Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B

Percentage Accurate: 99.4% → 99.6%

Time: 10.1s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. expm1-log1p-u 96.4%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)\right)} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

   2. expm1-udef 52.2%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)} - 1\right)} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

   3. *-commutative 52.2%

      \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\sqrt{x} \cdot 3}\right)} - 1\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

   4. metadata-eval 52.2%

      \[\leadsto \left(e^{\mathsf{log1p}\left(\sqrt{x} \cdot \color{blue}{\sqrt{9}}\right)} - 1\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

   5. sqrt-prod 52.2%

      \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\sqrt{x \cdot 9}}\right)} - 1\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

3. Applied egg-rr 52.2%

   \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\sqrt{x \cdot 9}\right)} - 1\right)} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
4. Step-by-step derivation

   1. expm1-def 96.5%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt{x \cdot 9}\right)\right)} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

   2. expm1-log1p 99.6%

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

5. Simplified 99.6%

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

6. Final simplification 99.6%

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

Alternative 2: 61.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.6 \cdot 10^{-16}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+57} \lor \neg \left(x \leq 2.4 \cdot 10^{+134}\right) \land \left(x \leq 4 \cdot 10^{+206} \lor \neg \left(x \leq 7.6 \cdot 10^{+230}\right) \land x \leq 1.58 \cdot 10^{+258}\right):\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 2.6e-16)
   (sqrt (/ 0.1111111111111111 x))
   (if (or (<= x 6.6e+57)
           (and (not (<= x 2.4e+134))
                (or (<= x 4e+206)
                    (and (not (<= x 7.6e+230)) (<= x 1.58e+258)))))
     (* 3.0 (* y (sqrt x)))
     (* (sqrt x) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 2.6e-16) {
		tmp = sqrt((0.1111111111111111 / x));
	} else if ((x <= 6.6e+57) || (!(x <= 2.4e+134) && ((x <= 4e+206) || (!(x <= 7.6e+230) && (x <= 1.58e+258))))) {
		tmp = 3.0 * (y * sqrt(x));
	} else {
		tmp = sqrt(x) * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 2.6d-16) then
        tmp = sqrt((0.1111111111111111d0 / x))
    else if ((x <= 6.6d+57) .or. (.not. (x <= 2.4d+134)) .and. (x <= 4d+206) .or. (.not. (x <= 7.6d+230)) .and. (x <= 1.58d+258)) then
        tmp = 3.0d0 * (y * sqrt(x))
    else
        tmp = sqrt(x) * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 2.6e-16) {
		tmp = Math.sqrt((0.1111111111111111 / x));
	} else if ((x <= 6.6e+57) || (!(x <= 2.4e+134) && ((x <= 4e+206) || (!(x <= 7.6e+230) && (x <= 1.58e+258))))) {
		tmp = 3.0 * (y * Math.sqrt(x));
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 2.6e-16:
		tmp = math.sqrt((0.1111111111111111 / x))
	elif (x <= 6.6e+57) or (not (x <= 2.4e+134) and ((x <= 4e+206) or (not (x <= 7.6e+230) and (x <= 1.58e+258)))):
		tmp = 3.0 * (y * math.sqrt(x))
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 2.6e-16)
		tmp = sqrt(Float64(0.1111111111111111 / x));
	elseif ((x <= 6.6e+57) || (!(x <= 2.4e+134) && ((x <= 4e+206) || (!(x <= 7.6e+230) && (x <= 1.58e+258)))))
		tmp = Float64(3.0 * Float64(y * sqrt(x)));
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 2.6e-16)
		tmp = sqrt((0.1111111111111111 / x));
	elseif ((x <= 6.6e+57) || (~((x <= 2.4e+134)) && ((x <= 4e+206) || (~((x <= 7.6e+230)) && (x <= 1.58e+258)))))
		tmp = 3.0 * (y * sqrt(x));
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 2.6e-16], N[Sqrt[N[(0.1111111111111111 / x), $MachinePrecision]], $MachinePrecision], If[Or[LessEqual[x, 6.6e+57], And[N[Not[LessEqual[x, 2.4e+134]], $MachinePrecision], Or[LessEqual[x, 4e+206], And[N[Not[LessEqual[x, 7.6e+230]], $MachinePrecision], LessEqual[x, 1.58e+258]]]]], N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 2.5999999999999998e-16

   1. Initial program 99.2%

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

      1. associate-*l* 99.1%

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

      2. sub-neg 99.1%

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

      3. +-commutative 99.1%

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

      4. associate-+l+ 99.1%

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

      5. *-commutative 99.1%

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

      6. associate-/r* 99.2%

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

      7. metadata-eval 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Applied egg-rr 45.0%

      \[\leadsto 3 \cdot \color{blue}{\sqrt{x \cdot {\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2}}} \]
   6. Step-by-step derivation

      1. *-commutative 45.0%

         \[\leadsto 3 \cdot \sqrt{\color{blue}{{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2} \cdot x}} \]

   7. Simplified 45.0%

      \[\leadsto 3 \cdot \color{blue}{\sqrt{{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2} \cdot x}} \]

   8. Taylor expanded in x around 0 81.2%

      \[\leadsto 3 \cdot \sqrt{\color{blue}{\frac{0.012345679012345678}{x}}} \]
   9. Step-by-step derivation

      1. add-sqr-sqrt 80.8%

         \[\leadsto \color{blue}{\sqrt{3 \cdot \sqrt{\frac{0.012345679012345678}{x}}} \cdot \sqrt{3 \cdot \sqrt{\frac{0.012345679012345678}{x}}}} \]

      2. sqrt-unprod 81.2%

         \[\leadsto \color{blue}{\sqrt{\left(3 \cdot \sqrt{\frac{0.012345679012345678}{x}}\right) \cdot \left(3 \cdot \sqrt{\frac{0.012345679012345678}{x}}\right)}} \]

      3. *-commutative 81.2%

         \[\leadsto \sqrt{\color{blue}{\left(\sqrt{\frac{0.012345679012345678}{x}} \cdot 3\right)} \cdot \left(3 \cdot \sqrt{\frac{0.012345679012345678}{x}}\right)} \]

      4. *-commutative 81.2%

         \[\leadsto \sqrt{\left(\sqrt{\frac{0.012345679012345678}{x}} \cdot 3\right) \cdot \color{blue}{\left(\sqrt{\frac{0.012345679012345678}{x}} \cdot 3\right)}} \]

      5. swap-sqr 81.2%

         \[\leadsto \sqrt{\color{blue}{\left(\sqrt{\frac{0.012345679012345678}{x}} \cdot \sqrt{\frac{0.012345679012345678}{x}}\right) \cdot \left(3 \cdot 3\right)}} \]

      6. add-sqr-sqrt 81.3%

         \[\leadsto \sqrt{\color{blue}{\frac{0.012345679012345678}{x}} \cdot \left(3 \cdot 3\right)} \]

      7. metadata-eval 81.3%

         \[\leadsto \sqrt{\frac{0.012345679012345678}{x} \cdot \color{blue}{9}} \]

   10. Applied egg-rr 81.3%

       \[\leadsto \color{blue}{\sqrt{\frac{0.012345679012345678}{x} \cdot 9}} \]
   11. Step-by-step derivation

       1. associate-*l/ 81.3%

          \[\leadsto \sqrt{\color{blue}{\frac{0.012345679012345678 \cdot 9}{x}}} \]

       2. metadata-eval 81.3%

          \[\leadsto \sqrt{\frac{\color{blue}{0.1111111111111111}}{x}} \]

