdot x}}\right) \]

      8. frac-times 69.9%

         \[\leadsto 1 + \left(-\sqrt{\color{blue}{\frac{-0.1111111111111111}{x} \cdot \frac{-0.1111111111111111}{x}}}\right) \]

      9. sqrt-unprod 0.0%

         \[\leadsto 1 + \left(-\color{blue}{\sqrt{\frac{-0.1111111111111111}{x}} \cdot \sqrt{\frac{-0.1111111111111111}{x}}}\right) \]

      10. add-sqr-sqrt 47.0%

          \[\leadsto 1 + \left(-\color{blue}{\frac{-0.1111111111111111}{x}}\right) \]

   7. Applied egg-rr 47.0%

      \[\leadsto 1 + \color{blue}{\left(-\frac{-0.1111111111111111}{x}\right)} \]
   8. Step-by-step derivation

      1. add-sqr-sqrt 0.0%

         \[\leadsto 1 + \left(-\color{blue}{\sqrt{\frac{-0.1111111111111111}{x}} \cdot \sqrt{\frac{-0.1111111111111111}{x}}}\right) \]

      2. sqrt-unprod 69.9%

         \[\leadsto 1 + \left(-\color{blue}{\sqrt{\frac{-0.1111111111111111}{x} \cdot \frac{-0.1111111111111111}{x}}}\right) \]

      3. frac-times 70.0%

         \[\leadsto 1 + \left(-\sqrt{\color{blue}{\frac{-0.1111111111111111 \cdot -0.1111111111111111}{x \cdot x}}}\right) \]

      4. metadata-eval 70.0%

         \[\leadsto 1 + \left(-\sqrt{\frac{\color{blue}{0.012345679012345678}}{x \cdot x}}\right) \]

      5. metadata-eval 70.0%

         \[\leadsto 1 + \left(-\sqrt{\frac{\color{blue}{0.1111111111111111 \cdot 0.1111111111111111}}{x \cdot x}}\right) \]

      6. frac-times 69.9%

         \[\leadsto 1 + \left(-\sqrt{\color{blue}{\frac{0.1111111111111111}{x} \cdot \frac{0.1111111111111111}{x}}}\right) \]

      7. sqrt-unprod 93.9%

         \[\leadsto 1 + \left(-\color{blue}{\sqrt{\frac{0.1111111111111111}{x}} \cdot \sqrt{\frac{0.1111111111111111}{x}}}\right) \]

      8. add-sqr-sqrt 94.0%

         \[\leadsto 1 + \left(-\color{blue}{\frac{0.1111111111111111}{x}}\right) \]

      9. clear-num 94.0%

         \[\leadsto 1 + \left(-\color{blue}{\frac{1}{\frac{x}{0.1111111111111111}}}\right) \]

      10. div-inv 94.1%

          \[\leadsto 1 + \left(-\frac{1}{\color{blue}{x \cdot \frac{1}{0.1111111111111111}}}\right) \]

      11. metadata-eval 94.1%

          \[\leadsto 1 + \left(-\frac{1}{x \cdot \color{blue}{9}}\right) \]

      12. inv-pow 94.1%

          \[\leadsto 1 + \left(-\color{blue}{{\left(x \cdot 9\right)}^{-1}}\right) \]

   9. Applied egg-rr 94.1%

      \[\leadsto 1 + \left(-\color{blue}{{\left(x \cdot 9\right)}^{-1}}\right) \]

   if 1.0499999999999999e93 < y

   1. Initial program 99.6%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x} \cdot 3}} \]

      2. metadata-eval 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\sqrt{x} \cdot \color{blue}{\sqrt{9}}} \]

      3. sqrt-prod 99.8%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

      4. pow1/2 99.8%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]

   4. Applied egg-rr 99.8%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]
   5. Step-by-step derivation

      1. unpow1/2 99.8%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   6. Simplified 99.8%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   7. Taylor expanded in y around inf 94.9%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \left(\sqrt{\frac{1}{x}} \cdot y\right)} \]
   8. Step-by-step derivation

      1. *-commutative 94.9%

         \[\leadsto \color{blue}{\left(\sqrt{\frac{1}{x}} \cdot y\right) \cdot -0.3333333333333333} \]

      2. associate-*l* 97.1%

         \[\leadsto \color{blue}{\sqrt{\frac{1}{x}} \cdot \left(y \cdot -0.3333333333333333\right)} \]

   9. Simplified 97.1%

      \[\leadsto \color{blue}{\sqrt{\frac{1}{x}} \cdot \left(y \cdot -0.3333333333333333\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+92}:\\ \;\;\;\;\frac{y}{\sqrt{x} \cdot -3}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+93}:\\ \;\;\;\;1 - {\left(x \cdot 9\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{x}} \cdot \left(y \cdot -0.3333333333333333\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+92} \lor \neg \left(y \leq 9.5 \cdot 10^{+93}\right):\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{\sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.1111111111111111}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5e+92) (not (<= y 9.5e+93)))
   (* y (/ -0.3333333333333333 (sqrt x)))
   (+ 1.0 (/ -0.1111111111111111 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5e+92) || !(y <= 9.5e+93)) {
		tmp = y * (-0.3333333333333333 / sqrt(x));
	} else {
		tmp = 1.0 + (-0.1111111111111111 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-5d+92)) .or. (.not. (y <= 9.5d+93))) then
        tmp = y * ((-0.3333333333333333d0) / sqrt(x))
    else
        tmp = 1.0d0 + ((-0.1111111111111111d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -5e+92) || !(y <= 9.5e+93)) {
		tmp = y * (-0.3333333333333333 / Math.sqrt(x));
	} else {
		tmp = 1.0 + (-0.1111111111111111 / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5e+92) or not (y <= 9.5e+93):
		tmp = y * (-0.3333333333333333 / math.sqrt(x))
	else:
		tmp = 1.0 + (-0.1111111111111111 / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5e+92) || !(y <= 9.5e+93))
		tmp = Float64(y * Float64(-0.3333333333333333 / sqrt(x)));
	else
		tmp = Float64(1.0 + Float64(-0.1111111111111111 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -5e+92) || ~((y <= 9.5e+93)))
		tmp = y * (-0.3333333333333333 / sqrt(x));
	else
		tmp = 1.0 + (-0.1111111111111111 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5e+92], N[Not[LessEqual[y, 9.5e+93]], $MachinePrecision]], N[(y * N[(-0.3333333333333333 / N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.00000000000000022e92 or 9.4999999999999991e93 < y

   1. Initial program 99.6%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x} \cdot 3}} \]

      2. metadata-eval 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\sqrt{x} \cdot \color{blue}{\sqrt{9}}} \]

      3. sqrt-prod 99.7%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

      4. pow1/2 99.7%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]

   4. Applied egg-rr 99.7%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]
   5. Step-by-step derivation

      1. unpow1/2 99.7%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   6. Simplified 99.7%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   7. Taylor expanded in y around inf 94.8%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \left(\sqrt{\frac{1}{x}} \cdot y\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 95.8%

         \[\leadsto \color{blue}{\left(-0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\right) \cdot y} \]

      2. *-commutative 95.8%

         \[\leadsto \color{blue}{y \cdot \left(-0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\right)} \]

      3. *-commutative 95.8%

         \[\leadsto y \cdot \color{blue}{\left(\sqrt{\frac{1}{x}} \cdot -0.3333333333333333\right)} \]

      4. unpow1/2 95.8%

         \[\leadsto y \cdot \left(\color{blue}{{\left(\frac{1}{x}\right)}^{0.5}} \cdot -0.3333333333333333\right) \]

      5. unpow-1 95.8%

         \[\leadsto y \cdot \left({\color{blue}{\left({x}^{-1}\right)}}^{0.5} \cdot -0.3333333333333333\right) \]

      6. exp-to-pow 90.7%

         \[\leadsto y \cdot \left({\color{blue}{\left(e^{\log x \cdot -1}\right)}}^{0.5} \cdot -0.3333333333333333\right) \]

      7. *-commutative 90.7%

         \[\leadsto y \cdot \left({\left(e^{\color{blue}{-1 \cdot \log x}}\right)}^{0.5} \cdot -0.3333333333333333\right) \]

      8. neg-mul-1 90.7%

         \[\leadsto y \cdot \left({\left(e^{\color{blue}{-\log x}}\right)}^{0.5} \cdot -0.3333333333333333\right) \]

      9. exp-prod 90.7%

         \[\leadsto y \cdot \left(\color{blue}{e^{\left(-\log x\right) \cdot 0.5}} \cdot -0.3333333333333333\right) \]

