Numeric.Integration.TanhSinh:everywhere from integration-0.2.1

Percentage Accurate: 93.9% → 99.9%

Time: 3.8s

Alternatives: 6

Speedup: 0.8×

• 26.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y) :precision binary64 (* x (+ 1.0 (* y y))))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x * (1.0 + (y * y))

Julia

function code(x, y)
	return Float64(x * Float64(1.0 + Float64(y * y)))
end

MATLAB

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

Wolfram

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

Initial Program: 93.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (* x (+ 1.0 (* y y))))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x * (1.0 + (y * y))

Julia

function code(x, y)
	return Float64(x * Float64(1.0 + Float64(y * y)))
end

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot y \leq 5 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot y, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* y y) 5e+22) (fma x (* y y) x) (* y (* y x))))

C

double code(double x, double y) {
	double tmp;
	if ((y * y) <= 5e+22) {
		tmp = fma(x, (y * y), x);
	} else {
		tmp = y * (y * x);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(y * y) <= 5e+22)
		tmp = fma(x, Float64(y * y), x);
	else
		tmp = Float64(y * Float64(y * x));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[N[(y * y), $MachinePrecision], 5e+22], N[(x * N[(y * y), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y y) < 4.9999999999999996e22

   1. Initial program 100.0%

      \[x \cdot \left(1 + y \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-rgt-identity 100.0%

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

      4. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot y, x\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot y, x\right)} \]

   if 4.9999999999999996e22 < (*.f64 y y)

   1. Initial program 81.1%

      \[x \cdot \left(1 + y \cdot y\right) \]

   2. Taylor expanded in y around inf 81.1%

      \[\leadsto \color{blue}{{y}^{2} \cdot x} \]
   3. Step-by-step derivation

      1. unpow2 81.1%

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

      2. associate-*l* 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot y \leq 5 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot y, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 2: 99.8% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{\mathsf{hypot}\left(1, y\right)}\\ \frac{1}{t_0} \cdot \frac{x}{t_0} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ 1.0 (hypot 1.0 y)))) (* (/ 1.0 t_0) (/ x t_0))))

C

double code(double x, double y) {
	double t_0 = 1.0 / hypot(1.0, y);
	return (1.0 / t_0) * (x / t_0);
}

Java

public static double code(double x, double y) {
	double t_0 = 1.0 / Math.hypot(1.0, y);
	return (1.0 / t_0) * (x / t_0);
}

Python

def code(x, y):
	t_0 = 1.0 / math.hypot(1.0, y)
	return (1.0 / t_0) * (x / t_0)

Julia

function code(x, y)
	t_0 = Float64(1.0 / hypot(1.0, y))
	return Float64(Float64(1.0 / t_0) * Float64(x / t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = 1.0 / hypot(1.0, y);
	tmp = (1.0 / t_0) * (x / t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 / N[Sqrt[1.0 ^ 2 + y ^ 2], $MachinePrecision]), $MachinePrecision]}, N[(N[(1.0 / t$95$0), $MachinePrecision] * N[(x / t$95$0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 90.8%

   \[x \cdot \left(1 + y \cdot y\right) \]
2. Step-by-step derivation

   1. +-commutative 90.8%

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

   2. distribute-lft-in 90.8%

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

   3. *-rgt-identity 90.8%

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

3. Applied egg-rr 90.8%

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

   1. *-commutative 90.8%

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

   2. distribute-lft1-in 90.8%

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

   3. fma-udef 90.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, y, 1\right)} \cdot x \]

   4. *-commutative 90.7%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(y, y, 1\right)} \]

   5. /-rgt-identity 90.7%

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

   6. associate-/r/ 90.7%

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

   7. *-un-lft-identity 90.7%

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

   8. add-sqr-sqrt 90.7%

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

   9. times-frac 90.7%

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

   10. clear-num 90.7%

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

   11. sqrt-div 90.7%

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

   12. metadata-eval 90.7%

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

   13. clear-num 90.7%

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

   14. remove-double-div 90.7%

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

   15. fma-udef 90.7%

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

   16. +-commutative 90.7%

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

   17. hypot-1-def 90.7%

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

   18. clear-num 90.7%

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

   19. sqrt-div 90.7%

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

   20. metadata-eval 90.7%

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

   21. clear-num 90.7%

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

5. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\frac{1}{\frac{1}{\mathsf{hypot}\left(1, y\right)}} \cdot \frac{x}{\frac{1}{\mathsf{hypot}\left(1, y\right)}}} \]

6. Final simplification 99.8%

   \[\leadsto \frac{1}{\frac{1}{\mathsf{hypot}\left(1, y\right)}} \cdot \frac{x}{\frac{1}{\mathsf{hypot}\left(1, y\right)}} \]

Alternative 3: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot y \leq 5 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \left(1 + y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* y y) 5e+22) (* x (+ 1.0 (* y y))) (* y (* y x))))