   12. Simplified 81.3%

       \[\leadsto \color{blue}{\sqrt{\frac{0.1111111111111111}{x}}} \]

   if 2.5999999999999998e-16 < x < 6.6000000000000002e57 or 2.40000000000000005e134 < x < 4.0000000000000002e206 or 7.6e230 < x < 1.58e258

   1. Initial program 99.6%

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

      1. distribute-lft-out-- 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. associate-*l* 99.6%

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

      4. *-commutative 99.6%

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

      5. associate-*r* 99.6%

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

      6. distribute-rgt-out-- 99.6%

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

      7. +-commutative 99.6%

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

      8. distribute-lft-in 99.6%

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

      9. associate--l+ 99.6%

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

      10. *-commutative 99.6%

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

      11. associate-/r* 99.6%

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

      12. associate-*r/ 99.6%

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

      13. metadata-eval 99.6%

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

      14. metadata-eval 99.6%

          \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(3 \cdot y - 3\right)\right) \]

      15. sub-neg 99.6%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\left(3 \cdot y + \left(-3\right)\right)}\right) \]

      16. metadata-eval 99.6%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{-3}\right)\right) \]

      17. metadata-eval 99.6%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{3 \cdot -1}\right)\right) \]

      18. metadata-eval 99.6%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + 3 \cdot \color{blue}{\left(-1\right)}\right)\right) \]

      19. fma-def 99.7%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\mathsf{fma}\left(3, y, 3 \cdot \left(-1\right)\right)}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \mathsf{fma}\left(3, y, -3\right)\right)} \]

   4. Taylor expanded in y around inf 68.1%

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

   if 6.6000000000000002e57 < x < 2.40000000000000005e134 or 4.0000000000000002e206 < x < 7.6e230 or 1.58e258 < x

   1. Initial program 99.4%

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

      1. distribute-lft-out-- 99.4%

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

      2. *-rgt-identity 99.4%

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

      3. associate-*l* 99.5%

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

      4. *-commutative 99.5%

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

      5. associate-*r* 99.5%

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

      6. distribute-rgt-out-- 99.5%

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

      7. +-commutative 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. associate--l+ 99.5%

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

      10. *-commutative 99.5%

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

      11. associate-/r* 99.5%

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

      12. associate-*r/ 99.5%

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

      13. metadata-eval 99.5%

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

      14. metadata-eval 99.5%

          \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(3 \cdot y - 3\right)\right) \]

      15. sub-neg 99.5%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\left(3 \cdot y + \left(-3\right)\right)}\right) \]

      16. metadata-eval 99.5%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{-3}\right)\right) \]

      17. metadata-eval 99.5%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{3 \cdot -1}\right)\right) \]

      18. metadata-eval 99.5%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + 3 \cdot \color{blue}{\left(-1\right)}\right)\right) \]

      19. fma-def 99.6%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\mathsf{fma}\left(3, y, 3 \cdot \left(-1\right)\right)}\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \mathsf{fma}\left(3, y, -3\right)\right)} \]

   4. Taylor expanded in y around 0 69.0%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(0.3333333333333333 \cdot \frac{1}{x} - 3\right)} \]
   5. Step-by-step derivation

      1. sub-neg 69.0%

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(0.3333333333333333 \cdot \frac{1}{x} + \left(-3\right)\right)} \]

      2. associate-*r/ 69.0%

         \[\leadsto \sqrt{x} \cdot \left(\color{blue}{\frac{0.3333333333333333 \cdot 1}{x}} + \left(-3\right)\right) \]

      3. metadata-eval 69.0%

         \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(-3\right)\right) \]

      4. metadata-eval 69.0%

         \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{-3}\right) \]

   6. Simplified 69.0%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)} \]

   7. Taylor expanded in x around inf 69.0%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.6 \cdot 10^{-16}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+57} \lor \neg \left(x \leq 2.4 \cdot 10^{+134}\right) \land \left(x \leq 4 \cdot 10^{+206} \lor \neg \left(x \leq 7.6 \cdot 10^{+230}\right) \land x \leq 1.58 \cdot 10^{+258}\right):\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]

Alternative 3: 62.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot -3\\ t_1 := 3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{if}\;x \leq 4.2 \cdot 10^{-15}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+134}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+206}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+231} \lor \neg \left(x \leq 1.1 \cdot 10^{+258}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) -3.0)) (t_1 (* 3.0 (* y (sqrt x)))))
   (if (<= x 4.2e-15)
     (sqrt (/ 0.1111111111111111 x))
     (if (<= x 5.8e+57)
       t_1
       (if (<= x 2e+134)
         t_0
         (if (<= x 7.2e+206)
           (* (sqrt x) (* y 3.0))
           (if (or (<= x 4.2e+231) (not (<= x 1.1e+258))) t_0 t_1)))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * -3.0;
	double t_1 = 3.0 * (y * sqrt(x));
	double tmp;
	if (x <= 4.2e-15) {
		tmp = sqrt((0.1111111111111111 / x));
	} else if (x <= 5.8e+57) {
		tmp = t_1;
	} else if (x <= 2e+134) {
		tmp = t_0;
	} else if (x <= 7.2e+206) {
		tmp = sqrt(x) * (y * 3.0);
	} else if ((x <= 4.2e+231) || !(x <= 1.1e+258)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = sqrt(x) * (-3.0d0)
    t_1 = 3.0d0 * (y * sqrt(x))
    if (x <= 4.2d-15) then
        tmp = sqrt((0.1111111111111111d0 / x))
    else if (x <= 5.8d+57) then
        tmp = t_1
    else if (x <= 2d+134) then
        tmp = t_0
    else if (x <= 7.2d+206) then
        tmp = sqrt(x) * (y * 3.0d0)
    else if ((x <= 4.2d+231) .or. (.not. (x <= 1.1d+258))) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(x) * -3.0;
	double t_1 = 3.0 * (y * Math.sqrt(x));
	double tmp;
	if (x <= 4.2e-15) {
		tmp = Math.sqrt((0.1111111111111111 / x));
	} else if (x <= 5.8e+57) {
		tmp = t_1;
	} else if (x <= 2e+134) {
		tmp = t_0;
	} else if (x <= 7.2e+206) {
		tmp = Math.sqrt(x) * (y * 3.0);
	} else if ((x <= 4.2e+231) || !(x <= 1.1e+258)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * -3.0
	t_1 = 3.0 * (y * math.sqrt(x))
	tmp = 0
	if x <= 4.2e-15:
		tmp = math.sqrt((0.1111111111111111 / x))
	elif x <= 5.8e+57:
		tmp = t_1
	elif x <= 2e+134:
		tmp = t_0
	elif x <= 7.2e+206:
		tmp = math.sqrt(x) * (y * 3.0)
	elif (x <= 4.2e+231) or not (x <= 1.1e+258):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * -3.0)
	t_1 = Float64(3.0 * Float64(y * sqrt(x)))
	tmp = 0.0
	if (x <= 4.2e-15)
		tmp = sqrt(Float64(0.1111111111111111 / x));
	elseif (x <= 5.8e+57)
		tmp = t_1;
	elseif (x <= 2e+134)
		tmp = t_0;
	elseif (x <= 7.2e+206)
		tmp = Float64(sqrt(x) * Float64(y * 3.0));
	elseif ((x <= 4.2e+231) || !(x <= 1.1e+258))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * -3.0;
	t_1 = 3.0 * (y * sqrt(x));
	tmp = 0.0;
	if (x <= 4.2e-15)
		tmp = sqrt((0.1111111111111111 / x));
	elseif (x <= 5.8e+57)
		tmp = t_1;
	elseif (x <= 2e+134)
		tmp = t_0;
	elseif (x <= 7.2e+206)
		tmp = sqrt(x) * (y * 3.0);
	elseif ((x <= 4.2e+231) || ~((x <= 1.1e+258)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 4.2e-15], N[Sqrt[N[(0.1111111111111111 / x), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 5.8e+57], t$95$1, If[LessEqual[x, 2e+134], t$95$0, If[LessEqual[x, 7.2e+206], N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 4.2e+231], N[Not[LessEqual[x, 1.1e+258]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < 4.19999999999999962e-15