      10. distribute-lft-neg-out 90.7%

          \[\leadsto y \cdot \left(e^{\color{blue}{-\log x \cdot 0.5}} \cdot -0.3333333333333333\right) \]

      11. exp-neg 90.7%

          \[\leadsto y \cdot \left(\color{blue}{\frac{1}{e^{\log x \cdot 0.5}}} \cdot -0.3333333333333333\right) \]

      12. exp-to-pow 95.7%

          \[\leadsto y \cdot \left(\frac{1}{\color{blue}{{x}^{0.5}}} \cdot -0.3333333333333333\right) \]

      13. unpow1/2 95.7%

          \[\leadsto y \cdot \left(\frac{1}{\color{blue}{\sqrt{x}}} \cdot -0.3333333333333333\right) \]

      14. unpow-1 95.7%

          \[\leadsto y \cdot \left(\color{blue}{{\left(\sqrt{x}\right)}^{-1}} \cdot -0.3333333333333333\right) \]

      15. metadata-eval 95.7%

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

      16. associate-/l* 95.8%

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

      17. *-rgt-identity 95.8%

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

      18. unpow-1 95.8%

          \[\leadsto y \cdot \frac{\color{blue}{\frac{1}{\sqrt{x}}}}{-3} \]

      19. associate-/r* 95.9%

          \[\leadsto y \cdot \color{blue}{\frac{1}{\sqrt{x} \cdot -3}} \]

      20. *-commutative 95.9%

          \[\leadsto y \cdot \frac{1}{\color{blue}{-3 \cdot \sqrt{x}}} \]

      21. associate-/r* 95.8%

          \[\leadsto y \cdot \color{blue}{\frac{\frac{1}{-3}}{\sqrt{x}}} \]

      22. metadata-eval 95.8%

          \[\leadsto y \cdot \frac{\color{blue}{-0.3333333333333333}}{\sqrt{x}} \]

   9. Simplified 95.8%

      \[\leadsto \color{blue}{y \cdot \frac{-0.3333333333333333}{\sqrt{x}}} \]

   if -5.00000000000000022e92 < y < 9.4999999999999991e93

   1. Initial program 99.8%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Step-by-step derivation

      1. associate--l- 99.8%

         \[\leadsto \color{blue}{1 - \left(\frac{1}{x \cdot 9} + \frac{y}{3 \cdot \sqrt{x}}\right)} \]

      2. sub-neg 99.8%

         \[\leadsto \color{blue}{1 + \left(-\left(\frac{1}{x \cdot 9} + \frac{y}{3 \cdot \sqrt{x}}\right)\right)} \]

      3. +-commutative 99.8%

         \[\leadsto 1 + \left(-\color{blue}{\left(\frac{y}{3 \cdot \sqrt{x}} + \frac{1}{x \cdot 9}\right)}\right) \]

      4. distribute-neg-in 99.8%

         \[\leadsto 1 + \color{blue}{\left(\left(-\frac{y}{3 \cdot \sqrt{x}}\right) + \left(-\frac{1}{x \cdot 9}\right)\right)} \]

      5. distribute-frac-neg 99.8%

         \[\leadsto 1 + \left(\color{blue}{\frac{-y}{3 \cdot \sqrt{x}}} + \left(-\frac{1}{x \cdot 9}\right)\right) \]

      6. sub-neg 99.8%

         \[\leadsto 1 + \color{blue}{\left(\frac{-y}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right)} \]

      7. neg-mul-1 99.8%

         \[\leadsto 1 + \left(\frac{\color{blue}{-1 \cdot y}}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right) \]

      8. *-commutative 99.8%

         \[\leadsto 1 + \left(\frac{\color{blue}{y \cdot -1}}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right) \]

      9. associate-/l* 99.8%

         \[\leadsto 1 + \left(\color{blue}{y \cdot \frac{-1}{3 \cdot \sqrt{x}}} - \frac{1}{x \cdot 9}\right) \]

      10. fma-neg 99.8%

          \[\leadsto 1 + \color{blue}{\mathsf{fma}\left(y, \frac{-1}{3 \cdot \sqrt{x}}, -\frac{1}{x \cdot 9}\right)} \]

      11. associate-/r* 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \color{blue}{\frac{\frac{-1}{3}}{\sqrt{x}}}, -\frac{1}{x \cdot 9}\right) \]

      12. metadata-eval 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{\color{blue}{-0.3333333333333333}}{\sqrt{x}}, -\frac{1}{x \cdot 9}\right) \]

      13. *-commutative 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, -\frac{1}{\color{blue}{9 \cdot x}}\right) \]

      14. associate-/r* 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, -\color{blue}{\frac{\frac{1}{9}}{x}}\right) \]

      15. distribute-neg-frac 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \color{blue}{\frac{-\frac{1}{9}}{x}}\right) \]

      16. metadata-eval 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{-\color{blue}{0.1111111111111111}}{x}\right) \]

      17. metadata-eval 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{\color{blue}{-0.1111111111111111}}{x}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{-0.1111111111111111}{x}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 94.0%

      \[\leadsto 1 + \color{blue}{\frac{-0.1111111111111111}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+92} \lor \neg \left(y \leq 9.5 \cdot 10^{+93}\right):\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{\sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.1111111111111111}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+92} \lor \neg \left(y \leq 3.6 \cdot 10^{+93}\right):\\ \;\;\;\;\frac{y}{\sqrt{x} \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.1111111111111111}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.8e+92) (not (<= y 3.6e+93)))
   (/ y (* (sqrt x) -3.0))
   (+ 1.0 (/ -0.1111111111111111 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.8e+92) || !(y <= 3.6e+93)) {
		tmp = y / (sqrt(x) * -3.0);
	} else {
		tmp = 1.0 + (-0.1111111111111111 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-4.8d+92)) .or. (.not. (y <= 3.6d+93))) then
        tmp = y / (sqrt(x) * (-3.0d0))
    else
        tmp = 1.0d0 + ((-0.1111111111111111d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -4.8e+92) || !(y <= 3.6e+93)) {
		tmp = y / (Math.sqrt(x) * -3.0);
	} else {
		tmp = 1.0 + (-0.1111111111111111 / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.8e+92) or not (y <= 3.6e+93):
		tmp = y / (math.sqrt(x) * -3.0)
	else:
		tmp = 1.0 + (-0.1111111111111111 / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.8e+92) || !(y <= 3.6e+93))
		tmp = Float64(y / Float64(sqrt(x) * -3.0));
	else
		tmp = Float64(1.0 + Float64(-0.1111111111111111 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4.8e+92) || ~((y <= 3.6e+93)))
		tmp = y / (sqrt(x) * -3.0);
	else
		tmp = 1.0 + (-0.1111111111111111 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.8e+92], N[Not[LessEqual[y, 3.6e+93]], $MachinePrecision]], N[(y / N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.80000000000000009e92 or 3.5999999999999999e93 < y

   1. Initial program 99.6%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x} \cdot 3}} \]

      2. metadata-eval 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\sqrt{x} \cdot \color{blue}{\sqrt{9}}} \]

      3. sqrt-prod 99.7%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

      4. pow1/2 99.7%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]

   4. Applied egg-rr 99.7%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]
   5. Step-by-step derivation

      1. unpow1/2 99.7%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   6. Simplified 99.7%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   7. Taylor expanded in y around inf 94.8%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \left(\sqrt{\frac{1}{x}} \cdot y\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 95.8%

         \[\leadsto \color{blue}{\left(-0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\right) \cdot y} \]

      2. *-commutative 95.8%

         \[\leadsto \color{blue}{y \cdot \left(-0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\right)} \]

      3. *-commutative 95.8%

         \[\leadsto y \cdot \color{blue}{\left(\sqrt{\frac{1}{x}} \cdot -0.3333333333333333\right)} \]

      4. unpow1/2 95.8%

         \[\leadsto y \cdot \left(\color{blue}{{\left(\frac{1}{x}\right)}^{0.5}} \cdot -0.3333333333333333\right) \]

      5. unpow-1 95.8%

         \[\leadsto y \cdot \left({\color{blue}{\left({x}^{-1}\right)}}^{0.5} \cdot -0.3333333333333333\right) \]

      6. exp-to-pow 90.7%

         \[\leadsto y \cdot \left({\color{blue}{\left(e^{\log x \cdot -1}\right)}}^{0.5} \cdot -0.3333333333333333\right) \]

      7. *-commutative 90.7%

         \[\leadsto y \cdot \left({\left(e^{\color{blue}{-1 \cdot \log x}}\right)}^{0.5} \cdot -0.3333333333333333\right) \]

