Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2

Percentage Accurate: 99.8% → 99.8%

Time: 6.4s

Alternatives: 7

Speedup: 1.0×

• 33.8% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_] := N[(x * N[(-2.0 * N[(x * x), $MachinePrecision] + N[(x * 3.0), $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* 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around 0 99.9%

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

   1. fma-def 99.9%

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

   2. unpow2 99.9%

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

6. Simplified 99.9%

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

7. Final simplification 99.9%

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

Alternative 2: 98.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \lor \neg \left(x \leq 1.5\right):\\ \;\;\;\;x \cdot \left(x \cdot \left(x \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= x -1.5) (not (<= x 1.5))) (* x (* x (* x -2.0))) (* x (* x 3.0))))

C

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

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-1.5d0)) .or. (.not. (x <= 1.5d0))) then
        tmp = x * (x * (x * (-2.0d0)))
    else
        tmp = x * (x * 3.0d0)
    end if
    code = tmp
end function

Java

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

Python

def code(x):
	tmp = 0
	if (x <= -1.5) or not (x <= 1.5):
		tmp = x * (x * (x * -2.0))
	else:
		tmp = x * (x * 3.0)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_] := If[Or[LessEqual[x, -1.5], N[Not[LessEqual[x, 1.5]], $MachinePrecision]], N[(x * N[(x * N[(x * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(x * 3.0), $MachinePrecision]), $MachinePrecision]]

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. Step-by-step derivation

      1. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 99.9%

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

      1. unpow2 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*l* 99.9%

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

   6. Simplified 99.9%

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

   if -1.5 < x < 1.5

   1. Initial program 99.7%

      \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]
   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 97.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \lor \neg \left(x \leq 1.5\right):\\ \;\;\;\;x \cdot \left(x \cdot \left(x \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot 3\right)\\ \end{array} \]

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* 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 4: 63.3% 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. Step-by-step derivation

   1. associate-*l* 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around 0 63.4%

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

   1. unpow2 63.4%

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

6. Simplified 63.4%

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

7. Final simplification 63.4%

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

Alternative 5: 63.3% 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* 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around 0 63.5%

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

5. Final simplification 63.5%

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

Alternative 6: 43.6% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x):
	return x * x

Julia

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

MATLAB

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

Wolfram

code[x_] := N[(x * x), $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* 99.9%

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

3. Simplified 99.9%

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

   1. associate-*r* 99.8%

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

   2. flip-- 99.8%

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

   3. *-commutative 99.8%

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

   4. metadata-eval 99.8%

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

   5. cancel-sign-sub-inv 99.8%

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

   6. *-commutative 99.8%

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

   7. associate-*r/ 97.2%

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

5. Applied egg-rr 50.0%

   \[\leadsto \color{blue}{\frac{\left(x \cdot x\right) \cdot \left(9 + \left(x \cdot x\right) \cdot 4\right)}{\mathsf{fma}\left(x, 2, 3\right)}} \]
6. Step-by-step derivation

   1. associate-/l* 50.0%

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

   2. associate-*l* 50.0%

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

7. Simplified 50.0%

   \[\leadsto \color{blue}{\frac{x \cdot x}{\frac{\mathsf{fma}\left(x, 2, 3\right)}{9 + x \cdot \left(x \cdot 4\right)}}} \]
8. Step-by-step derivation

   1. div-inv 50.0%

      \[\leadsto \frac{x \cdot x}{\color{blue}{\mathsf{fma}\left(x, 2, 3\right) \cdot \frac{1}{9 + x \cdot \left(x \cdot 4\right)}}} \]

   2. times-frac 50.0%

      \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(x, 2, 3\right)} \cdot \frac{x}{\frac{1}{9 + x \cdot \left(x \cdot 4\right)}}} \]

   3. +-commutative 50.0%

      \[\leadsto \frac{x}{\mathsf{fma}\left(x, 2, 3\right)} \cdot \frac{x}{\frac{1}{\color{blue}{x \cdot \left(x \cdot 4\right) + 9}}} \]

   4. associate-*r* 50.0%

      \[\leadsto \frac{x}{\mathsf{fma}\left(x, 2, 3\right)} \cdot \frac{x}{\frac{1}{\color{blue}{\left(x \cdot x\right) \cdot 4} + 9}} \]

   5. *-commutative 50.0%

      \[\leadsto \frac{x}{\mathsf{fma}\left(x, 2, 3\right)} \cdot \frac{x}{\frac{1}{\color{blue}{4 \cdot \left(x \cdot x\right)} + 9}} \]

   6. metadata-eval 50.0%

      \[\leadsto \frac{x}{\mathsf{fma}\left(x, 2, 3\right)} \cdot \frac{x}{\frac{1}{\color{blue}{\left(2 \cdot 2\right)} \cdot \left(x \cdot x\right) + 9}} \]

   7. swap-sqr 50.0%

      \[\leadsto \frac{x}{\mathsf{fma}\left(x, 2, 3\right)} \cdot \frac{x}{\frac{1}{\color{blue}{\left(2 \cdot x\right) \cdot \left(2 \cdot x\right)} + 9}} \]

   8. count-2 50.0%

      \[\leadsto \frac{x}{\mathsf{fma}\left(x, 2, 3\right)} \cdot \frac{x}{\frac{1}{\left(2 \cdot x\right) \cdot \color{blue}{\left(x + x\right)} + 9}} \]

