Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2

Percentage Accurate: 99.8% → 99.8%

Time: 7.9s

Alternatives: 5

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. Final simplification 99.8%

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

Alternative 2: 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* 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 3: 62.0% 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* 99.8%

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

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 60.0%

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

6. Final simplification 60.0%

   \[\leadsto x \cdot \left(x \cdot 3\right) \]
7. Add Preprocessing

Alternative 4: 2.5% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ -6.75 \end{array} \]

FPCore

(FPCore (x) :precision binary64 -6.75)

C

double code(double x) {
	return -6.75;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = -6.75d0
end function

Java

public static double code(double x) {
	return -6.75;
}

Python

def code(x):
	return -6.75

Julia

function code(x)
	return -6.75
end

MATLAB

function tmp = code(x)
	tmp = -6.75;
end

Wolfram

code[x_] := -6.75

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* 99.8%

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

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 99.8%

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

   2. flip3-- 74.0%

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

   3. associate-*l/ 71.5%

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

   4. metadata-eval 71.5%

      \[\leadsto x \cdot \frac{\left(\color{blue}{27} - {\left(x \cdot 2\right)}^{3}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   5. add-sqr-sqrt 39.0%

      \[\leadsto x \cdot \frac{\left(27 - {\color{blue}{\left(\sqrt{x \cdot 2} \cdot \sqrt{x \cdot 2}\right)}}^{3}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   6. sqrt-unprod 63.2%

      \[\leadsto x \cdot \frac{\left(27 - {\color{blue}{\left(\sqrt{\left(x \cdot 2\right) \cdot \left(x \cdot 2\right)}\right)}}^{3}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   7. swap-sqr 63.2%

      \[\leadsto x \cdot \frac{\left(27 - {\left(\sqrt{\color{blue}{\left(x \cdot x\right) \cdot \left(2 \cdot 2\right)}}\right)}^{3}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   8. metadata-eval 63.2%

      \[\leadsto x \cdot \frac{\left(27 - {\left(\sqrt{\left(x \cdot x\right) \cdot \color{blue}{4}}\right)}^{3}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   9. metadata-eval 63.2%

      \[\leadsto x \cdot \frac{\left(27 - {\left(\sqrt{\left(x \cdot x\right) \cdot \color{blue}{\left(-2 \cdot -2\right)}}\right)}^{3}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   10. swap-sqr 63.2%

       \[\leadsto x \cdot \frac{\left(27 - {\left(\sqrt{\color{blue}{\left(x \cdot -2\right) \cdot \left(x \cdot -2\right)}}\right)}^{3}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   11. sqrt-unprod 24.0%

       \[\leadsto x \cdot \frac{\left(27 - {\color{blue}{\left(\sqrt{x \cdot -2} \cdot \sqrt{x \cdot -2}\right)}}^{3}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   12. add-sqr-sqrt 48.3%

       \[\leadsto x \cdot \frac{\left(27 - {\color{blue}{\left(x \cdot -2\right)}}^{3}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   13. unpow-prod-down 48.3%

       \[\leadsto x \cdot \frac{\left(27 - \color{blue}{{x}^{3} \cdot {-2}^{3}}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   14. metadata-eval 48.3%

       \[\leadsto x \cdot \frac{\left(27 - {x}^{3} \cdot \color{blue}{-8}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   15. metadata-eval 48.3%

       \[\leadsto x \cdot \frac{\left(27 - {x}^{3} \cdot -8\right) \cdot x}{\color{blue}{9} + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   16. distribute-rgt-out 48.3%

       \[\leadsto x \cdot \frac{\left(27 - {x}^{3} \cdot -8\right) \cdot x}{9 + \color{blue}{\left(x \cdot 2\right) \cdot \left(x \cdot 2 + 3\right)}} \]

6. Applied egg-rr 70.2%

   \[\leadsto x \cdot \color{blue}{\frac{\left(27 - {x}^{3} \cdot -8\right) \cdot x}{9 + \left(x \cdot 2\right) \cdot \mathsf{fma}\left(x, -2, 3\right)}} \]

7. Taylor expanded in x around 0 49.4%

   \[\leadsto x \cdot \frac{\color{blue}{27 \cdot x}}{9 + \left(x \cdot 2\right) \cdot \mathsf{fma}\left(x, -2, 3\right)} \]
8. Step-by-step derivation