      8. neg-mul-1 90.7%

         \[\leadsto y \cdot \left({\left(e^{\color{blue}{-\log x}}\right)}^{0.5} \cdot -0.3333333333333333\right) \]

      9. exp-prod 90.7%

         \[\leadsto y \cdot \left(\color{blue}{e^{\left(-\log x\right) \cdot 0.5}} \cdot -0.3333333333333333\right) \]

      10. distribute-lft-neg-out 90.7%

          \[\leadsto y \cdot \left(e^{\color{blue}{-\log x \cdot 0.5}} \cdot -0.3333333333333333\right) \]

      11. exp-neg 90.7%

          \[\leadsto y \cdot \left(\color{blue}{\frac{1}{e^{\log x \cdot 0.5}}} \cdot -0.3333333333333333\right) \]

      12. exp-to-pow 95.7%

          \[\leadsto y \cdot \left(\frac{1}{\color{blue}{{x}^{0.5}}} \cdot -0.3333333333333333\right) \]

      13. unpow1/2 95.7%

          \[\leadsto y \cdot \left(\frac{1}{\color{blue}{\sqrt{x}}} \cdot -0.3333333333333333\right) \]

      14. unpow-1 95.7%

          \[\leadsto y \cdot \left(\color{blue}{{\left(\sqrt{x}\right)}^{-1}} \cdot -0.3333333333333333\right) \]

      15. metadata-eval 95.7%

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

      16. associate-/l* 95.8%

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

      17. *-rgt-identity 95.8%

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

      18. unpow-1 95.8%

          \[\leadsto y \cdot \frac{\color{blue}{\frac{1}{\sqrt{x}}}}{-3} \]

      19. associate-/r* 95.9%

          \[\leadsto y \cdot \color{blue}{\frac{1}{\sqrt{x} \cdot -3}} \]

      20. *-commutative 95.9%

          \[\leadsto y \cdot \frac{1}{\color{blue}{-3 \cdot \sqrt{x}}} \]

      21. associate-/r* 95.8%

          \[\leadsto y \cdot \color{blue}{\frac{\frac{1}{-3}}{\sqrt{x}}} \]

      22. metadata-eval 95.8%

          \[\leadsto y \cdot \frac{\color{blue}{-0.3333333333333333}}{\sqrt{x}} \]

   9. Simplified 95.8%

      \[\leadsto \color{blue}{y \cdot \frac{-0.3333333333333333}{\sqrt{x}}} \]
   10. Step-by-step derivation

       1. clear-num 95.7%

          \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{\sqrt{x}}{-0.3333333333333333}}} \]

       2. un-div-inv 95.7%

          \[\leadsto \color{blue}{\frac{y}{\frac{\sqrt{x}}{-0.3333333333333333}}} \]

       3. div-inv 95.9%

          \[\leadsto \frac{y}{\color{blue}{\sqrt{x} \cdot \frac{1}{-0.3333333333333333}}} \]

       4. metadata-eval 95.9%

          \[\leadsto \frac{y}{\sqrt{x} \cdot \color{blue}{-3}} \]

   11. Applied egg-rr 95.9%

       \[\leadsto \color{blue}{\frac{y}{\sqrt{x} \cdot -3}} \]

   if -4.80000000000000009e92 < y < 3.5999999999999999e93

   1. Initial program 99.8%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Step-by-step derivation

      1. associate--l- 99.8%

         \[\leadsto \color{blue}{1 - \left(\frac{1}{x \cdot 9} + \frac{y}{3 \cdot \sqrt{x}}\right)} \]

      2. sub-neg 99.8%

         \[\leadsto \color{blue}{1 + \left(-\left(\frac{1}{x \cdot 9} + \frac{y}{3 \cdot \sqrt{x}}\right)\right)} \]

      3. +-commutative 99.8%

         \[\leadsto 1 + \left(-\color{blue}{\left(\frac{y}{3 \cdot \sqrt{x}} + \frac{1}{x \cdot 9}\right)}\right) \]

      4. distribute-neg-in 99.8%

         \[\leadsto 1 + \color{blue}{\left(\left(-\frac{y}{3 \cdot \sqrt{x}}\right) + \left(-\frac{1}{x \cdot 9}\right)\right)} \]

      5. distribute-frac-neg 99.8%

         \[\leadsto 1 + \left(\color{blue}{\frac{-y}{3 \cdot \sqrt{x}}} + \left(-\frac{1}{x \cdot 9}\right)\right) \]

      6. sub-neg 99.8%

         \[\leadsto 1 + \color{blue}{\left(\frac{-y}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right)} \]

      7. neg-mul-1 99.8%

         \[\leadsto 1 + \left(\frac{\color{blue}{-1 \cdot y}}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right) \]

      8. *-commutative 99.8%

         \[\leadsto 1 + \left(\frac{\color{blue}{y \cdot -1}}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right) \]

      9. associate-/l* 99.8%

         \[\leadsto 1 + \left(\color{blue}{y \cdot \frac{-1}{3 \cdot \sqrt{x}}} - \frac{1}{x \cdot 9}\right) \]

      10. fma-neg 99.8%

          \[\leadsto 1 + \color{blue}{\mathsf{fma}\left(y, \frac{-1}{3 \cdot \sqrt{x}}, -\frac{1}{x \cdot 9}\right)} \]

      11. associate-/r* 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \color{blue}{\frac{\frac{-1}{3}}{\sqrt{x}}}, -\frac{1}{x \cdot 9}\right) \]

      12. metadata-eval 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{\color{blue}{-0.3333333333333333}}{\sqrt{x}}, -\frac{1}{x \cdot 9}\right) \]

      13. *-commutative 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, -\frac{1}{\color{blue}{9 \cdot x}}\right) \]

      14. associate-/r* 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, -\color{blue}{\frac{\frac{1}{9}}{x}}\right) \]

      15. distribute-neg-frac 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \color{blue}{\frac{-\frac{1}{9}}{x}}\right) \]

      16. metadata-eval 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{-\color{blue}{0.1111111111111111}}{x}\right) \]

      17. metadata-eval 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{\color{blue}{-0.1111111111111111}}{x}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{-0.1111111111111111}{x}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 94.0%

      \[\leadsto 1 + \color{blue}{\frac{-0.1111111111111111}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+92} \lor \neg \left(y \leq 3.6 \cdot 10^{+93}\right):\\ \;\;\;\;\frac{y}{\sqrt{x} \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.1111111111111111}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+92}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{\sqrt{x}}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+93}:\\ \;\;\;\;1 + \frac{-0.1111111111111111}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{\sqrt{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.1e+92)
   (* -0.3333333333333333 (/ y (sqrt x)))
   (if (<= y 7e+93)
     (+ 1.0 (/ -0.1111111111111111 x))
     (* y (/ -0.3333333333333333 (sqrt x))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.1e+92) {
		tmp = -0.3333333333333333 * (y / sqrt(x));
	} else if (y <= 7e+93) {
		tmp = 1.0 + (-0.1111111111111111 / x);
	} else {
		tmp = y * (-0.3333333333333333 / sqrt(x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-5.1d+92)) then
        tmp = (-0.3333333333333333d0) * (y / sqrt(x))
    else if (y <= 7d+93) then
        tmp = 1.0d0 + ((-0.1111111111111111d0) / x)
    else
        tmp = y * ((-0.3333333333333333d0) / sqrt(x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5.1e+92) {
		tmp = -0.3333333333333333 * (y / Math.sqrt(x));
	} else if (y <= 7e+93) {
		tmp = 1.0 + (-0.1111111111111111 / x);
	} else {
		tmp = y * (-0.3333333333333333 / Math.sqrt(x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.1e+92:
		tmp = -0.3333333333333333 * (y / math.sqrt(x))
	elif y <= 7e+93:
		tmp = 1.0 + (-0.1111111111111111 / x)
	else:
		tmp = y * (-0.3333333333333333 / math.sqrt(x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.1e+92)
		tmp = Float64(-0.3333333333333333 * Float64(y / sqrt(x)));
	elseif (y <= 7e+93)
		tmp = Float64(1.0 + Float64(-0.1111111111111111 / x));
	else
		tmp = Float64(y * Float64(-0.3333333333333333 / sqrt(x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.1e+92)
		tmp = -0.3333333333333333 * (y / sqrt(x));
	elseif (y <= 7e+93)
		tmp = 1.0 + (-0.1111111111111111 / x);
	else
		tmp = y * (-0.3333333333333333 / sqrt(x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.1e+92], N[(-0.3333333333333333 * N[(y / N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+93], N[(1.0 + N[(-0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision], N[(y * N[(-0.3333333333333333 / N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.1000000000000003e92

