Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2

Percentage Accurate: 99.8% → 99.8%

Time: 6.6s

Alternatives: 6

Speedup: 1.0×

• 33.4% 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. Final simplification 99.8%

   \[\leadsto \left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]

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. Final simplification 99.8%

   \[\leadsto x \cdot \left(x \cdot \left(3 - x \cdot 2\right)\right) \]

Alternative 3: 62.3% accurate, 1.5× speedup

Math

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

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(Float64(x * x) * Float64(-(-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. 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. Step-by-step derivation

   1. flip-- 99.8%

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

   2. clear-num 99.7%

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

   3. associate-*r/ 99.6%

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

   4. *-commutative 99.6%

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

   5. *-un-lft-identity 99.6%

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

   6. *-commutative 99.6%

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

   7. metadata-eval 99.6%

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

   8. cancel-sign-sub-inv 99.6%

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

   9. *-commutative 99.6%

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

   10. add-sqr-sqrt 49.0%

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

   11. sqrt-unprod 65.0%

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

   12. swap-sqr 65.0%

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

   13. metadata-eval 65.0%

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

   14. metadata-eval 65.0%

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

   15. swap-sqr 65.0%

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

   16. sqrt-unprod 25.3%

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

   17. add-sqr-sqrt 50.5%

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

   18. *-un-lft-identity 50.5%

       \[\leadsto x \cdot \frac{x}{\frac{\color{blue}{1 \cdot \left(3 - x \cdot 2\right)}}{3 \cdot 3 - \left(x \cdot 2\right) \cdot \left(x \cdot 2\right)}} \]

   19. associate-/l* 50.5%

       \[\leadsto x \cdot \frac{x}{\color{blue}{\frac{1}{\frac{3 \cdot 3 - \left(x \cdot 2\right) \cdot \left(x \cdot 2\right)}{3 - x \cdot 2}}}} \]

5. Applied egg-rr 99.6%

   \[\leadsto x \cdot \color{blue}{\frac{x}{\frac{1}{\mathsf{fma}\left(x, -2, 3\right)}}} \]
6. Step-by-step derivation

   1. clear-num 99.7%

      \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{\frac{1}{\mathsf{fma}\left(x, -2, 3\right)}}{x}}} \]

   2. un-div-inv 99.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{\frac{1}{\mathsf{fma}\left(x, -2, 3\right)}}{x}}} \]

7. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\frac{x}{\frac{\frac{1}{\mathsf{fma}\left(x, -2, 3\right)}}{x}}} \]

8. Taylor expanded in x around 0 61.0%

   \[\leadsto \frac{x}{\color{blue}{\frac{0.3333333333333333}{x}}} \]
9. Step-by-step derivation

   1. clear-num 60.3%

      \[\leadsto \color{blue}{\frac{1}{\frac{\frac{0.3333333333333333}{x}}{x}}} \]

   2. frac-2neg 60.3%

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

   3. associate-/l/ 60.3%

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

   4. associate-/r/ 61.1%

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

   5. metadata-eval 61.1%

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

   6. metadata-eval 61.1%

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

10. Applied egg-rr 61.1%

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

11. Final simplification 61.1%

    \[\leadsto \left(x \cdot x\right) \cdot \left(--3\right) \]

Alternative 4: 62.3% 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. Taylor expanded in x around 0 61.1%

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

5. Final simplification 61.1%

   \[\leadsto x \cdot \left(x \cdot 3\right) \]

Alternative 5: 6.2% 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* 99.8%

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

3. Simplified 99.8%

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

5. Applied egg-rr 95.2%

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

6. Taylor expanded in x around 0 74.7%

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

   1. *-commutative 74.7%

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

8. Simplified 74.7%

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

9. Taylor expanded in x around inf 6.0%

   \[\leadsto \color{blue}{-4.5 \cdot x} \]
10. Step-by-step derivation

    1. *-commutative 6.0%

       \[\leadsto \color{blue}{x \cdot -4.5} \]

11. Simplified 6.0%

    \[\leadsto \color{blue}{x \cdot -4.5} \]

12. Final simplification 6.0%

    \[\leadsto x \cdot -4.5 \]

Alternative 6: 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%

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

5. Applied egg-rr 95.2%

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

6. Taylor expanded in x around 0 74.7%

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

   1. *-commutative 74.7%

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

8. Simplified 74.7%

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

9. Taylor expanded in x around inf 4.5%

   \[\leadsto \color{blue}{-4.5 \cdot x - 6.75} \]

10. Taylor expanded in x around 0 2.6%

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

11. Final simplification 2.6%

    \[\leadsto -6.75 \]

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 2023301 
(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))))