   1. *-commutative 49.4%

      \[\leadsto x \cdot \frac{\color{blue}{x \cdot 27}}{9 + \left(x \cdot 2\right) \cdot \mathsf{fma}\left(x, -2, 3\right)} \]

9. Simplified 49.4%

   \[\leadsto x \cdot \frac{\color{blue}{x \cdot 27}}{9 + \left(x \cdot 2\right) \cdot \mathsf{fma}\left(x, -2, 3\right)} \]

10. Taylor expanded in x around inf 2.7%

    \[\leadsto \color{blue}{-6.75} \]

11. Final simplification 2.7%

    \[\leadsto -6.75 \]
12. Add Preprocessing

Alternative 5: 3.3% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ 6.75 \end{array} \]

FPCore

(FPCore (x) :precision binary64 6.75)

C

double code(double x) {
	return 6.75;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 6.75d0
end function

Java

public static double code(double x) {
	return 6.75;
}

Python

def code(x):
	return 6.75

Julia

function code(x)
	return 6.75
end

MATLAB

function tmp = code(x)
	tmp = 6.75;
end

Wolfram

code[x_] := 6.75

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* 99.8%

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

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 99.8%

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

   2. flip3-- 74.0%

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

   3. associate-*l/ 71.5%

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

   4. metadata-eval 71.5%

      \[\leadsto x \cdot \frac{\left(\color{blue}{27} - {\left(x \cdot 2\right)}^{3}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   5. add-sqr-sqrt 39.0%

      \[\leadsto x \cdot \frac{\left(27 - {\color{blue}{\left(\sqrt{x \cdot 2} \cdot \sqrt{x \cdot 2}\right)}}^{3}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   6. sqrt-unprod 63.2%

      \[\leadsto x \cdot \frac{\left(27 - {\color{blue}{\left(\sqrt{\left(x \cdot 2\right) \cdot \left(x \cdot 2\right)}\right)}}^{3}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   7. swap-sqr 63.2%

      \[\leadsto x \cdot \frac{\left(27 - {\left(\sqrt{\color{blue}{\left(x \cdot x\right) \cdot \left(2 \cdot 2\right)}}\right)}^{3}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   8. metadata-eval 63.2%

      \[\leadsto x \cdot \frac{\left(27 - {\left(\sqrt{\left(x \cdot x\right) \cdot \color{blue}{4}}\right)}^{3}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   9. metadata-eval 63.2%

      \[\leadsto x \cdot \frac{\left(27 - {\left(\sqrt{\left(x \cdot x\right) \cdot \color{blue}{\left(-2 \cdot -2\right)}}\right)}^{3}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   10. swap-sqr 63.2%

       \[\leadsto x \cdot \frac{\left(27 - {\left(\sqrt{\color{blue}{\left(x \cdot -2\right) \cdot \left(x \cdot -2\right)}}\right)}^{3}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   11. sqrt-unprod 24.0%

       \[\leadsto x \cdot \frac{\left(27 - {\color{blue}{\left(\sqrt{x \cdot -2} \cdot \sqrt{x \cdot -2}\right)}}^{3}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   12. add-sqr-sqrt 48.3%

       \[\leadsto x \cdot \frac{\left(27 - {\color{blue}{\left(x \cdot -2\right)}}^{3}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   13. unpow-prod-down 48.3%

       \[\leadsto x \cdot \frac{\left(27 - \color{blue}{{x}^{3} \cdot {-2}^{3}}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   14. metadata-eval 48.3%

       \[\leadsto x \cdot \frac{\left(27 - {x}^{3} \cdot \color{blue}{-8}\right) \cdot x}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   15. metadata-eval 48.3%

       \[\leadsto x \cdot \frac{\left(27 - {x}^{3} \cdot -8\right) \cdot x}{\color{blue}{9} + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) + 3 \cdot \left(x \cdot 2\right)\right)} \]

   16. distribute-rgt-out 48.3%

       \[\leadsto x \cdot \frac{\left(27 - {x}^{3} \cdot -8\right) \cdot x}{9 + \color{blue}{\left(x \cdot 2\right) \cdot \left(x \cdot 2 + 3\right)}} \]