   1. Initial program 99.5%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.5%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x} \cdot 3}} \]

      2. metadata-eval 99.5%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\sqrt{x} \cdot \color{blue}{\sqrt{9}}} \]

      3. sqrt-prod 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

      4. pow1/2 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]

   4. Applied egg-rr 99.6%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]
   5. Step-by-step derivation

      1. unpow1/2 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   6. Simplified 99.6%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   7. Taylor expanded in y around inf 94.7%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \left(\sqrt{\frac{1}{x}} \cdot y\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 94.7%

         \[\leadsto \color{blue}{\left(-0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\right) \cdot y} \]

      2. *-commutative 94.7%

         \[\leadsto \color{blue}{y \cdot \left(-0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\right)} \]

      3. *-commutative 94.7%

         \[\leadsto y \cdot \color{blue}{\left(\sqrt{\frac{1}{x}} \cdot -0.3333333333333333\right)} \]

      4. unpow1/2 94.7%

         \[\leadsto y \cdot \left(\color{blue}{{\left(\frac{1}{x}\right)}^{0.5}} \cdot -0.3333333333333333\right) \]

      5. unpow-1 94.7%

         \[\leadsto y \cdot \left({\color{blue}{\left({x}^{-1}\right)}}^{0.5} \cdot -0.3333333333333333\right) \]

      6. exp-to-pow 89.4%

         \[\leadsto y \cdot \left({\color{blue}{\left(e^{\log x \cdot -1}\right)}}^{0.5} \cdot -0.3333333333333333\right) \]

      7. *-commutative 89.4%

         \[\leadsto y \cdot \left({\left(e^{\color{blue}{-1 \cdot \log x}}\right)}^{0.5} \cdot -0.3333333333333333\right) \]

      8. neg-mul-1 89.4%

         \[\leadsto y \cdot \left({\left(e^{\color{blue}{-\log x}}\right)}^{0.5} \cdot -0.3333333333333333\right) \]

      9. exp-prod 89.4%

         \[\leadsto y \cdot \left(\color{blue}{e^{\left(-\log x\right) \cdot 0.5}} \cdot -0.3333333333333333\right) \]

      10. distribute-lft-neg-out 89.4%

          \[\leadsto y \cdot \left(e^{\color{blue}{-\log x \cdot 0.5}} \cdot -0.3333333333333333\right) \]

      11. exp-neg 89.4%

          \[\leadsto y \cdot \left(\color{blue}{\frac{1}{e^{\log x \cdot 0.5}}} \cdot -0.3333333333333333\right) \]

      12. exp-to-pow 94.5%

          \[\leadsto y \cdot \left(\frac{1}{\color{blue}{{x}^{0.5}}} \cdot -0.3333333333333333\right) \]

      13. unpow1/2 94.5%

          \[\leadsto y \cdot \left(\frac{1}{\color{blue}{\sqrt{x}}} \cdot -0.3333333333333333\right) \]

      14. unpow-1 94.5%

          \[\leadsto y \cdot \left(\color{blue}{{\left(\sqrt{x}\right)}^{-1}} \cdot -0.3333333333333333\right) \]

      15. metadata-eval 94.5%

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

      16. associate-/l* 94.7%

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

      17. *-rgt-identity 94.7%

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

      18. unpow-1 94.7%

          \[\leadsto y \cdot \frac{\color{blue}{\frac{1}{\sqrt{x}}}}{-3} \]

      19. associate-/r* 94.8%

          \[\leadsto y \cdot \color{blue}{\frac{1}{\sqrt{x} \cdot -3}} \]

      20. *-commutative 94.8%

          \[\leadsto y \cdot \frac{1}{\color{blue}{-3 \cdot \sqrt{x}}} \]

      21. associate-/r* 94.6%

          \[\leadsto y \cdot \color{blue}{\frac{\frac{1}{-3}}{\sqrt{x}}} \]

      22. metadata-eval 94.6%

          \[\leadsto y \cdot \frac{\color{blue}{-0.3333333333333333}}{\sqrt{x}} \]

   9. Simplified 94.6%

      \[\leadsto \color{blue}{y \cdot \frac{-0.3333333333333333}{\sqrt{x}}} \]
   10. Step-by-step derivation

       1. clear-num 94.7%

          \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{\sqrt{x}}{-0.3333333333333333}}} \]

       2. un-div-inv 94.7%

          \[\leadsto \color{blue}{\frac{y}{\frac{\sqrt{x}}{-0.3333333333333333}}} \]

       3. div-inv 94.8%

          \[\leadsto \frac{y}{\color{blue}{\sqrt{x} \cdot \frac{1}{-0.3333333333333333}}} \]

       4. metadata-eval 94.8%

          \[\leadsto \frac{y}{\sqrt{x} \cdot \color{blue}{-3}} \]

   11. Applied egg-rr 94.8%

       \[\leadsto \color{blue}{\frac{y}{\sqrt{x} \cdot -3}} \]
   12. Step-by-step derivation

       1. associate-/r* 94.6%

          \[\leadsto \color{blue}{\frac{\frac{y}{\sqrt{x}}}{-3}} \]

       2. div-inv 94.7%

          \[\leadsto \color{blue}{\frac{y}{\sqrt{x}} \cdot \frac{1}{-3}} \]

       3. metadata-eval 94.7%

          \[\leadsto \frac{y}{\sqrt{x}} \cdot \color{blue}{-0.3333333333333333} \]

   13. Applied egg-rr 94.7%

       \[\leadsto \color{blue}{\frac{y}{\sqrt{x}} \cdot -0.3333333333333333} \]

   if -5.1000000000000003e92 < y < 6.99999999999999996e93

   1. Initial program 99.8%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Step-by-step derivation

      1. associate--l- 99.8%

         \[\leadsto \color{blue}{1 - \left(\frac{1}{x \cdot 9} + \frac{y}{3 \cdot \sqrt{x}}\right)} \]

      2. sub-neg 99.8%

         \[\leadsto \color{blue}{1 + \left(-\left(\frac{1}{x \cdot 9} + \frac{y}{3 \cdot \sqrt{x}}\right)\right)} \]

      3. +-commutative 99.8%

         \[\leadsto 1 + \left(-\color{blue}{\left(\frac{y}{3 \cdot \sqrt{x}} + \frac{1}{x \cdot 9}\right)}\right) \]

      4. distribute-neg-in 99.8%

         \[\leadsto 1 + \color{blue}{\left(\left(-\frac{y}{3 \cdot \sqrt{x}}\right) + \left(-\frac{1}{x \cdot 9}\right)\right)} \]

      5. distribute-frac-neg 99.8%

         \[\leadsto 1 + \left(\color{blue}{\frac{-y}{3 \cdot \sqrt{x}}} + \left(-\frac{1}{x \cdot 9}\right)\right) \]

      6. sub-neg 99.8%

         \[\leadsto 1 + \color{blue}{\left(\frac{-y}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right)} \]

      7. neg-mul-1 99.8%

         \[\leadsto 1 + \left(\frac{\color{blue}{-1 \cdot y}}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right) \]

      8. *-commutative 99.8%

         \[\leadsto 1 + \left(\frac{\color{blue}{y \cdot -1}}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right) \]

      9. associate-/l* 99.8%

         \[\leadsto 1 + \left(\color{blue}{y \cdot \frac{-1}{3 \cdot \sqrt{x}}} - \frac{1}{x \cdot 9}\right) \]

      10. fma-neg 99.8%

          \[\leadsto 1 + \color{blue}{\mathsf{fma}\left(y, \frac{-1}{3 \cdot \sqrt{x}}, -\frac{1}{x \cdot 9}\right)} \]

      11. associate-/r* 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \color{blue}{\frac{\frac{-1}{3}}{\sqrt{x}}}, -\frac{1}{x \cdot 9}\right) \]

      12. metadata-eval 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{\color{blue}{-0.3333333333333333}}{\sqrt{x}}, -\frac{1}{x \cdot 9}\right) \]

      13. *-commutative 99.8%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, -\frac{1}{\color{blue}{9 \cdot x}}\right) \]

      14. associate-/r* 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, -\color{blue}{\frac{\frac{1}{9}}{x}}\right) \]

      15. distribute-neg-frac 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \color{blue}{\frac{-\frac{1}{9}}{x}}\right) \]

      16. metadata-eval 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{-\color{blue}{0.1111111111111111}}{x}\right) \]