   1. Initial program 99.2%

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

      1. associate-*l* 99.1%

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

      2. sub-neg 99.1%

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

      3. +-commutative 99.1%

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

      4. associate-+l+ 99.1%

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

      5. *-commutative 99.1%

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

      6. associate-/r* 99.2%

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

      7. metadata-eval 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Applied egg-rr 45.0%

      \[\leadsto 3 \cdot \color{blue}{\sqrt{x \cdot {\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2}}} \]
   6. Step-by-step derivation

      1. *-commutative 45.0%

         \[\leadsto 3 \cdot \sqrt{\color{blue}{{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2} \cdot x}} \]

   7. Simplified 45.0%

      \[\leadsto 3 \cdot \color{blue}{\sqrt{{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2} \cdot x}} \]

   8. Taylor expanded in x around 0 81.2%

      \[\leadsto 3 \cdot \sqrt{\color{blue}{\frac{0.012345679012345678}{x}}} \]
   9. Step-by-step derivation

      1. add-sqr-sqrt 80.8%

         \[\leadsto \color{blue}{\sqrt{3 \cdot \sqrt{\frac{0.012345679012345678}{x}}} \cdot \sqrt{3 \cdot \sqrt{\frac{0.012345679012345678}{x}}}} \]

      2. sqrt-unprod 81.2%

         \[\leadsto \color{blue}{\sqrt{\left(3 \cdot \sqrt{\frac{0.012345679012345678}{x}}\right) \cdot \left(3 \cdot \sqrt{\frac{0.012345679012345678}{x}}\right)}} \]

      3. *-commutative 81.2%

         \[\leadsto \sqrt{\color{blue}{\left(\sqrt{\frac{0.012345679012345678}{x}} \cdot 3\right)} \cdot \left(3 \cdot \sqrt{\frac{0.012345679012345678}{x}}\right)} \]

      4. *-commutative 81.2%

         \[\leadsto \sqrt{\left(\sqrt{\frac{0.012345679012345678}{x}} \cdot 3\right) \cdot \color{blue}{\left(\sqrt{\frac{0.012345679012345678}{x}} \cdot 3\right)}} \]

      5. swap-sqr 81.2%

         \[\leadsto \sqrt{\color{blue}{\left(\sqrt{\frac{0.012345679012345678}{x}} \cdot \sqrt{\frac{0.012345679012345678}{x}}\right) \cdot \left(3 \cdot 3\right)}} \]

      6. add-sqr-sqrt 81.3%

         \[\leadsto \sqrt{\color{blue}{\frac{0.012345679012345678}{x}} \cdot \left(3 \cdot 3\right)} \]

      7. metadata-eval 81.3%

         \[\leadsto \sqrt{\frac{0.012345679012345678}{x} \cdot \color{blue}{9}} \]

   10. Applied egg-rr 81.3%

       \[\leadsto \color{blue}{\sqrt{\frac{0.012345679012345678}{x} \cdot 9}} \]
   11. Step-by-step derivation

       1. associate-*l/ 81.3%

          \[\leadsto \sqrt{\color{blue}{\frac{0.012345679012345678 \cdot 9}{x}}} \]

       2. metadata-eval 81.3%

          \[\leadsto \sqrt{\frac{\color{blue}{0.1111111111111111}}{x}} \]

   12. Simplified 81.3%

       \[\leadsto \color{blue}{\sqrt{\frac{0.1111111111111111}{x}}} \]

   if 4.19999999999999962e-15 < x < 5.8000000000000003e57 or 4.19999999999999969e231 < x < 1.09999999999999991e258

   1. Initial program 99.5%

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

      1. distribute-lft-out-- 99.4%

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

      2. *-rgt-identity 99.4%

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

      3. associate-*l* 99.5%

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

      4. *-commutative 99.5%

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

      5. associate-*r* 99.4%

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

      6. distribute-rgt-out-- 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. associate--l+ 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-/r* 99.4%

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

      12. associate-*r/ 99.4%

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

      13. metadata-eval 99.4%

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

      14. metadata-eval 99.4%

          \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(3 \cdot y - 3\right)\right) \]

      15. sub-neg 99.4%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\left(3 \cdot y + \left(-3\right)\right)}\right) \]

      16. metadata-eval 99.4%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{-3}\right)\right) \]

      17. metadata-eval 99.4%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{3 \cdot -1}\right)\right) \]

      18. metadata-eval 99.4%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + 3 \cdot \color{blue}{\left(-1\right)}\right)\right) \]

      19. fma-def 99.5%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\mathsf{fma}\left(3, y, 3 \cdot \left(-1\right)\right)}\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \mathsf{fma}\left(3, y, -3\right)\right)} \]

   4. Taylor expanded in y around inf 71.2%

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

   if 5.8000000000000003e57 < x < 1.99999999999999984e134 or 7.20000000000000057e206 < x < 4.19999999999999969e231 or 1.09999999999999991e258 < x

   1. Initial program 99.4%

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

      1. distribute-lft-out-- 99.4%

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

      2. *-rgt-identity 99.4%

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

      3. associate-*l* 99.5%

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

      4. *-commutative 99.5%

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

      5. associate-*r* 99.5%

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

      6. distribute-rgt-out-- 99.5%

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

      7. +-commutative 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. associate--l+ 99.5%

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

      10. *-commutative 99.5%

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

      11. associate-/r* 99.5%

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

      12. associate-*r/ 99.5%

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

      13. metadata-eval 99.5%

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

      14. metadata-eval 99.5%

          \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(3 \cdot y - 3\right)\right) \]

      15. sub-neg 99.5%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\left(3 \cdot y + \left(-3\right)\right)}\right) \]

      16. metadata-eval 99.5%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{-3}\right)\right) \]

      17. metadata-eval 99.5%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{3 \cdot -1}\right)\right) \]

      18. metadata-eval 99.5%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + 3 \cdot \color{blue}{\left(-1\right)}\right)\right) \]

      19. fma-def 99.6%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\mathsf{fma}\left(3, y, 3 \cdot \left(-1\right)\right)}\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \mathsf{fma}\left(3, y, -3\right)\right)} \]

   4. Taylor expanded in y around 0 69.0%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(0.3333333333333333 \cdot \frac{1}{x} - 3\right)} \]
   5. Step-by-step derivation

      1. sub-neg 69.0%

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(0.3333333333333333 \cdot \frac{1}{x} + \left(-3\right)\right)} \]

      2. associate-*r/ 69.0%

         \[\leadsto \sqrt{x} \cdot \left(\color{blue}{\frac{0.3333333333333333 \cdot 1}{x}} + \left(-3\right)\right) \]

      3. metadata-eval 69.0%

         \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(-3\right)\right) \]

      4. metadata-eval 69.0%

         \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{-3}\right) \]

   6. Simplified 69.0%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)} \]

   7. Taylor expanded in x around inf 69.0%

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

   if 1.99999999999999984e134 < x < 7.20000000000000057e206

   1. Initial program 99.7%

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

      1. distribute-lft-out-- 99.7%

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

      2. *-rgt-identity 99.7%

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

      3. associate-*l* 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-*r* 99.8%

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

      6. distribute-rgt-out-- 99.8%

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

      7. +-commutative 99.8%

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

      8. distribute-lft-in 99.8%

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

      9. associate--l+ 99.8%

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

      10. *-commutative 99.8%

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

      11. associate-/r* 99.8%

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

      12. associate-*r/ 99.8%

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

      13. metadata-eval 99.8%

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

      14. metadata-eval 99.8%

          \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(3 \cdot y - 3\right)\right) \]