C

double code(double x, double y) {
	double tmp;
	if ((y * y) <= 5e+22) {
		tmp = x * (1.0 + (y * y));
	} else {
		tmp = y * (y * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y * y) <= 5d+22) then
        tmp = x * (1.0d0 + (y * y))
    else
        tmp = y * (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y * y) <= 5e+22) {
		tmp = x * (1.0 + (y * y));
	} else {
		tmp = y * (y * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y * y) <= 5e+22:
		tmp = x * (1.0 + (y * y))
	else:
		tmp = y * (y * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(y * y) <= 5e+22)
		tmp = Float64(x * Float64(1.0 + Float64(y * y)));
	else
		tmp = Float64(y * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y * y) <= 5e+22)
		tmp = x * (1.0 + (y * y));
	else
		tmp = y * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(y * y), $MachinePrecision], 5e+22], N[(x * N[(1.0 + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y y) < 4.9999999999999996e22

   1. Initial program 100.0%

      \[x \cdot \left(1 + y \cdot y\right) \]

   if 4.9999999999999996e22 < (*.f64 y y)

   1. Initial program 81.1%

      \[x \cdot \left(1 + y \cdot y\right) \]

   2. Taylor expanded in y around inf 81.1%

      \[\leadsto \color{blue}{{y}^{2} \cdot x} \]
   3. Step-by-step derivation

      1. unpow2 81.1%

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

      2. associate-*l* 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot y \leq 5 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \left(1 + y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 4: 92.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= (* y y) 1.0) x (* x (* y y))))

C

double code(double x, double y) {
	double tmp;
	if ((y * y) <= 1.0) {
		tmp = x;
	} else {
		tmp = x * (y * y);
	}
	return tmp;
}

Fortran

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

Java

public static double code(double x, double y) {
	double tmp;
	if ((y * y) <= 1.0) {
		tmp = x;
	} else {
		tmp = x * (y * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y * y) <= 1.0:
		tmp = x
	else:
		tmp = x * (y * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(y * y) <= 1.0)
		tmp = x;
	else
		tmp = Float64(x * Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y * y) <= 1.0)
		tmp = x;
	else
		tmp = x * (y * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(y * y), $MachinePrecision], 1.0], x, N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

      \[x \cdot \left(1 + y \cdot y\right) \]

   2. Taylor expanded in y around 0 98.0%

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

   if 1 < (*.f64 y y)

   1. Initial program 81.9%

      \[x \cdot \left(1 + y \cdot y\right) \]

   2. Taylor expanded in y around inf 81.0%

      \[\leadsto \color{blue}{{y}^{2} \cdot x} \]
   3. Step-by-step derivation

      1. unpow2 81.0%

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

      2. *-commutative 81.0%

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

   4. Simplified 81.0%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 5: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot y \leq 0.2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= (* y y) 0.2) x (* y (* y x))))

C

double code(double x, double y) {
	double tmp;
	if ((y * y) <= 0.2) {
		tmp = x;
	} else {
		tmp = y * (y * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y * y) <= 0.2d0) then
        tmp = x
    else
        tmp = y * (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y * y) <= 0.2) {
		tmp = x;
	} else {
		tmp = y * (y * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y * y) <= 0.2:
		tmp = x
	else:
		tmp = y * (y * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(y * y) <= 0.2)
		tmp = x;
	else
		tmp = Float64(y * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y * y) <= 0.2)
		tmp = x;
	else
		tmp = y * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(y * y), $MachinePrecision], 0.2], x, N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y y) < 0.20000000000000001

   1. Initial program 100.0%

      \[x \cdot \left(1 + y \cdot y\right) \]

   2. Taylor expanded in y around 0 98.0%

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

   if 0.20000000000000001 < (*.f64 y y)

   1. Initial program 81.9%

      \[x \cdot \left(1 + y \cdot y\right) \]

   2. Taylor expanded in y around inf 81.0%

      \[\leadsto \color{blue}{{y}^{2} \cdot x} \]
   3. Step-by-step derivation

      1. unpow2 81.0%

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

      2. associate-*l* 98.9%

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

   4. Simplified 98.9%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot y \leq 0.2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 6: 51.0% accurate, 7.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 90.8%

   \[x \cdot \left(1 + y \cdot y\right) \]

2. Taylor expanded in y around 0 50.4%

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

3. Final simplification 50.4%

   \[\leadsto x \]

Developer target: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(x \cdot y\right) \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (* (* x y) y)))

C

double code(double x, double y) {
	return x + ((x * y) * y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + ((x * y) * y)
end function

Java

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

Python

def code(x, y):
	return x + ((x * y) * y)

Julia

function code(x, y)
	return Float64(x + Float64(Float64(x * y) * y))
end

MATLAB

function tmp = code(x, y)
	tmp = x + ((x * y) * y);
end

Wolfram

code[x_, y_] := N[(x + N[(N[(x * y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023214 
(FPCore (x y)
  :name "Numeric.Integration.TanhSinh:everywhere from integration-0.2.1"
  :precision binary64

  :herbie-target
  (+ x (* (* x y) y))

  (* x (+ 1.0 (* y y))))