      17. metadata-eval 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{\color{blue}{-0.1111111111111111}}{x}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{-0.1111111111111111}{x}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 94.0%

      \[\leadsto 1 + \color{blue}{\frac{-0.1111111111111111}{x}} \]

   if 6.99999999999999996e93 < y

   1. Initial program 99.6%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x} \cdot 3}} \]

      2. metadata-eval 99.6%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\sqrt{x} \cdot \color{blue}{\sqrt{9}}} \]

      3. sqrt-prod 99.8%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

      4. pow1/2 99.8%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]

   4. Applied egg-rr 99.8%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]
   5. Step-by-step derivation

      1. unpow1/2 99.8%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   6. Simplified 99.8%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   7. Taylor expanded in y around inf 94.9%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \left(\sqrt{\frac{1}{x}} \cdot y\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 97.0%

         \[\leadsto \color{blue}{\left(-0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\right) \cdot y} \]

      2. *-commutative 97.0%

         \[\leadsto \color{blue}{y \cdot \left(-0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\right)} \]

      3. *-commutative 97.0%

         \[\leadsto y \cdot \color{blue}{\left(\sqrt{\frac{1}{x}} \cdot -0.3333333333333333\right)} \]

      4. unpow1/2 97.0%

         \[\leadsto y \cdot \left(\color{blue}{{\left(\frac{1}{x}\right)}^{0.5}} \cdot -0.3333333333333333\right) \]

      5. unpow-1 97.0%

         \[\leadsto y \cdot \left({\color{blue}{\left({x}^{-1}\right)}}^{0.5} \cdot -0.3333333333333333\right) \]

      6. exp-to-pow 92.1%

         \[\leadsto y \cdot \left({\color{blue}{\left(e^{\log x \cdot -1}\right)}}^{0.5} \cdot -0.3333333333333333\right) \]

      7. *-commutative 92.1%

         \[\leadsto y \cdot \left({\left(e^{\color{blue}{-1 \cdot \log x}}\right)}^{0.5} \cdot -0.3333333333333333\right) \]

      8. neg-mul-1 92.1%

         \[\leadsto y \cdot \left({\left(e^{\color{blue}{-\log x}}\right)}^{0.5} \cdot -0.3333333333333333\right) \]

      9. exp-prod 92.1%

         \[\leadsto y \cdot \left(\color{blue}{e^{\left(-\log x\right) \cdot 0.5}} \cdot -0.3333333333333333\right) \]

      10. distribute-lft-neg-out 92.1%

          \[\leadsto y \cdot \left(e^{\color{blue}{-\log x \cdot 0.5}} \cdot -0.3333333333333333\right) \]

      11. exp-neg 92.1%

          \[\leadsto y \cdot \left(\color{blue}{\frac{1}{e^{\log x \cdot 0.5}}} \cdot -0.3333333333333333\right) \]

      12. exp-to-pow 96.9%

          \[\leadsto y \cdot \left(\frac{1}{\color{blue}{{x}^{0.5}}} \cdot -0.3333333333333333\right) \]

      13. unpow1/2 96.9%

          \[\leadsto y \cdot \left(\frac{1}{\color{blue}{\sqrt{x}}} \cdot -0.3333333333333333\right) \]

      14. unpow-1 96.9%

          \[\leadsto y \cdot \left(\color{blue}{{\left(\sqrt{x}\right)}^{-1}} \cdot -0.3333333333333333\right) \]

      15. metadata-eval 96.9%

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

      16. associate-/l* 97.0%

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

      17. *-rgt-identity 97.0%

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

      18. unpow-1 97.0%

          \[\leadsto y \cdot \frac{\color{blue}{\frac{1}{\sqrt{x}}}}{-3} \]

      19. associate-/r* 97.1%

          \[\leadsto y \cdot \color{blue}{\frac{1}{\sqrt{x} \cdot -3}} \]

      20. *-commutative 97.1%

          \[\leadsto y \cdot \frac{1}{\color{blue}{-3 \cdot \sqrt{x}}} \]

      21. associate-/r* 96.9%

          \[\leadsto y \cdot \color{blue}{\frac{\frac{1}{-3}}{\sqrt{x}}} \]

      22. metadata-eval 96.9%

          \[\leadsto y \cdot \frac{\color{blue}{-0.3333333333333333}}{\sqrt{x}} \]

   9. Simplified 96.9%

      \[\leadsto \color{blue}{y \cdot \frac{-0.3333333333333333}{\sqrt{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+92}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{\sqrt{x}}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+93}:\\ \;\;\;\;1 + \frac{-0.1111111111111111}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{\sqrt{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.112:\\ \;\;\;\;\frac{-0.1111111111111111 - \sqrt{x} \cdot \left(y \cdot 0.3333333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{\sqrt{x \cdot 9}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.112)
   (/ (- -0.1111111111111111 (* (sqrt x) (* y 0.3333333333333333))) x)
   (- 1.0 (/ y (sqrt (* x 9.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.112) {
		tmp = (-0.1111111111111111 - (sqrt(x) * (y * 0.3333333333333333))) / x;
	} else {
		tmp = 1.0 - (y / sqrt((x * 9.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 0.112d0) then
        tmp = ((-0.1111111111111111d0) - (sqrt(x) * (y * 0.3333333333333333d0))) / x
    else
        tmp = 1.0d0 - (y / sqrt((x * 9.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.112) {
		tmp = (-0.1111111111111111 - (Math.sqrt(x) * (y * 0.3333333333333333))) / x;
	} else {
		tmp = 1.0 - (y / Math.sqrt((x * 9.0)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.112:
		tmp = (-0.1111111111111111 - (math.sqrt(x) * (y * 0.3333333333333333))) / x
	else:
		tmp = 1.0 - (y / math.sqrt((x * 9.0)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.112)
		tmp = Float64(Float64(-0.1111111111111111 - Float64(sqrt(x) * Float64(y * 0.3333333333333333))) / x);
	else
		tmp = Float64(1.0 - Float64(y / sqrt(Float64(x * 9.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.112)
		tmp = (-0.1111111111111111 - (sqrt(x) * (y * 0.3333333333333333))) / x;
	else
		tmp = 1.0 - (y / sqrt((x * 9.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.112], N[(N[(-0.1111111111111111 - N[(N[Sqrt[x], $MachinePrecision] * N[(y * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(1.0 - N[(y / N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.112000000000000002

   1. Initial program 99.7%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.7%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x} \cdot 3}} \]

      2. metadata-eval 99.7%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\sqrt{x} \cdot \color{blue}{\sqrt{9}}} \]

      3. sqrt-prod 99.7%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

      4. pow1/2 99.7%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]

   4. Applied egg-rr 99.7%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]
   5. Step-by-step derivation

      1. unpow1/2 99.7%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   6. Simplified 99.7%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   7. Taylor expanded in x around 0 99.6%

      \[\leadsto \left(1 - \color{blue}{\frac{0.1111111111111111}{x}}\right) - \frac{y}{\sqrt{x \cdot 9}} \]

   8. Taylor expanded in x around 0 99.5%

      \[\leadsto \color{blue}{\frac{x - \left(0.1111111111111111 + 0.3333333333333333 \cdot \left(\sqrt{x} \cdot y\right)\right)}{x}} \]
   9. Step-by-step derivation

      1. associate--r+ 99.5%

         \[\leadsto \frac{\color{blue}{\left(x - 0.1111111111111111\right) - 0.3333333333333333 \cdot \left(\sqrt{x} \cdot y\right)}}{x} \]

      2. associate-*r* 99.5%

         \[\leadsto \frac{\left(x - 0.1111111111111111\right) - \color{blue}{\left(0.3333333333333333 \cdot \sqrt{x}\right) \cdot y}}{x} \]

      3. *-commutative 99.5%

         \[\leadsto \frac{\left(x - 0.1111111111111111\right) - \color{blue}{y \cdot \left(0.3333333333333333 \cdot \sqrt{x}\right)}}{x} \]

      4. associate-*r* 99.5%

         \[\leadsto \frac{\left(x - 0.1111111111111111\right) - \color{blue}{\left(y \cdot 0.3333333333333333\right) \cdot \sqrt{x}}}{x} \]

   10. Simplified 99.5%

       \[\leadsto \color{blue}{\frac{\left(x - 0.1111111111111111\right) - \left(y \cdot 0.3333333333333333\right) \cdot \sqrt{x}}{x}} \]

   11. Taylor expanded in x around 0 96.9%

       \[\leadsto \frac{\color{blue}{-1 \cdot \left(0.1111111111111111 + 0.3333333333333333 \cdot \left(\sqrt{x} \cdot y\right)\right)}}{x} \]
   12. Step-by-step derivation