      15. sub-neg 99.8%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\left(3 \cdot y + \left(-3\right)\right)}\right) \]

      16. metadata-eval 99.8%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{-3}\right)\right) \]

      17. metadata-eval 99.8%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{3 \cdot -1}\right)\right) \]

      18. metadata-eval 99.8%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + 3 \cdot \color{blue}{\left(-1\right)}\right)\right) \]

      19. fma-def 99.8%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\mathsf{fma}\left(3, y, 3 \cdot \left(-1\right)\right)}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \mathsf{fma}\left(3, y, -3\right)\right)} \]

   4. Taylor expanded in y around inf 64.2%

      \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.2 \cdot 10^{-15}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+57}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+134}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+206}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+231} \lor \neg \left(x \leq 1.1 \cdot 10^{+258}\right):\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \end{array} \]

Alternative 4: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+101} \lor \neg \left(y \leq 1.35 \cdot 10^{+15}\right):\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -6.5e+101) (not (<= y 1.35e+15)))
   (* 3.0 (* y (sqrt x)))
   (* (sqrt x) (+ (/ 0.3333333333333333 x) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -6.5e+101) || !(y <= 1.35e+15)) {
		tmp = 3.0 * (y * sqrt(x));
	} else {
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-6.5d+101)) .or. (.not. (y <= 1.35d+15))) then
        tmp = 3.0d0 * (y * sqrt(x))
    else
        tmp = sqrt(x) * ((0.3333333333333333d0 / x) + (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -6.5e+101) || !(y <= 1.35e+15)) {
		tmp = 3.0 * (y * Math.sqrt(x));
	} else {
		tmp = Math.sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -6.5e+101) or not (y <= 1.35e+15):
		tmp = 3.0 * (y * math.sqrt(x))
	else:
		tmp = math.sqrt(x) * ((0.3333333333333333 / x) + -3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -6.5e+101) || !(y <= 1.35e+15))
		tmp = Float64(3.0 * Float64(y * sqrt(x)));
	else
		tmp = Float64(sqrt(x) * Float64(Float64(0.3333333333333333 / x) + -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -6.5e+101) || ~((y <= 1.35e+15)))
		tmp = 3.0 * (y * sqrt(x));
	else
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -6.5e+101], N[Not[LessEqual[y, 1.35e+15]], $MachinePrecision]], N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.3333333333333333 / x), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.50000000000000016e101 or 1.35e15 < y

   1. Initial program 99.5%

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

      1. distribute-lft-out-- 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. associate-*l* 99.5%

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

      4. *-commutative 99.5%

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

      5. associate-*r* 99.5%

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

      6. distribute-rgt-out-- 99.5%

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

      7. +-commutative 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. associate--l+ 99.5%

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

      10. *-commutative 99.5%

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

      11. associate-/r* 99.5%

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

      12. associate-*r/ 99.5%

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

      13. metadata-eval 99.5%

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

      14. metadata-eval 99.5%

          \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(3 \cdot y - 3\right)\right) \]

      15. sub-neg 99.5%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\left(3 \cdot y + \left(-3\right)\right)}\right) \]

      16. metadata-eval 99.5%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{-3}\right)\right) \]

      17. metadata-eval 99.5%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{3 \cdot -1}\right)\right) \]

      18. metadata-eval 99.5%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + 3 \cdot \color{blue}{\left(-1\right)}\right)\right) \]

      19. fma-def 99.6%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\mathsf{fma}\left(3, y, 3 \cdot \left(-1\right)\right)}\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \mathsf{fma}\left(3, y, -3\right)\right)} \]

   4. Taylor expanded in y around inf 82.2%

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

   if -6.50000000000000016e101 < y < 1.35e15

   1. Initial program 99.3%

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

      1. distribute-lft-out-- 99.2%

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

      2. *-rgt-identity 99.2%

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

      3. associate-*l* 99.3%

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

      4. *-commutative 99.3%

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

      5. associate-*r* 99.3%

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

      6. distribute-rgt-out-- 99.3%

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

      7. +-commutative 99.3%

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

      8. distribute-lft-in 99.3%

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

      9. associate--l+ 99.3%

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

      10. *-commutative 99.3%

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

      11. associate-/r* 99.3%

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

      12. associate-*r/ 99.4%

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

      13. metadata-eval 99.4%

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

      14. metadata-eval 99.4%

          \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(3 \cdot y - 3\right)\right) \]

      15. sub-neg 99.4%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\left(3 \cdot y + \left(-3\right)\right)}\right) \]

      16. metadata-eval 99.4%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{-3}\right)\right) \]

      17. metadata-eval 99.4%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{3 \cdot -1}\right)\right) \]

      18. metadata-eval 99.4%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + 3 \cdot \color{blue}{\left(-1\right)}\right)\right) \]

      19. fma-def 99.4%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\mathsf{fma}\left(3, y, 3 \cdot \left(-1\right)\right)}\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \mathsf{fma}\left(3, y, -3\right)\right)} \]

   4. Taylor expanded in y around 0 96.2%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(0.3333333333333333 \cdot \frac{1}{x} - 3\right)} \]
   5. Step-by-step derivation

      1. sub-neg 96.2%

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(0.3333333333333333 \cdot \frac{1}{x} + \left(-3\right)\right)} \]

      2. associate-*r/ 96.2%

         \[\leadsto \sqrt{x} \cdot \left(\color{blue}{\frac{0.3333333333333333 \cdot 1}{x}} + \left(-3\right)\right) \]

      3. metadata-eval 96.2%

         \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(-3\right)\right) \]

      4. metadata-eval 96.2%

         \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{-3}\right) \]

   6. Simplified 96.2%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+101} \lor \neg \left(y \leq 1.35 \cdot 10^{+15}\right):\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \end{array} \]

Alternative 5: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 58:\\ \;\;\;\;\sqrt{x} \cdot \left(0.3333333333333333 \cdot \frac{1}{x} - 3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 58.0)
   (* (sqrt x) (- (* 0.3333333333333333 (/ 1.0 x)) 3.0))
   (* (sqrt (* x 9.0)) (+ y -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 58.0) {
		tmp = sqrt(x) * ((0.3333333333333333 * (1.0 / x)) - 3.0);
	} else {
		tmp = sqrt((x * 9.0)) * (y + -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 (x <= 58.0d0) then
        tmp = sqrt(x) * ((0.3333333333333333d0 * (1.0d0 / x)) - 3.0d0)
    else
        tmp = sqrt((x * 9.0d0)) * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 58.0) {
		tmp = Math.sqrt(x) * ((0.3333333333333333 * (1.0 / x)) - 3.0);
	} else {
		tmp = Math.sqrt((x * 9.0)) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 58.0:
		tmp = math.sqrt(x) * ((0.3333333333333333 * (1.0 / x)) - 3.0)
	else:
		tmp = math.sqrt((x * 9.0)) * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 58.0)
		tmp = Float64(sqrt(x) * Float64(Float64(0.3333333333333333 * Float64(1.0 / x)) - 3.0));
	else
		tmp = Float64(sqrt(Float64(x * 9.0)) * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 58.0)
		tmp = sqrt(x) * ((0.3333333333333333 * (1.0 / x)) - 3.0);
	else
		tmp = sqrt((x * 9.0)) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 58.0], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.3333333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 58

