Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2

Percentage Accurate: 99.8% → 99.8%

Time: 7.4s

Alternatives: 6

Speedup: 1.0×

• 32.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (* x x) (- 3.0 (* x 2.0))))

C

double code(double x) {
	return (x * x) * (3.0 - (x * 2.0));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x * x) * (3.0d0 - (x * 2.0d0))
end function

Java

public static double code(double x) {
	return (x * x) * (3.0 - (x * 2.0));
}

Python

def code(x):
	return (x * x) * (3.0 - (x * 2.0))

Julia

function code(x)
	return Float64(Float64(x * x) * Float64(3.0 - Float64(x * 2.0)))
end

MATLAB

function tmp = code(x)
	tmp = (x * x) * (3.0 - (x * 2.0));
end

Wolfram

code[x_] := N[(N[(x * x), $MachinePrecision] * N[(3.0 - N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (* x x) (- 3.0 (* x 2.0))))

C

double code(double x) {
	return (x * x) * (3.0 - (x * 2.0));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x * x) * (3.0d0 - (x * 2.0d0))
end function

Java

public static double code(double x) {
	return (x * x) * (3.0 - (x * 2.0));
}

Python

def code(x):
	return (x * x) * (3.0 - (x * 2.0))

Julia

function code(x)
	return Float64(Float64(x * x) * Float64(3.0 - Float64(x * 2.0)))
end

MATLAB

function tmp = code(x)
	tmp = (x * x) * (3.0 - (x * 2.0));
end

Wolfram

code[x_] := N[(N[(x * x), $MachinePrecision] * N[(3.0 - N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (* x x) (- 3.0 (* x 2.0))))

C

double code(double x) {
	return (x * x) * (3.0 - (x * 2.0));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x * x) * (3.0d0 - (x * 2.0d0))
end function

Java

public static double code(double x) {
	return (x * x) * (3.0 - (x * 2.0));
}

Python

def code(x):
	return (x * x) * (3.0 - (x * 2.0))

Julia

function code(x)
	return Float64(Float64(x * x) * Float64(3.0 - Float64(x * 2.0)))
end

MATLAB

function tmp = code(x)
	tmp = (x * x) * (3.0 - (x * 2.0));
end

Wolfram

code[x_] := N[(N[(x * x), $MachinePrecision] * N[(3.0 - N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x \cdot x\right) \cdot \left(x \cdot -2\right)\\ \mathbf{if}\;x \leq -1.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.5:\\ \;\;\;\;\left(x \cdot x\right) \cdot 3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* (* x x) (* x -2.0))))
   (if (<= x -1.5) t_0 (if (<= x 1.5) (* (* x x) 3.0) t_0))))

C

double code(double x) {
	double t_0 = (x * x) * (x * -2.0);
	double tmp;
	if (x <= -1.5) {
		tmp = t_0;
	} else if (x <= 1.5) {
		tmp = (x * x) * 3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * x) * (x * (-2.0d0))
    if (x <= (-1.5d0)) then
        tmp = t_0
    else if (x <= 1.5d0) then
        tmp = (x * x) * 3.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = (x * x) * (x * -2.0);
	double tmp;
	if (x <= -1.5) {
		tmp = t_0;
	} else if (x <= 1.5) {
		tmp = (x * x) * 3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x):
	t_0 = (x * x) * (x * -2.0)
	tmp = 0
	if x <= -1.5:
		tmp = t_0
	elif x <= 1.5:
		tmp = (x * x) * 3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x)
	t_0 = Float64(Float64(x * x) * Float64(x * -2.0))
	tmp = 0.0
	if (x <= -1.5)
		tmp = t_0;
	elseif (x <= 1.5)
		tmp = Float64(Float64(x * x) * 3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = (x * x) * (x * -2.0);
	tmp = 0.0;
	if (x <= -1.5)
		tmp = t_0;
	elseif (x <= 1.5)
		tmp = (x * x) * 3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(x * x), $MachinePrecision] * N[(x * -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.5], t$95$0, If[LessEqual[x, 1.5], N[(N[(x * x), $MachinePrecision] * 3.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5 or 1.5 < x

   1. Initial program 99.9%

      \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \color{blue}{\left(-2 \cdot x\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \left(x \cdot \color{blue}{-2}\right)\right) \]

      2. *-lowering-*.f64 98.3%

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

   5. Simplified 98.3%

      \[\leadsto \left(x \cdot x\right) \cdot \color{blue}{\left(x \cdot -2\right)} \]

   if -1.5 < x < 1.5

   1. Initial program 99.8%

      \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \color{blue}{3}\right) \]
   4. Step-by-step derivation

   5. Simplified 99.2%

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

Alternative 3: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(x \cdot \left(3 + x \cdot -2\right)\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* x (* x (+ 3.0 (* x -2.0)))))

C

double code(double x) {
	return x * (x * (3.0 + (x * -2.0)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x * (x * (3.0d0 + (x * (-2.0d0))))
end function