       1. distribute-lft-in 96.9%

          \[\leadsto \frac{\color{blue}{-1 \cdot 0.1111111111111111 + -1 \cdot \left(0.3333333333333333 \cdot \left(\sqrt{x} \cdot y\right)\right)}}{x} \]

       2. *-commutative 96.9%

          \[\leadsto \frac{-1 \cdot 0.1111111111111111 + -1 \cdot \color{blue}{\left(\left(\sqrt{x} \cdot y\right) \cdot 0.3333333333333333\right)}}{x} \]

       3. associate-*r* 96.9%

          \[\leadsto \frac{-1 \cdot 0.1111111111111111 + -1 \cdot \color{blue}{\left(\sqrt{x} \cdot \left(y \cdot 0.3333333333333333\right)\right)}}{x} \]

       4. metadata-eval 96.9%

          \[\leadsto \frac{\color{blue}{-0.1111111111111111} + -1 \cdot \left(\sqrt{x} \cdot \left(y \cdot 0.3333333333333333\right)\right)}{x} \]

       5. neg-mul-1 96.9%

          \[\leadsto \frac{-0.1111111111111111 + \color{blue}{\left(-\sqrt{x} \cdot \left(y \cdot 0.3333333333333333\right)\right)}}{x} \]

       6. sub-neg 96.9%

          \[\leadsto \frac{\color{blue}{-0.1111111111111111 - \sqrt{x} \cdot \left(y \cdot 0.3333333333333333\right)}}{x} \]

   13. Simplified 96.9%

       \[\leadsto \frac{\color{blue}{-0.1111111111111111 - \sqrt{x} \cdot \left(y \cdot 0.3333333333333333\right)}}{x} \]

   if 0.112000000000000002 < x

   1. Initial program 99.8%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 98.1%

      \[\leadsto \color{blue}{1 - 0.3333333333333333 \cdot \left(\sqrt{\frac{1}{x}} \cdot y\right)} \]
   4. Step-by-step derivation

      1. metadata-eval 98.1%

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

      2. *-commutative 98.1%

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

      3. sqrt-div 98.1%

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

      4. metadata-eval 98.1%

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

      5. un-div-inv 98.2%

         \[\leadsto 1 - \frac{1}{3} \cdot \color{blue}{\frac{y}{\sqrt{x}}} \]

      6. times-frac 98.1%

         \[\leadsto 1 - \color{blue}{\frac{1 \cdot y}{3 \cdot \sqrt{x}}} \]

      7. *-un-lft-identity 98.1%

         \[\leadsto 1 - \frac{\color{blue}{y}}{3 \cdot \sqrt{x}} \]

   5. Applied egg-rr 98.1%

      \[\leadsto 1 - \color{blue}{\frac{y}{3 \cdot \sqrt{x}}} \]
   6. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x} \cdot 3}} \]

      2. metadata-eval 99.8%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\sqrt{x} \cdot \color{blue}{\sqrt{9}}} \]

      3. sqrt-prod 99.8%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

      4. pow1/2 99.8%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]

   7. Applied egg-rr 98.2%

      \[\leadsto 1 - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]
   8. Step-by-step derivation

      1. unpow1/2 99.8%

         \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   9. Simplified 98.2%

      \[\leadsto 1 - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.112:\\ \;\;\;\;\frac{-0.1111111111111111 - \sqrt{x} \cdot \left(y \cdot 0.3333333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{\sqrt{x \cdot 9}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - \frac{0.1111111111111111}{x}\right) + -0.3333333333333333 \cdot \frac{y}{\sqrt{x}} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (+ (- 1.0 (/ 0.1111111111111111 x)) (* -0.3333333333333333 (/ y (sqrt x)))))

C

double code(double x, double y) {
	return (1.0 - (0.1111111111111111 / x)) + (-0.3333333333333333 * (y / sqrt(x)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - (0.1111111111111111d0 / x)) + ((-0.3333333333333333d0) * (y / sqrt(x)))
end function

Java

public static double code(double x, double y) {
	return (1.0 - (0.1111111111111111 / x)) + (-0.3333333333333333 * (y / Math.sqrt(x)));
}

Python

def code(x, y):
	return (1.0 - (0.1111111111111111 / x)) + (-0.3333333333333333 * (y / math.sqrt(x)))

Julia

function code(x, y)
	return Float64(Float64(1.0 - Float64(0.1111111111111111 / x)) + Float64(-0.3333333333333333 * Float64(y / sqrt(x))))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - (0.1111111111111111 / x)) + (-0.3333333333333333 * (y / sqrt(x)));
end

Wolfram

code[x_, y_] := N[(N[(1.0 - N[(0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision] + N[(-0.3333333333333333 * N[(y / N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
2. Step-by-step derivation

   1. sub-neg 99.7%

      \[\leadsto \color{blue}{\left(1 - \frac{1}{x \cdot 9}\right) + \left(-\frac{y}{3 \cdot \sqrt{x}}\right)} \]

   2. *-commutative 99.7%

      \[\leadsto \left(1 - \frac{1}{\color{blue}{9 \cdot x}}\right) + \left(-\frac{y}{3 \cdot \sqrt{x}}\right) \]

   3. associate-/r* 99.6%

      \[\leadsto \left(1 - \color{blue}{\frac{\frac{1}{9}}{x}}\right) + \left(-\frac{y}{3 \cdot \sqrt{x}}\right) \]

   4. metadata-eval 99.6%

      \[\leadsto \left(1 - \frac{\color{blue}{0.1111111111111111}}{x}\right) + \left(-\frac{y}{3 \cdot \sqrt{x}}\right) \]

   5. distribute-frac-neg 99.6%

      \[\leadsto \left(1 - \frac{0.1111111111111111}{x}\right) + \color{blue}{\frac{-y}{3 \cdot \sqrt{x}}} \]

   6. neg-mul-1 99.6%

      \[\leadsto \left(1 - \frac{0.1111111111111111}{x}\right) + \frac{\color{blue}{-1 \cdot y}}{3 \cdot \sqrt{x}} \]

   7. times-frac 99.3%

      \[\leadsto \left(1 - \frac{0.1111111111111111}{x}\right) + \color{blue}{\frac{-1}{3} \cdot \frac{y}{\sqrt{x}}} \]

   8. metadata-eval 99.3%

      \[\leadsto \left(1 - \frac{0.1111111111111111}{x}\right) + \color{blue}{-0.3333333333333333} \cdot \frac{y}{\sqrt{x}} \]

3. Simplified 99.3%

   \[\leadsto \color{blue}{\left(1 - \frac{0.1111111111111111}{x}\right) + -0.3333333333333333 \cdot \frac{y}{\sqrt{x}}} \]
4. Add Preprocessing

5. Final simplification 99.3%

   \[\leadsto \left(1 - \frac{0.1111111111111111}{x}\right) + -0.3333333333333333 \cdot \frac{y}{\sqrt{x}} \]
6. Add Preprocessing

Alternative 11: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - \frac{0.1111111111111111}{x}\right) - \frac{y}{\sqrt{x \cdot 9}} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (- (- 1.0 (/ 0.1111111111111111 x)) (/ y (sqrt (* x 9.0)))))

C

double code(double x, double y) {
	return (1.0 - (0.1111111111111111 / x)) - (y / sqrt((x * 9.0)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - (0.1111111111111111d0 / x)) - (y / sqrt((x * 9.0d0)))
end function

Java

public static double code(double x, double y) {
	return (1.0 - (0.1111111111111111 / x)) - (y / Math.sqrt((x * 9.0)));
}

Python

def code(x, y):
	return (1.0 - (0.1111111111111111 / x)) - (y / math.sqrt((x * 9.0)))

Julia

function code(x, y)
	return Float64(Float64(1.0 - Float64(0.1111111111111111 / x)) - Float64(y / sqrt(Float64(x * 9.0))))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - (0.1111111111111111 / x)) - (y / sqrt((x * 9.0)));
end

Wolfram

code[x_, y_] := N[(N[(1.0 - N[(0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision] - N[(y / N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. *-commutative 99.7%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x} \cdot 3}} \]

   2. metadata-eval 99.7%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\sqrt{x} \cdot \color{blue}{\sqrt{9}}} \]

   3. sqrt-prod 99.8%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

   4. pow1/2 99.8%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]

4. Applied egg-rr 99.8%

   \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{{\left(x \cdot 9\right)}^{0.5}}} \]
5. Step-by-step derivation

   1. unpow1/2 99.8%

      \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

6. Simplified 99.8%

   \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

7. Taylor expanded in x around 0 99.7%

   \[\leadsto \left(1 - \color{blue}{\frac{0.1111111111111111}{x}}\right) - \frac{y}{\sqrt{x \cdot 9}} \]