   1. Initial program 99.1%

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

      1. distribute-lft-out-- 99.1%

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

      2. *-rgt-identity 99.1%

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

      3. associate-*l* 99.2%

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

      4. *-commutative 99.2%

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

      5. associate-*r* 99.2%

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

      6. distribute-rgt-out-- 99.2%

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

      7. +-commutative 99.2%

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

      8. distribute-lft-in 99.2%

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

      9. associate--l+ 99.2%

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

      10. *-commutative 99.2%

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

      11. associate-/r* 99.2%

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

      12. associate-*r/ 99.3%

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

      13. metadata-eval 99.3%

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

      14. metadata-eval 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(3 \cdot y - 3\right)\right) \]

      15. sub-neg 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\left(3 \cdot y + \left(-3\right)\right)}\right) \]

      16. metadata-eval 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{-3}\right)\right) \]

      17. metadata-eval 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{3 \cdot -1}\right)\right) \]

      18. metadata-eval 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + 3 \cdot \color{blue}{\left(-1\right)}\right)\right) \]

      19. fma-def 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\mathsf{fma}\left(3, y, 3 \cdot \left(-1\right)\right)}\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \mathsf{fma}\left(3, y, -3\right)\right)} \]

   4. Taylor expanded in y around 0 79.4%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(0.3333333333333333 \cdot \frac{1}{x} - 3\right)} \]

   if 58 < x

   1. Initial program 99.5%

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

      1. associate-*l* 99.6%

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

      2. sub-neg 99.6%

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

      3. +-commutative 99.6%

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

      4. associate-+l+ 99.6%

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

      5. *-commutative 99.6%

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

      6. associate-/r* 99.6%

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

      7. metadata-eval 99.6%

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

      8. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Applied egg-rr 24.2%

      \[\leadsto \color{blue}{\log \left({\left(e^{\sqrt{x \cdot 9}}\right)}^{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}\right)} \]
   6. Step-by-step derivation

      1. log-pow 24.2%

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

      2. rem-log-exp 99.8%

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

      3. *-commutative 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around inf 99.8%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 58:\\ \;\;\;\;\sqrt{x} \cdot \left(0.3333333333333333 \cdot \frac{1}{x} - 3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \end{array} \]

Alternative 6: 85.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.29:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{1}{x \cdot 3} - 3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.29)
   (* (sqrt x) (- (/ 1.0 (* x 3.0)) 3.0))
   (* (sqrt (* x 9.0)) (+ y -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.29) {
		tmp = sqrt(x) * ((1.0 / (x * 3.0)) - 3.0);
	} else {
		tmp = sqrt((x * 9.0)) * (y + -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 (x <= 0.29d0) then
        tmp = sqrt(x) * ((1.0d0 / (x * 3.0d0)) - 3.0d0)
    else
        tmp = sqrt((x * 9.0d0)) * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.29) {
		tmp = Math.sqrt(x) * ((1.0 / (x * 3.0)) - 3.0);
	} else {
		tmp = Math.sqrt((x * 9.0)) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.29:
		tmp = math.sqrt(x) * ((1.0 / (x * 3.0)) - 3.0)
	else:
		tmp = math.sqrt((x * 9.0)) * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.29)
		tmp = Float64(sqrt(x) * Float64(Float64(1.0 / Float64(x * 3.0)) - 3.0));
	else
		tmp = Float64(sqrt(Float64(x * 9.0)) * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.29)
		tmp = sqrt(x) * ((1.0 / (x * 3.0)) - 3.0);
	else
		tmp = sqrt((x * 9.0)) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.29], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(1.0 / N[(x * 3.0), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.28999999999999998

   1. Initial program 99.1%

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

      1. distribute-lft-out-- 99.1%

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

      2. *-rgt-identity 99.1%

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

      3. associate-*l* 99.2%

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

      4. *-commutative 99.2%

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

      5. associate-*r* 99.2%

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

      6. distribute-rgt-out-- 99.2%

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

      7. +-commutative 99.2%

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

      8. distribute-lft-in 99.2%

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

      9. associate--l+ 99.2%

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

      10. *-commutative 99.2%

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

      11. associate-/r* 99.2%

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

      12. associate-*r/ 99.3%

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

      13. metadata-eval 99.3%

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

      14. metadata-eval 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(3 \cdot y - 3\right)\right) \]

      15. sub-neg 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\left(3 \cdot y + \left(-3\right)\right)}\right) \]

      16. metadata-eval 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{-3}\right)\right) \]

      17. metadata-eval 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{3 \cdot -1}\right)\right) \]

      18. metadata-eval 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + 3 \cdot \color{blue}{\left(-1\right)}\right)\right) \]

      19. fma-def 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\mathsf{fma}\left(3, y, 3 \cdot \left(-1\right)\right)}\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \mathsf{fma}\left(3, y, -3\right)\right)} \]

   4. Taylor expanded in y around 0 79.4%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(0.3333333333333333 \cdot \frac{1}{x} - 3\right)} \]
   5. Step-by-step derivation

      1. div-inv 79.3%

         \[\leadsto \sqrt{x} \cdot \left(\color{blue}{\frac{0.3333333333333333}{x}} - 3\right) \]

      2. clear-num 79.2%

         \[\leadsto \sqrt{x} \cdot \left(\color{blue}{\frac{1}{\frac{x}{0.3333333333333333}}} - 3\right) \]

      3. div-inv 79.4%

         \[\leadsto \sqrt{x} \cdot \left(\frac{1}{\color{blue}{x \cdot \frac{1}{0.3333333333333333}}} - 3\right) \]

      4. metadata-eval 79.4%

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

   6. Applied egg-rr 79.4%

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

   if 0.28999999999999998 < x

   1. Initial program 99.5%

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

      1. associate-*l* 99.6%

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

      2. sub-neg 99.6%

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

      3. +-commutative 99.6%

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

      4. associate-+l+ 99.6%

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

      5. *-commutative 99.6%

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

      6. associate-/r* 99.6%

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

      7. metadata-eval 99.6%

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

      8. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Applied egg-rr 24.2%

      \[\leadsto \color{blue}{\log \left({\left(e^{\sqrt{x \cdot 9}}\right)}^{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}\right)} \]
   6. Step-by-step derivation

      1. log-pow 24.2%

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

      2. rem-log-exp 99.8%

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

      3. *-commutative 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around inf 99.8%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.29:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{1}{x \cdot 3} - 3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \end{array} \]

Alternative 7: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 3 \cdot \left(\sqrt{x} \cdot \left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)\right) \end{array} \]

FPCore

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

C

double code(double x, double y) {
	return 3.0 * (sqrt(x) * ((0.1111111111111111 / x) + (y + -1.0)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 3.0d0 * (sqrt(x) * ((0.1111111111111111d0 / x) + (y + (-1.0d0))))
end function

Java

public static double code(double x, double y) {
	return 3.0 * (Math.sqrt(x) * ((0.1111111111111111 / x) + (y + -1.0)));
}

Python

def code(x, y):
	return 3.0 * (math.sqrt(x) * ((0.1111111111111111 / x) + (y + -1.0)))

Julia

function code(x, y)
	return Float64(3.0 * Float64(sqrt(x) * Float64(Float64(0.1111111111111111 / x) + Float64(y + -1.0))))
end

MATLAB

function tmp = code(x, y)
	tmp = 3.0 * (sqrt(x) * ((0.1111111111111111 / x) + (y + -1.0)));
end

Wolfram

code[x_, y_] := N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.1111111111111111 / x), $MachinePrecision] + N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.3%