   9. count-2 50.0%

      \[\leadsto \frac{x}{\mathsf{fma}\left(x, 2, 3\right)} \cdot \frac{x}{\frac{1}{\color{blue}{\left(x + x\right)} \cdot \left(x + x\right) + 9}} \]

   10. flip-+ 0.0%

       \[\leadsto \frac{x}{\mathsf{fma}\left(x, 2, 3\right)} \cdot \frac{x}{\frac{1}{\left(x + x\right) \cdot \color{blue}{\frac{x \cdot x - x \cdot x}{x - x}} + 9}} \]

   11. +-inverses 0.0%

       \[\leadsto \frac{x}{\mathsf{fma}\left(x, 2, 3\right)} \cdot \frac{x}{\frac{1}{\left(x + x\right) \cdot \frac{x \cdot x - x \cdot x}{\color{blue}{0}} + 9}} \]

   12. +-inverses 0.0%

       \[\leadsto \frac{x}{\mathsf{fma}\left(x, 2, 3\right)} \cdot \frac{x}{\frac{1}{\left(x + x\right) \cdot \frac{x \cdot x - x \cdot x}{\color{blue}{x \cdot x - x \cdot x}} + 9}} \]

   13. associate-*r/ 0.0%

       \[\leadsto \frac{x}{\mathsf{fma}\left(x, 2, 3\right)} \cdot \frac{x}{\frac{1}{\color{blue}{\frac{\left(x + x\right) \cdot \left(x \cdot x - x \cdot x\right)}{x \cdot x - x \cdot x}} + 9}} \]

   14. +-inverses 0.0%

       \[\leadsto \frac{x}{\mathsf{fma}\left(x, 2, 3\right)} \cdot \frac{x}{\frac{1}{\frac{\left(x + x\right) \cdot \color{blue}{0}}{x \cdot x - x \cdot x} + 9}} \]

   15. +-inverses 0.0%

       \[\leadsto \frac{x}{\mathsf{fma}\left(x, 2, 3\right)} \cdot \frac{x}{\frac{1}{\frac{\left(x + x\right) \cdot \color{blue}{\left(x - x\right)}}{x \cdot x - x \cdot x} + 9}} \]

   16. difference-of-squares 0.0%

       \[\leadsto \frac{x}{\mathsf{fma}\left(x, 2, 3\right)} \cdot \frac{x}{\frac{1}{\frac{\color{blue}{x \cdot x - x \cdot x}}{x \cdot x - x \cdot x} + 9}} \]

   17. +-inverses 0.0%

       \[\leadsto \frac{x}{\mathsf{fma}\left(x, 2, 3\right)} \cdot \frac{x}{\frac{1}{\frac{x \cdot x - x \cdot x}{\color{blue}{0}} + 9}} \]

   18. +-inverses 0.0%

       \[\leadsto \frac{x}{\mathsf{fma}\left(x, 2, 3\right)} \cdot \frac{x}{\frac{1}{\frac{x \cdot x - x \cdot x}{\color{blue}{x - x}} + 9}} \]

   19. flip-+ 63.5%

       \[\leadsto \frac{x}{\mathsf{fma}\left(x, 2, 3\right)} \cdot \frac{x}{\frac{1}{\color{blue}{\left(x + x\right)} + 9}} \]

9. Applied egg-rr 63.5%

   \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(x, 2, 3\right)} \cdot \frac{x}{\frac{1}{\left(x + x\right) + 9}}} \]

10. Taylor expanded in x around inf 43.0%

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

    1. unpow2 43.0%

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

12. Simplified 43.0%

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

13. Final simplification 43.0%

    \[\leadsto x \cdot x \]

Alternative 7: 27.1% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x) :precision binary64 0.0)

C

double code(double x) {
	return 0.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 0.0d0
end function

Java

public static double code(double x) {
	return 0.0;
}

Python

def code(x):
	return 0.0

Julia

function code(x)
	return 0.0
end

MATLAB

function tmp = code(x)
	tmp = 0.0;
end

Wolfram

code[x_] := 0.0

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* 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around inf 74.9%

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

   1. unpow2 74.9%

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

   2. *-commutative 74.9%

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

   3. associate-*l* 74.9%

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

6. Simplified 74.9%

   \[\leadsto x \cdot \color{blue}{\left(x \cdot \left(x \cdot -2\right)\right)} \]
7. Step-by-step derivation

   1. add-sqr-sqrt 50.4%

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

   2. sqrt-unprod 47.1%

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

   3. associate-*r* 47.1%

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

   4. associate-*r* 47.1%

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

   5. swap-sqr 47.1%

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

   6. swap-sqr 47.1%

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

   7. metadata-eval 47.1%

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

   8. *-commutative 47.1%

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

   9. metadata-eval 47.1%

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

   10. swap-sqr 47.1%

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

   11. count-2 47.1%

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

   12. count-2 47.1%

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

   13. swap-sqr 47.1%

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

   14. sqrt-unprod 25.5%

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

   15. add-sqr-sqrt 25.9%

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

   16. flip-+ 0.0%

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

   17. +-inverses 0.0%

       \[\leadsto \left(x \cdot x\right) \cdot \frac{x \cdot x - x \cdot x}{\color{blue}{0}} \]

   18. +-inverses 0.0%

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

   19. associate-*r/ 0.0%

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

8. Applied egg-rr 0.0%

   \[\leadsto \color{blue}{\frac{x \cdot x}{0} - \frac{x \cdot x}{0}} \]

10. Simplified 26.4%

    \[\leadsto \color{blue}{0} \]

11. Final simplification 26.4%

    \[\leadsto 0 \]

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 2023279 
(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))))