6. Applied egg-rr 70.2%

   \[\leadsto x \cdot \color{blue}{\frac{\left(27 - {x}^{3} \cdot -8\right) \cdot x}{9 + \left(x \cdot 2\right) \cdot \mathsf{fma}\left(x, -2, 3\right)}} \]

7. Taylor expanded in x around 0 49.4%

   \[\leadsto x \cdot \frac{\color{blue}{27 \cdot x}}{9 + \left(x \cdot 2\right) \cdot \mathsf{fma}\left(x, -2, 3\right)} \]
8. Step-by-step derivation

   1. *-commutative 49.4%

      \[\leadsto x \cdot \frac{\color{blue}{x \cdot 27}}{9 + \left(x \cdot 2\right) \cdot \mathsf{fma}\left(x, -2, 3\right)} \]

9. Simplified 49.4%

   \[\leadsto x \cdot \frac{\color{blue}{x \cdot 27}}{9 + \left(x \cdot 2\right) \cdot \mathsf{fma}\left(x, -2, 3\right)} \]

10. Taylor expanded in x around inf 2.7%

    \[\leadsto x \cdot \color{blue}{\frac{-6.75}{x}} \]
11. Step-by-step derivation

    1. add-sqr-sqrt 0.0%

       \[\leadsto \color{blue}{\sqrt{x \cdot \frac{-6.75}{x}} \cdot \sqrt{x \cdot \frac{-6.75}{x}}} \]

    2. sqrt-unprod 3.1%

       \[\leadsto \color{blue}{\sqrt{\left(x \cdot \frac{-6.75}{x}\right) \cdot \left(x \cdot \frac{-6.75}{x}\right)}} \]

    3. pow2 3.1%

       \[\leadsto \sqrt{\color{blue}{{\left(x \cdot \frac{-6.75}{x}\right)}^{2}}} \]

12. Applied egg-rr 3.1%

    \[\leadsto \color{blue}{\sqrt{{\left(x \cdot \frac{-6.75}{x}\right)}^{2}}} \]
13. Step-by-step derivation

    1. unpow2 3.1%

       \[\leadsto \sqrt{\color{blue}{\left(x \cdot \frac{-6.75}{x}\right) \cdot \left(x \cdot \frac{-6.75}{x}\right)}} \]

    2. rem-sqrt-square 3.1%

       \[\leadsto \color{blue}{\left|x \cdot \frac{-6.75}{x}\right|} \]

    3. associate-*r/ 3.1%

       \[\leadsto \left|\color{blue}{\frac{x \cdot -6.75}{x}}\right| \]

    4. /-rgt-identity 3.1%

       \[\leadsto \left|\frac{\color{blue}{\frac{x \cdot -6.75}{1}}}{x}\right| \]

    5. associate-/l* 3.1%

       \[\leadsto \left|\frac{\color{blue}{\frac{x}{\frac{1}{-6.75}}}}{x}\right| \]

    6. metadata-eval 3.1%

       \[\leadsto \left|\frac{\frac{x}{\color{blue}{-0.14814814814814814}}}{x}\right| \]

    7. associate-/r* 3.1%

       \[\leadsto \left|\color{blue}{\frac{x}{-0.14814814814814814 \cdot x}}\right| \]

    8. associate-/l/ 3.1%

       \[\leadsto \left|\color{blue}{\frac{\frac{x}{x}}{-0.14814814814814814}}\right| \]

    9. *-inverses 3.1%

       \[\leadsto \left|\frac{\color{blue}{1}}{-0.14814814814814814}\right| \]

    10. metadata-eval 3.1%

        \[\leadsto \left|\color{blue}{-6.75}\right| \]

    11. metadata-eval 3.1%

        \[\leadsto \color{blue}{6.75} \]

14. Simplified 3.1%

    \[\leadsto \color{blue}{6.75} \]

15. Final simplification 3.1%

    \[\leadsto 6.75 \]
16. Add Preprocessing

Developer target: 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 2024034 
(FPCore (x)
  :name "Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2"
  :precision binary64

  :herbie-target
  (* x (* x (- 3.0 (* x 2.0))))

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