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

   1. associate-*l* 99.4%

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

   2. sub-neg 99.4%

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

   3. +-commutative 99.4%

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

   4. associate-+l+ 99.4%

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

   5. *-commutative 99.4%

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

   6. associate-/r* 99.4%

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

   7. metadata-eval 99.4%

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

   8. metadata-eval 99.4%

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

3. Simplified 99.4%

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

4. Final simplification 99.4%

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

Alternative 8: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(y \cdot 3 - 3\right)\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (* (sqrt x) (+ (/ 0.3333333333333333 x) (- (* y 3.0) 3.0))))

C

double code(double x, double y) {
	return sqrt(x) * ((0.3333333333333333 / x) + ((y * 3.0) - 3.0));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = sqrt(x) * ((0.3333333333333333d0 / x) + ((y * 3.0d0) - 3.0d0))
end function

Java

public static double code(double x, double y) {
	return Math.sqrt(x) * ((0.3333333333333333 / x) + ((y * 3.0) - 3.0));
}

Python

def code(x, y):
	return math.sqrt(x) * ((0.3333333333333333 / x) + ((y * 3.0) - 3.0))

Julia

function code(x, y)
	return Float64(sqrt(x) * Float64(Float64(0.3333333333333333 / x) + Float64(Float64(y * 3.0) - 3.0)))
end

MATLAB

function tmp = code(x, y)
	tmp = sqrt(x) * ((0.3333333333333333 / x) + ((y * 3.0) - 3.0));
end

Wolfram

code[x_, y_] := N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.3333333333333333 / x), $MachinePrecision] + N[(N[(y * 3.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.3%

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

   1. distribute-lft-out-- 99.3%

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

   2. *-rgt-identity 99.3%

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

   3. associate-*l* 99.4%

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

   4. *-commutative 99.4%

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

   5. associate-*r* 99.4%

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

   6. distribute-rgt-out-- 99.4%

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

   7. +-commutative 99.4%

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

   8. distribute-lft-in 99.4%

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

   9. associate--l+ 99.4%

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

   10. *-commutative 99.4%

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

   11. associate-/r* 99.4%

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

   12. associate-*r/ 99.4%

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

   13. metadata-eval 99.4%

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

   14. metadata-eval 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(3 \cdot y - 3\right)\right) \]

   15. sub-neg 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\left(3 \cdot y + \left(-3\right)\right)}\right) \]

   16. metadata-eval 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{-3}\right)\right) \]

   17. metadata-eval 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{3 \cdot -1}\right)\right) \]

   18. metadata-eval 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + 3 \cdot \color{blue}{\left(-1\right)}\right)\right) \]

   19. fma-def 99.5%

       \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\mathsf{fma}\left(3, y, 3 \cdot \left(-1\right)\right)}\right) \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \mathsf{fma}\left(3, y, -3\right)\right)} \]

4. Taylor expanded in x around 0 99.4%

   \[\leadsto \sqrt{x} \cdot \color{blue}{\left(\left(3 \cdot y + 0.3333333333333333 \cdot \frac{1}{x}\right) - 3\right)} \]
5. Step-by-step derivation

   1. +-commutative 99.4%

      \[\leadsto \sqrt{x} \cdot \left(\color{blue}{\left(0.3333333333333333 \cdot \frac{1}{x} + 3 \cdot y\right)} - 3\right) \]

   2. associate--l+ 99.4%

      \[\leadsto \sqrt{x} \cdot \color{blue}{\left(0.3333333333333333 \cdot \frac{1}{x} + \left(3 \cdot y - 3\right)\right)} \]

   3. un-div-inv 99.4%

      \[\leadsto \sqrt{x} \cdot \left(\color{blue}{\frac{0.3333333333333333}{x}} + \left(3 \cdot y - 3\right)\right) \]

6. Applied egg-rr 99.4%

   \[\leadsto \sqrt{x} \cdot \color{blue}{\left(\frac{0.3333333333333333}{x} + \left(3 \cdot y - 3\right)\right)} \]

7. Final simplification 99.4%

   \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(y \cdot 3 - 3\right)\right) \]

Alternative 9: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. associate-*l* 99.4%

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

   2. sub-neg 99.4%

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

   3. +-commutative 99.4%

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

   4. associate-+l+ 99.4%

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

   5. *-commutative 99.4%

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

   6. associate-/r* 99.4%

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

   7. metadata-eval 99.4%

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

   8. metadata-eval 99.4%

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

3. Simplified 99.4%

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

5. Applied egg-rr 14.5%

   \[\leadsto \color{blue}{\log \left({\left(e^{\sqrt{x \cdot 9}}\right)}^{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}\right)} \]
6. Step-by-step derivation

   1. log-pow 17.7%

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

   2. rem-log-exp 99.5%

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

   3. *-commutative 99.5%

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

7. Simplified 99.5%

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

8. Final simplification 99.5%

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

Alternative 10: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5000:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3 - 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 5000.0)
   (* (sqrt x) (+ (/ 0.3333333333333333 x) -3.0))
   (* (sqrt x) (- (* y 3.0) 3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 5000.0) {
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	} else {
		tmp = sqrt(x) * ((y * 3.0) - 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 5000.0d0) then
        tmp = sqrt(x) * ((0.3333333333333333d0 / x) + (-3.0d0))
    else
        tmp = sqrt(x) * ((y * 3.0d0) - 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 5000.0) {
		tmp = Math.sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	} else {
		tmp = Math.sqrt(x) * ((y * 3.0) - 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 5000.0:
		tmp = math.sqrt(x) * ((0.3333333333333333 / x) + -3.0)
	else:
		tmp = math.sqrt(x) * ((y * 3.0) - 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 5000.0)
		tmp = Float64(sqrt(x) * Float64(Float64(0.3333333333333333 / x) + -3.0));
	else
		tmp = Float64(sqrt(x) * Float64(Float64(y * 3.0) - 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 5000.0)
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	else
		tmp = sqrt(x) * ((y * 3.0) - 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 5000.0], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.3333333333333333 / x), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(y * 3.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5e3

   1. Initial program 99.1%

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

      1. distribute-lft-out-- 99.1%

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

      2. *-rgt-identity 99.1%

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

      3. associate-*l* 99.2%

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

      4. *-commutative 99.2%

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

      5. associate-*r* 99.2%

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

      6. distribute-rgt-out-- 99.2%

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

      7. +-commutative 99.2%

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

      8. distribute-lft-in 99.2%

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

      9. associate--l+ 99.2%

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

      10. *-commutative 99.2%

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

      11. associate-/r* 99.2%

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

      12. associate-*r/ 99.3%

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

      13. metadata-eval 99.3%

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

      14. metadata-eval 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(3 \cdot y - 3\right)\right) \]

      15. sub-neg 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\left(3 \cdot y + \left(-3\right)\right)}\right) \]

      16. metadata-eval 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{-3}\right)\right) \]

      17. metadata-eval 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{3 \cdot -1}\right)\right) \]

      18. metadata-eval 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + 3 \cdot \color{blue}{\left(-1\right)}\right)\right) \]

      19. fma-def 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\mathsf{fma}\left(3, y, 3 \cdot \left(-1\right)\right)}\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \mathsf{fma}\left(3, y, -3\right)\right)} \]

   4. Taylor expanded in y around 0 79.4%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(0.3333333333333333 \cdot \frac{1}{x} - 3\right)} \]
   5. Step-by-step derivation

      1. sub-neg 79.4%

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(0.3333333333333333 \cdot \frac{1}{x} + \left(-3\right)\right)} \]

      2. associate-*r/ 79.3%

         \[\leadsto \sqrt{x} \cdot \left(\color{blue}{\frac{0.3333333333333333 \cdot 1}{x}} + \left(-3\right)\right) \]

      3. metadata-eval 79.3%

         \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(-3\right)\right) \]

      4. metadata-eval 79.3%

         \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{-3}\right) \]