8. Final simplification 99.7%

   \[\leadsto \left(1 - \frac{0.1111111111111111}{x}\right) - \frac{y}{\sqrt{x \cdot 9}} \]
9. Add Preprocessing

Alternative 12: 65.3% accurate, 8.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{+81}:\\ \;\;\;\;1 + \frac{-0.1111111111111111}{x}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.1111111111111111}{y} \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 8.5e+81)
   (+ 1.0 (/ -0.1111111111111111 x))
   (+ 1.0 (* (/ -0.1111111111111111 y) (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 8.5e+81) {
		tmp = 1.0 + (-0.1111111111111111 / x);
	} else {
		tmp = 1.0 + ((-0.1111111111111111 / y) * (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 8.5d+81) then
        tmp = 1.0d0 + ((-0.1111111111111111d0) / x)
    else
        tmp = 1.0d0 + (((-0.1111111111111111d0) / y) * (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 8.5e+81) {
		tmp = 1.0 + (-0.1111111111111111 / x);
	} else {
		tmp = 1.0 + ((-0.1111111111111111 / y) * (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 8.5e+81:
		tmp = 1.0 + (-0.1111111111111111 / x)
	else:
		tmp = 1.0 + ((-0.1111111111111111 / y) * (y / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 8.5e+81)
		tmp = Float64(1.0 + Float64(-0.1111111111111111 / x));
	else
		tmp = Float64(1.0 + Float64(Float64(-0.1111111111111111 / y) * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 8.5e+81)
		tmp = 1.0 + (-0.1111111111111111 / x);
	else
		tmp = 1.0 + ((-0.1111111111111111 / y) * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 8.5e+81], N[(1.0 + N[(-0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(-0.1111111111111111 / y), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.49999999999999986e81

   1. Initial program 99.8%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Step-by-step derivation

      1. associate--l- 99.8%

         \[\leadsto \color{blue}{1 - \left(\frac{1}{x \cdot 9} + \frac{y}{3 \cdot \sqrt{x}}\right)} \]

      2. sub-neg 99.8%

         \[\leadsto \color{blue}{1 + \left(-\left(\frac{1}{x \cdot 9} + \frac{y}{3 \cdot \sqrt{x}}\right)\right)} \]

      3. +-commutative 99.8%

         \[\leadsto 1 + \left(-\color{blue}{\left(\frac{y}{3 \cdot \sqrt{x}} + \frac{1}{x \cdot 9}\right)}\right) \]

      4. distribute-neg-in 99.8%

         \[\leadsto 1 + \color{blue}{\left(\left(-\frac{y}{3 \cdot \sqrt{x}}\right) + \left(-\frac{1}{x \cdot 9}\right)\right)} \]

      5. distribute-frac-neg 99.8%

         \[\leadsto 1 + \left(\color{blue}{\frac{-y}{3 \cdot \sqrt{x}}} + \left(-\frac{1}{x \cdot 9}\right)\right) \]

      6. sub-neg 99.8%

         \[\leadsto 1 + \color{blue}{\left(\frac{-y}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right)} \]

      7. neg-mul-1 99.8%

         \[\leadsto 1 + \left(\frac{\color{blue}{-1 \cdot y}}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right) \]

      8. *-commutative 99.8%

         \[\leadsto 1 + \left(\frac{\color{blue}{y \cdot -1}}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right) \]

      9. associate-/l* 99.7%

         \[\leadsto 1 + \left(\color{blue}{y \cdot \frac{-1}{3 \cdot \sqrt{x}}} - \frac{1}{x \cdot 9}\right) \]

      10. fma-neg 99.7%

          \[\leadsto 1 + \color{blue}{\mathsf{fma}\left(y, \frac{-1}{3 \cdot \sqrt{x}}, -\frac{1}{x \cdot 9}\right)} \]

      11. associate-/r* 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \color{blue}{\frac{\frac{-1}{3}}{\sqrt{x}}}, -\frac{1}{x \cdot 9}\right) \]

      12. metadata-eval 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{\color{blue}{-0.3333333333333333}}{\sqrt{x}}, -\frac{1}{x \cdot 9}\right) \]

      13. *-commutative 99.7%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, -\frac{1}{\color{blue}{9 \cdot x}}\right) \]

      14. associate-/r* 99.6%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, -\color{blue}{\frac{\frac{1}{9}}{x}}\right) \]

      15. distribute-neg-frac 99.6%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \color{blue}{\frac{-\frac{1}{9}}{x}}\right) \]

      16. metadata-eval 99.6%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{-\color{blue}{0.1111111111111111}}{x}\right) \]

      17. metadata-eval 99.6%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{\color{blue}{-0.1111111111111111}}{x}\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{-0.1111111111111111}{x}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 77.9%

      \[\leadsto 1 + \color{blue}{\frac{-0.1111111111111111}{x}} \]

   if 8.49999999999999986e81 < y

   1. Initial program 99.6%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Step-by-step derivation

      1. associate--l- 99.6%

         \[\leadsto \color{blue}{1 - \left(\frac{1}{x \cdot 9} + \frac{y}{3 \cdot \sqrt{x}}\right)} \]

      2. sub-neg 99.6%

         \[\leadsto \color{blue}{1 + \left(-\left(\frac{1}{x \cdot 9} + \frac{y}{3 \cdot \sqrt{x}}\right)\right)} \]

      3. +-commutative 99.6%

         \[\leadsto 1 + \left(-\color{blue}{\left(\frac{y}{3 \cdot \sqrt{x}} + \frac{1}{x \cdot 9}\right)}\right) \]

      4. distribute-neg-in 99.6%

         \[\leadsto 1 + \color{blue}{\left(\left(-\frac{y}{3 \cdot \sqrt{x}}\right) + \left(-\frac{1}{x \cdot 9}\right)\right)} \]

      5. distribute-frac-neg 99.6%

         \[\leadsto 1 + \left(\color{blue}{\frac{-y}{3 \cdot \sqrt{x}}} + \left(-\frac{1}{x \cdot 9}\right)\right) \]

      6. sub-neg 99.6%

         \[\leadsto 1 + \color{blue}{\left(\frac{-y}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right)} \]

      7. neg-mul-1 99.6%

         \[\leadsto 1 + \left(\frac{\color{blue}{-1 \cdot y}}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right) \]

      8. *-commutative 99.6%

         \[\leadsto 1 + \left(\frac{\color{blue}{y \cdot -1}}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right) \]

      9. associate-/l* 99.6%

         \[\leadsto 1 + \left(\color{blue}{y \cdot \frac{-1}{3 \cdot \sqrt{x}}} - \frac{1}{x \cdot 9}\right) \]

      10. fma-neg 99.6%

          \[\leadsto 1 + \color{blue}{\mathsf{fma}\left(y, \frac{-1}{3 \cdot \sqrt{x}}, -\frac{1}{x \cdot 9}\right)} \]

      11. associate-/r* 99.5%

          \[\leadsto 1 + \mathsf{fma}\left(y, \color{blue}{\frac{\frac{-1}{3}}{\sqrt{x}}}, -\frac{1}{x \cdot 9}\right) \]

      12. metadata-eval 99.5%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{\color{blue}{-0.3333333333333333}}{\sqrt{x}}, -\frac{1}{x \cdot 9}\right) \]

      13. *-commutative 99.5%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, -\frac{1}{\color{blue}{9 \cdot x}}\right) \]

      14. associate-/r* 99.5%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, -\color{blue}{\frac{\frac{1}{9}}{x}}\right) \]

      15. distribute-neg-frac 99.5%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \color{blue}{\frac{-\frac{1}{9}}{x}}\right) \]

      16. metadata-eval 99.5%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{-\color{blue}{0.1111111111111111}}{x}\right) \]

      17. metadata-eval 99.5%

          \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{\color{blue}{-0.1111111111111111}}{x}\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{-0.1111111111111111}{x}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 99.5%

      \[\leadsto 1 + \color{blue}{y \cdot \left(-0.3333333333333333 \cdot \sqrt{\frac{1}{x}} - 0.1111111111111111 \cdot \frac{1}{x \cdot y}\right)} \]

   6. Taylor expanded in x around 0 91.5%

      \[\leadsto 1 + \color{blue}{\frac{y \cdot \left(-0.3333333333333333 \cdot \sqrt{x} - 0.1111111111111111 \cdot \frac{1}{y}\right)}{x}} \]
   7. Step-by-step derivation