Java

public static double code(double x) {
	return x * (x * (3.0 + (x * -2.0)));
}

Python

def code(x):
	return x * (x * (3.0 + (x * -2.0)))

Julia

function code(x)
	return Float64(x * Float64(x * Float64(3.0 + Float64(x * -2.0))))
end

MATLAB

function tmp = code(x)
	tmp = x * (x * (3.0 + (x * -2.0)));
end

Wolfram

code[x_] := N[(x * N[(x * N[(3.0 + N[(x * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]
2. Step-by-step derivation

   1. associate-*l* N/A

      \[\leadsto x \cdot \color{blue}{\left(x \cdot \left(3 - x \cdot 2\right)\right)} \]

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

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(x \cdot \left(3 - x \cdot 2\right)\right)}\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{\left(3 - x \cdot 2\right)}\right)\right) \]

   4. sub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \left(3 + \color{blue}{\left(\mathsf{neg}\left(x \cdot 2\right)\right)}\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(3, \color{blue}{\left(\mathsf{neg}\left(x \cdot 2\right)\right)}\right)\right)\right) \]

   6. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(3, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right)\right) \]

   8. metadata-eval 99.8%

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, -2\right)\right)\right)\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{x \cdot \left(x \cdot \left(3 + x \cdot -2\right)\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 4: 62.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot x\right) \cdot 3 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (* x x) 3.0))

C

double code(double x) {
	return (x * x) * 3.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x * x) * 3.0d0
end function

Java

public static double code(double x) {
	return (x * x) * 3.0;
}

Python

def code(x):
	return (x * x) * 3.0

Julia

function code(x)
	return Float64(Float64(x * x) * 3.0)
end

MATLAB

function tmp = code(x)
	tmp = (x * x) * 3.0;
end

Wolfram

code[x_] := N[(N[(x * x), $MachinePrecision] * 3.0), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \color{blue}{3}\right) \]
4. Step-by-step derivation

5. Simplified 63.3%

   \[\leadsto \left(x \cdot x\right) \cdot \color{blue}{3} \]
6. Add Preprocessing

Alternative 5: 62.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(x \cdot 3\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* x (* x 3.0)))

C

double code(double x) {
	return x * (x * 3.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x * (x * 3.0d0)
end function

Java

public static double code(double x) {
	return x * (x * 3.0);
}

Python

def code(x):
	return x * (x * 3.0)

Julia

function code(x)
	return Float64(x * Float64(x * 3.0))
end

MATLAB

function tmp = code(x)
	tmp = x * (x * 3.0);
end

Wolfram

code[x_] := N[(x * N[(x * 3.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]
2. Step-by-step derivation

   1. associate-*l* N/A

      \[\leadsto x \cdot \color{blue}{\left(x \cdot \left(3 - x \cdot 2\right)\right)} \]

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

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(x \cdot \left(3 - x \cdot 2\right)\right)}\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{\left(3 - x \cdot 2\right)}\right)\right) \]

   4. sub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \left(3 + \color{blue}{\left(\mathsf{neg}\left(x \cdot 2\right)\right)}\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(3, \color{blue}{\left(\mathsf{neg}\left(x \cdot 2\right)\right)}\right)\right)\right) \]

   6. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(3, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right)\right) \]

   8. metadata-eval 99.8%

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, -2\right)\right)\right)\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{x \cdot \left(x \cdot \left(3 + x \cdot -2\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around 0

   \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{3}\right)\right) \]
6. Step-by-step derivation

7. Simplified 63.3%

   \[\leadsto x \cdot \left(x \cdot \color{blue}{3}\right) \]
8. Add Preprocessing

Alternative 6: 3.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 4.5 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* x 4.5))

C

double code(double x) {
	return x * 4.5;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x * 4.5d0
end function

Java

public static double code(double x) {
	return x * 4.5;
}

Python

def code(x):
	return x * 4.5

Julia

function code(x)
	return Float64(x * 4.5)
end

MATLAB

function tmp = code(x)
	tmp = x * 4.5;
end

Wolfram

code[x_] := N[(x * 4.5), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]
2. Step-by-step derivation

   1. associate-*l* N/A

      \[\leadsto x \cdot \color{blue}{\left(x \cdot \left(3 - x \cdot 2\right)\right)} \]

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

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(x \cdot \left(3 - x \cdot 2\right)\right)}\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{\left(3 - x \cdot 2\right)}\right)\right) \]

   4. sub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \left(3 + \color{blue}{\left(\mathsf{neg}\left(x \cdot 2\right)\right)}\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(3, \color{blue}{\left(\mathsf{neg}\left(x \cdot 2\right)\right)}\right)\right)\right) \]

   6. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(3, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right)\right) \]

   8. metadata-eval 99.8%

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, -2\right)\right)\right)\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{x \cdot \left(x \cdot \left(3 + x \cdot -2\right)\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(x, \left(\left(3 + x \cdot -2\right) \cdot \color{blue}{x}\right)\right) \]

   2. +-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(x, \left(\left(x \cdot -2 + 3\right) \cdot x\right)\right) \]