   6. Simplified 79.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)} \]

   if 5e3 < x

   1. Initial program 99.5%

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

      1. distribute-lft-out-- 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. associate-*l* 99.6%

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

      4. *-commutative 99.6%

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

      5. associate-*r* 99.6%

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

      6. distribute-rgt-out-- 99.6%

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

      7. +-commutative 99.6%

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

      8. distribute-lft-in 99.6%

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

      9. associate--l+ 99.6%

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

      10. *-commutative 99.6%

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

      11. associate-/r* 99.6%

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

      12. associate-*r/ 99.6%

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

      13. metadata-eval 99.6%

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

      14. metadata-eval 99.6%

          \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(3 \cdot y - 3\right)\right) \]

      15. sub-neg 99.6%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\left(3 \cdot y + \left(-3\right)\right)}\right) \]

      16. metadata-eval 99.6%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{-3}\right)\right) \]

      17. metadata-eval 99.6%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{3 \cdot -1}\right)\right) \]

      18. metadata-eval 99.6%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + 3 \cdot \color{blue}{\left(-1\right)}\right)\right) \]

      19. fma-def 99.6%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\mathsf{fma}\left(3, y, 3 \cdot \left(-1\right)\right)}\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \mathsf{fma}\left(3, y, -3\right)\right)} \]

   4. Taylor expanded in x around inf 99.6%

      \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot y - 3\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5000:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3 - 3\right)\\ \end{array} \]

Alternative 11: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.5:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 1.5)
   (* (sqrt x) (+ (/ 0.3333333333333333 x) -3.0))
   (* (sqrt (* x 9.0)) (+ y -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 1.5) {
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	} else {
		tmp = sqrt((x * 9.0)) * (y + -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 (x <= 1.5d0) then
        tmp = sqrt(x) * ((0.3333333333333333d0 / x) + (-3.0d0))
    else
        tmp = sqrt((x * 9.0d0)) * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 1.5) {
		tmp = Math.sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	} else {
		tmp = Math.sqrt((x * 9.0)) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 1.5:
		tmp = math.sqrt(x) * ((0.3333333333333333 / x) + -3.0)
	else:
		tmp = math.sqrt((x * 9.0)) * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 1.5)
		tmp = Float64(sqrt(x) * Float64(Float64(0.3333333333333333 / x) + -3.0));
	else
		tmp = Float64(sqrt(Float64(x * 9.0)) * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 1.5)
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	else
		tmp = sqrt((x * 9.0)) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 1.5], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.3333333333333333 / x), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.5

   1. Initial program 99.1%

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

      1. distribute-lft-out-- 99.1%

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

      2. *-rgt-identity 99.1%

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

      3. associate-*l* 99.2%

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

      4. *-commutative 99.2%

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

      5. associate-*r* 99.2%

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

      6. distribute-rgt-out-- 99.2%

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

      7. +-commutative 99.2%

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

      8. distribute-lft-in 99.2%

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

      9. associate--l+ 99.2%

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

      10. *-commutative 99.2%

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

      11. associate-/r* 99.2%

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

      12. associate-*r/ 99.3%

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

      13. metadata-eval 99.3%

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

      14. metadata-eval 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(3 \cdot y - 3\right)\right) \]

      15. sub-neg 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\left(3 \cdot y + \left(-3\right)\right)}\right) \]

      16. metadata-eval 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{-3}\right)\right) \]

      17. metadata-eval 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{3 \cdot -1}\right)\right) \]

      18. metadata-eval 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + 3 \cdot \color{blue}{\left(-1\right)}\right)\right) \]

      19. fma-def 99.3%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\mathsf{fma}\left(3, y, 3 \cdot \left(-1\right)\right)}\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \mathsf{fma}\left(3, y, -3\right)\right)} \]

   4. Taylor expanded in y around 0 79.4%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(0.3333333333333333 \cdot \frac{1}{x} - 3\right)} \]
   5. Step-by-step derivation

      1. sub-neg 79.4%

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(0.3333333333333333 \cdot \frac{1}{x} + \left(-3\right)\right)} \]

      2. associate-*r/ 79.3%

         \[\leadsto \sqrt{x} \cdot \left(\color{blue}{\frac{0.3333333333333333 \cdot 1}{x}} + \left(-3\right)\right) \]

      3. metadata-eval 79.3%

         \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(-3\right)\right) \]

      4. metadata-eval 79.3%

         \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{-3}\right) \]

   6. Simplified 79.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)} \]

   if 1.5 < x

   1. Initial program 99.5%

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

      1. associate-*l* 99.6%

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

      2. sub-neg 99.6%

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

      3. +-commutative 99.6%

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

      4. associate-+l+ 99.6%

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

      5. *-commutative 99.6%

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

      6. associate-/r* 99.6%

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

      7. metadata-eval 99.6%

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

      8. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Applied egg-rr 24.2%

      \[\leadsto \color{blue}{\log \left({\left(e^{\sqrt{x \cdot 9}}\right)}^{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}\right)} \]
   6. Step-by-step derivation

      1. log-pow 24.2%

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

      2. rem-log-exp 99.8%

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

      3. *-commutative 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around inf 99.8%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.5:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \end{array} \]

Alternative 12: 61.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.112:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.112) (sqrt (/ 0.1111111111111111 x)) (* (sqrt x) -3.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.112) {
		tmp = sqrt((0.1111111111111111 / x));
	} else {
		tmp = sqrt(x) * -3.0;
	}
	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 = sqrt((0.1111111111111111d0 / x))
    else
        tmp = sqrt(x) * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.112) {
		tmp = Math.sqrt((0.1111111111111111 / x));
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.112:
		tmp = math.sqrt((0.1111111111111111 / x))
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.112)
		tmp = sqrt(Float64(0.1111111111111111 / x));
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.112)
		tmp = sqrt((0.1111111111111111 / x));
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.112], N[Sqrt[N[(0.1111111111111111 / x), $MachinePrecision]], $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.112000000000000002

   1. Initial program 99.2%

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

      1. associate-*l* 99.2%

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

      2. sub-neg 99.2%

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

      3. +-commutative 99.2%

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

      4. associate-+l+ 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-/r* 99.2%

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

      7. metadata-eval 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Applied egg-rr 46.5%

      \[\leadsto 3 \cdot \color{blue}{\sqrt{x \cdot {\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2}}} \]
   6. Step-by-step derivation

      1. *-commutative 46.5%

         \[\leadsto 3 \cdot \sqrt{\color{blue}{{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2} \cdot x}} \]

   7. Simplified 46.5%

      \[\leadsto 3 \cdot \color{blue}{\sqrt{{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2} \cdot x}} \]

   8. Taylor expanded in x around 0 77.9%

      \[\leadsto 3 \cdot \sqrt{\color{blue}{\frac{0.012345679012345678}{x}}} \]
   9. Step-by-step derivation

      1. add-sqr-sqrt 77.5%

         \[\leadsto \color{blue}{\sqrt{3 \cdot \sqrt{\frac{0.012345679012345678}{x}}} \cdot \sqrt{3 \cdot \sqrt{\frac{0.012345679012345678}{x}}}} \]

      2. sqrt-unprod 77.9%

         \[\leadsto \color{blue}{\sqrt{\left(3 \cdot \sqrt{\frac{0.012345679012345678}{x}}\right) \cdot \left(3 \cdot \sqrt{\frac{0.012345679012345678}{x}}\right)}} \]

      3. *-commutative 77.9%

         \[\leadsto \sqrt{\color{blue}{\left(\sqrt{\frac{0.012345679012345678}{x}} \cdot 3\right)} \cdot \left(3 \cdot \sqrt{\frac{0.012345679012345678}{x}}\right)} \]