      1. *-commutative 91.5%

         \[\leadsto 1 + \frac{\color{blue}{\left(-0.3333333333333333 \cdot \sqrt{x} - 0.1111111111111111 \cdot \frac{1}{y}\right) \cdot y}}{x} \]

      2. associate-/l* 88.4%

         \[\leadsto 1 + \color{blue}{\left(-0.3333333333333333 \cdot \sqrt{x} - 0.1111111111111111 \cdot \frac{1}{y}\right) \cdot \frac{y}{x}} \]

      3. *-commutative 88.4%

         \[\leadsto 1 + \left(\color{blue}{\sqrt{x} \cdot -0.3333333333333333} - 0.1111111111111111 \cdot \frac{1}{y}\right) \cdot \frac{y}{x} \]

      4. fma-neg 88.4%

         \[\leadsto 1 + \color{blue}{\mathsf{fma}\left(\sqrt{x}, -0.3333333333333333, -0.1111111111111111 \cdot \frac{1}{y}\right)} \cdot \frac{y}{x} \]

      5. associate-*r/ 88.4%

         \[\leadsto 1 + \mathsf{fma}\left(\sqrt{x}, -0.3333333333333333, -\color{blue}{\frac{0.1111111111111111 \cdot 1}{y}}\right) \cdot \frac{y}{x} \]

      6. metadata-eval 88.4%

         \[\leadsto 1 + \mathsf{fma}\left(\sqrt{x}, -0.3333333333333333, -\frac{\color{blue}{0.1111111111111111}}{y}\right) \cdot \frac{y}{x} \]

      7. distribute-neg-frac 88.4%

         \[\leadsto 1 + \mathsf{fma}\left(\sqrt{x}, -0.3333333333333333, \color{blue}{\frac{-0.1111111111111111}{y}}\right) \cdot \frac{y}{x} \]

      8. metadata-eval 88.4%

         \[\leadsto 1 + \mathsf{fma}\left(\sqrt{x}, -0.3333333333333333, \frac{\color{blue}{-0.1111111111111111}}{y}\right) \cdot \frac{y}{x} \]

   8. Simplified 88.4%

      \[\leadsto 1 + \color{blue}{\mathsf{fma}\left(\sqrt{x}, -0.3333333333333333, \frac{-0.1111111111111111}{y}\right) \cdot \frac{y}{x}} \]

   9. Taylor expanded in y around 0 36.9%

      \[\leadsto 1 + \color{blue}{\frac{-0.1111111111111111}{y}} \cdot \frac{y}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{+81}:\\ \;\;\;\;1 + \frac{-0.1111111111111111}{x}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.1111111111111111}{y} \cdot \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.8% accurate, 22.6× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{-0.1111111111111111}{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ 1.0 (/ -0.1111111111111111 x)))

C

double code(double x, double y) {
	return 1.0 + (-0.1111111111111111 / x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 + ((-0.1111111111111111d0) / x)
end function

Java

public static double code(double x, double y) {
	return 1.0 + (-0.1111111111111111 / x);
}

Python

def code(x, y):
	return 1.0 + (-0.1111111111111111 / x)

Julia

function code(x, y)
	return Float64(1.0 + Float64(-0.1111111111111111 / x))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 + (-0.1111111111111111 / x);
end

Wolfram

code[x_, y_] := N[(1.0 + N[(-0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
2. Step-by-step derivation

   1. associate--l- 99.7%

      \[\leadsto \color{blue}{1 - \left(\frac{1}{x \cdot 9} + \frac{y}{3 \cdot \sqrt{x}}\right)} \]

   2. sub-neg 99.7%

      \[\leadsto \color{blue}{1 + \left(-\left(\frac{1}{x \cdot 9} + \frac{y}{3 \cdot \sqrt{x}}\right)\right)} \]

   3. +-commutative 99.7%

      \[\leadsto 1 + \left(-\color{blue}{\left(\frac{y}{3 \cdot \sqrt{x}} + \frac{1}{x \cdot 9}\right)}\right) \]

   4. distribute-neg-in 99.7%

      \[\leadsto 1 + \color{blue}{\left(\left(-\frac{y}{3 \cdot \sqrt{x}}\right) + \left(-\frac{1}{x \cdot 9}\right)\right)} \]

   5. distribute-frac-neg 99.7%

      \[\leadsto 1 + \left(\color{blue}{\frac{-y}{3 \cdot \sqrt{x}}} + \left(-\frac{1}{x \cdot 9}\right)\right) \]

   6. sub-neg 99.7%

      \[\leadsto 1 + \color{blue}{\left(\frac{-y}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right)} \]

   7. neg-mul-1 99.7%

      \[\leadsto 1 + \left(\frac{\color{blue}{-1 \cdot y}}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right) \]

   8. *-commutative 99.7%

      \[\leadsto 1 + \left(\frac{\color{blue}{y \cdot -1}}{3 \cdot \sqrt{x}} - \frac{1}{x \cdot 9}\right) \]

   9. associate-/l* 99.7%

      \[\leadsto 1 + \left(\color{blue}{y \cdot \frac{-1}{3 \cdot \sqrt{x}}} - \frac{1}{x \cdot 9}\right) \]

   10. fma-neg 99.7%

       \[\leadsto 1 + \color{blue}{\mathsf{fma}\left(y, \frac{-1}{3 \cdot \sqrt{x}}, -\frac{1}{x \cdot 9}\right)} \]

   11. associate-/r* 99.7%

       \[\leadsto 1 + \mathsf{fma}\left(y, \color{blue}{\frac{\frac{-1}{3}}{\sqrt{x}}}, -\frac{1}{x \cdot 9}\right) \]

   12. metadata-eval 99.7%

       \[\leadsto 1 + \mathsf{fma}\left(y, \frac{\color{blue}{-0.3333333333333333}}{\sqrt{x}}, -\frac{1}{x \cdot 9}\right) \]

   13. *-commutative 99.7%

       \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, -\frac{1}{\color{blue}{9 \cdot x}}\right) \]

   14. associate-/r* 99.6%

       \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, -\color{blue}{\frac{\frac{1}{9}}{x}}\right) \]

   15. distribute-neg-frac 99.6%

       \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \color{blue}{\frac{-\frac{1}{9}}{x}}\right) \]

   16. metadata-eval 99.6%

       \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{-\color{blue}{0.1111111111111111}}{x}\right) \]

   17. metadata-eval 99.6%

       \[\leadsto 1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{\color{blue}{-0.1111111111111111}}{x}\right) \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{1 + \mathsf{fma}\left(y, \frac{-0.3333333333333333}{\sqrt{x}}, \frac{-0.1111111111111111}{x}\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 66.5%

   \[\leadsto 1 + \color{blue}{\frac{-0.1111111111111111}{x}} \]

6. Final simplification 66.5%

   \[\leadsto 1 + \frac{-0.1111111111111111}{x} \]
7. Add Preprocessing

Alternative 14: 32.1% accurate, 113.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

double code(double x, double y) {
	return 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

Java

public static double code(double x, double y) {
	return 1.0;
}

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0;
end

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 99.7%

   \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 66.5%

   \[\leadsto \color{blue}{1 - 0.3333333333333333 \cdot \left(\sqrt{\frac{1}{x}} \cdot y\right)} \]

4. Taylor expanded in y around 0 33.8%

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

5. Final simplification 33.8%

   \[\leadsto 1 \]
6. Add Preprocessing

Developer target: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (- (- 1.0 (/ (/ 1.0 x) 9.0)) (/ y (* 3.0 (sqrt x)))))

C

double code(double x, double y) {
	return (1.0 - ((1.0 / x) / 9.0)) - (y / (3.0 * sqrt(x)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - ((1.0d0 / x) / 9.0d0)) - (y / (3.0d0 * sqrt(x)))
end function

Java

public static double code(double x, double y) {
	return (1.0 - ((1.0 / x) / 9.0)) - (y / (3.0 * Math.sqrt(x)));
}

Python

def code(x, y):
	return (1.0 - ((1.0 / x) / 9.0)) - (y / (3.0 * math.sqrt(x)))

Julia

function code(x, y)
	return Float64(Float64(1.0 - Float64(Float64(1.0 / x) / 9.0)) - Float64(y / Float64(3.0 * sqrt(x))))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - ((1.0 / x) / 9.0)) - (y / (3.0 * sqrt(x)));
end

Wolfram

code[x_, y_] := N[(N[(1.0 - N[(N[(1.0 / x), $MachinePrecision] / 9.0), $MachinePrecision]), $MachinePrecision] - N[(y / N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024079 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :alt
  (- (- 1.0 (/ (/ 1.0 x) 9.0)) (/ y (* 3.0 (sqrt x))))

  (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))