   3. flip-+ N/A

      \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{\left(x \cdot -2\right) \cdot \left(x \cdot -2\right) - 3 \cdot 3}{x \cdot -2 - 3} \cdot x\right)\right) \]

   4. associate-*l/ N/A

      \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{\left(\left(x \cdot -2\right) \cdot \left(x \cdot -2\right) - 3 \cdot 3\right) \cdot x}{\color{blue}{x \cdot -2 - 3}}\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\left(\left(x \cdot -2\right) \cdot \left(x \cdot -2\right) - 3 \cdot 3\right) \cdot x\right), \color{blue}{\left(x \cdot -2 - 3\right)}\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot -2\right) \cdot \left(x \cdot -2\right) - 3 \cdot 3\right), x\right), \left(\color{blue}{x \cdot -2} - 3\right)\right)\right) \]

   7. sub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot -2\right) \cdot \left(x \cdot -2\right) + \left(\mathsf{neg}\left(3 \cdot 3\right)\right)\right), x\right), \left(\color{blue}{x} \cdot -2 - 3\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot -2\right) \cdot \left(x \cdot -2\right)\right), \left(\mathsf{neg}\left(3 \cdot 3\right)\right)\right), x\right), \left(\color{blue}{x} \cdot -2 - 3\right)\right)\right) \]

   9. swap-sqr N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot x\right) \cdot \left(-2 \cdot -2\right)\right), \left(\mathsf{neg}\left(3 \cdot 3\right)\right)\right), x\right), \left(x \cdot -2 - 3\right)\right)\right) \]

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

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(x \cdot x\right), \left(-2 \cdot -2\right)\right), \left(\mathsf{neg}\left(3 \cdot 3\right)\right)\right), x\right), \left(x \cdot -2 - 3\right)\right)\right) \]

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

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), \left(-2 \cdot -2\right)\right), \left(\mathsf{neg}\left(3 \cdot 3\right)\right)\right), x\right), \left(x \cdot -2 - 3\right)\right)\right) \]

   12. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \left(\mathsf{neg}\left(3 \cdot 3\right)\right)\right), x\right), \left(x \cdot -2 - 3\right)\right)\right) \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \left(\mathsf{neg}\left(9\right)\right)\right), x\right), \left(x \cdot -2 - 3\right)\right)\right) \]

   14. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), -9\right), x\right), \left(x \cdot -2 - 3\right)\right)\right) \]

   15. sub-neg N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), -9\right), x\right), \left(x \cdot -2 + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right)\right) \]

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

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), -9\right), x\right), \mathsf{+.f64}\left(\left(x \cdot -2\right), \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right)\right) \]

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

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), -9\right), x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, -2\right), \left(\mathsf{neg}\left(\color{blue}{3}\right)\right)\right)\right)\right) \]

   18. metadata-eval 99.8%

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), -9\right), x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, -2\right), -3\right)\right)\right) \]

6. Applied egg-rr 99.8%

   \[\leadsto x \cdot \color{blue}{\frac{\left(\left(x \cdot x\right) \cdot 4 + -9\right) \cdot x}{x \cdot -2 + -3}} \]

7. Taylor expanded in x around 0

   \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{\left(-9 \cdot x\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, -2\right), -3\right)\right)\right) \]
8. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(x \cdot -9\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(x, -2\right)}, -3\right)\right)\right) \]

   2. *-lowering-*.f64 50.1%

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, -9\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(x, -2\right)}, -3\right)\right)\right) \]

9. Simplified 50.1%

   \[\leadsto x \cdot \frac{\color{blue}{x \cdot -9}}{x \cdot -2 + -3} \]

10. Taylor expanded in x around inf

    \[\leadsto \color{blue}{\frac{9}{2} \cdot x} \]
11. Step-by-step derivation

    1. *-commutative N/A

       \[\leadsto x \cdot \color{blue}{\frac{9}{2}} \]

    2. *-lowering-*.f64 3.1%

       \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{9}{2}}\right) \]

12. Simplified 3.1%

    \[\leadsto \color{blue}{x \cdot 4.5} \]
13. Add Preprocessing

Developer Target 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(x \cdot \left(3 - x \cdot 2\right)\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* x (* x (- 3.0 (* x 2.0)))))

C

double code(double x) {
	return x * (x * (3.0 - (x * 2.0)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x * (x * (3.0d0 - (x * 2.0d0)))
end function

Java

public static double code(double x) {
	return x * (x * (3.0 - (x * 2.0)));
}

Python

def code(x):
	return x * (x * (3.0 - (x * 2.0)))

Julia

function code(x)
	return Float64(x * Float64(x * Float64(3.0 - Float64(x * 2.0))))
end

MATLAB

function tmp = code(x)
	tmp = x * (x * (3.0 - (x * 2.0)));
end

Wolfram

code[x_] := N[(x * N[(x * N[(3.0 - N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024155 
(FPCore (x)
  :name "Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (* x (* x (- 3 (* x 2)))))

  (* (* x x) (- 3.0 (* x 2.0))))