      4. *-commutative 77.9%

         \[\leadsto \sqrt{\left(\sqrt{\frac{0.012345679012345678}{x}} \cdot 3\right) \cdot \color{blue}{\left(\sqrt{\frac{0.012345679012345678}{x}} \cdot 3\right)}} \]

      5. swap-sqr 77.8%

         \[\leadsto \sqrt{\color{blue}{\left(\sqrt{\frac{0.012345679012345678}{x}} \cdot \sqrt{\frac{0.012345679012345678}{x}}\right) \cdot \left(3 \cdot 3\right)}} \]

      6. add-sqr-sqrt 78.0%

         \[\leadsto \sqrt{\color{blue}{\frac{0.012345679012345678}{x}} \cdot \left(3 \cdot 3\right)} \]

      7. metadata-eval 78.0%

         \[\leadsto \sqrt{\frac{0.012345679012345678}{x} \cdot \color{blue}{9}} \]

   10. Applied egg-rr 78.0%

       \[\leadsto \color{blue}{\sqrt{\frac{0.012345679012345678}{x} \cdot 9}} \]
   11. Step-by-step derivation

       1. associate-*l/ 78.0%

          \[\leadsto \sqrt{\color{blue}{\frac{0.012345679012345678 \cdot 9}{x}}} \]

       2. metadata-eval 78.0%

          \[\leadsto \sqrt{\frac{\color{blue}{0.1111111111111111}}{x}} \]

   12. Simplified 78.0%

       \[\leadsto \color{blue}{\sqrt{\frac{0.1111111111111111}{x}}} \]

   if 0.112000000000000002 < x

   1. Initial program 99.5%

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

      1. distribute-lft-out-- 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. associate-*l* 99.6%

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

      4. *-commutative 99.6%

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

      5. associate-*r* 99.5%

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

      6. distribute-rgt-out-- 99.6%

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

      7. +-commutative 99.6%

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

      8. distribute-lft-in 99.6%

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

      9. associate--l+ 99.6%

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

      10. *-commutative 99.6%

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

      11. associate-/r* 99.6%

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

      12. associate-*r/ 99.6%

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

      13. metadata-eval 99.6%

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

      14. metadata-eval 99.6%

          \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(3 \cdot y - 3\right)\right) \]

      15. sub-neg 99.6%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\left(3 \cdot y + \left(-3\right)\right)}\right) \]

      16. metadata-eval 99.6%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{-3}\right)\right) \]

      17. metadata-eval 99.6%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{3 \cdot -1}\right)\right) \]

      18. metadata-eval 99.6%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + 3 \cdot \color{blue}{\left(-1\right)}\right)\right) \]

      19. fma-def 99.6%

          \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\mathsf{fma}\left(3, y, 3 \cdot \left(-1\right)\right)}\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \mathsf{fma}\left(3, y, -3\right)\right)} \]

   4. Taylor expanded in y around 0 51.9%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(0.3333333333333333 \cdot \frac{1}{x} - 3\right)} \]
   5. Step-by-step derivation

      1. sub-neg 51.9%

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(0.3333333333333333 \cdot \frac{1}{x} + \left(-3\right)\right)} \]

      2. associate-*r/ 51.9%

         \[\leadsto \sqrt{x} \cdot \left(\color{blue}{\frac{0.3333333333333333 \cdot 1}{x}} + \left(-3\right)\right) \]

      3. metadata-eval 51.9%

         \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(-3\right)\right) \]

      4. metadata-eval 51.9%

         \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{-3}\right) \]

   6. Simplified 51.9%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)} \]

   7. Taylor expanded in x around inf 50.7%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.112:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]

Alternative 13: 37.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \sqrt{\frac{0.1111111111111111}{x}} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (sqrt (/ 0.1111111111111111 x)))

C

double code(double x, double y) {
	return sqrt((0.1111111111111111 / x));
}

Fortran

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

Java

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

Python

def code(x, y):
	return math.sqrt((0.1111111111111111 / x))

Julia

function code(x, y)
	return sqrt(Float64(0.1111111111111111 / x))
end

MATLAB

function tmp = code(x, y)
	tmp = sqrt((0.1111111111111111 / x));
end

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. associate-*l* 99.4%

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

   2. sub-neg 99.4%

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

   3. +-commutative 99.4%

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

   4. associate-+l+ 99.4%

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

   5. *-commutative 99.4%

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

   6. associate-/r* 99.4%

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

   7. metadata-eval 99.4%

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

   8. metadata-eval 99.4%

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

3. Simplified 99.4%

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

5. Applied egg-rr 31.2%

   \[\leadsto 3 \cdot \color{blue}{\sqrt{x \cdot {\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2}}} \]
6. Step-by-step derivation

   1. *-commutative 31.2%

      \[\leadsto 3 \cdot \sqrt{\color{blue}{{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2} \cdot x}} \]

7. Simplified 31.2%

   \[\leadsto 3 \cdot \color{blue}{\sqrt{{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2} \cdot x}} \]

8. Taylor expanded in x around 0 39.6%

   \[\leadsto 3 \cdot \sqrt{\color{blue}{\frac{0.012345679012345678}{x}}} \]
9. Step-by-step derivation

   1. add-sqr-sqrt 39.4%

      \[\leadsto \color{blue}{\sqrt{3 \cdot \sqrt{\frac{0.012345679012345678}{x}}} \cdot \sqrt{3 \cdot \sqrt{\frac{0.012345679012345678}{x}}}} \]

   2. sqrt-unprod 39.6%

      \[\leadsto \color{blue}{\sqrt{\left(3 \cdot \sqrt{\frac{0.012345679012345678}{x}}\right) \cdot \left(3 \cdot \sqrt{\frac{0.012345679012345678}{x}}\right)}} \]

   3. *-commutative 39.6%

      \[\leadsto \sqrt{\color{blue}{\left(\sqrt{\frac{0.012345679012345678}{x}} \cdot 3\right)} \cdot \left(3 \cdot \sqrt{\frac{0.012345679012345678}{x}}\right)} \]

   4. *-commutative 39.6%

      \[\leadsto \sqrt{\left(\sqrt{\frac{0.012345679012345678}{x}} \cdot 3\right) \cdot \color{blue}{\left(\sqrt{\frac{0.012345679012345678}{x}} \cdot 3\right)}} \]

   5. swap-sqr 39.6%

      \[\leadsto \sqrt{\color{blue}{\left(\sqrt{\frac{0.012345679012345678}{x}} \cdot \sqrt{\frac{0.012345679012345678}{x}}\right) \cdot \left(3 \cdot 3\right)}} \]

   6. add-sqr-sqrt 39.6%

      \[\leadsto \sqrt{\color{blue}{\frac{0.012345679012345678}{x}} \cdot \left(3 \cdot 3\right)} \]

   7. metadata-eval 39.6%

      \[\leadsto \sqrt{\frac{0.012345679012345678}{x} \cdot \color{blue}{9}} \]

10. Applied egg-rr 39.6%

    \[\leadsto \color{blue}{\sqrt{\frac{0.012345679012345678}{x} \cdot 9}} \]
11. Step-by-step derivation

    1. associate-*l/ 39.7%

       \[\leadsto \sqrt{\color{blue}{\frac{0.012345679012345678 \cdot 9}{x}}} \]

    2. metadata-eval 39.7%

       \[\leadsto \sqrt{\frac{\color{blue}{0.1111111111111111}}{x}} \]

12. Simplified 39.7%

    \[\leadsto \color{blue}{\sqrt{\frac{0.1111111111111111}{x}}} \]

13. Final simplification 39.7%

    \[\leadsto \sqrt{\frac{0.1111111111111111}{x}} \]

Developer target: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023312 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x))))

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