Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2

Percentage Accurate: 99.8% → 99.8%

Time: 9.0s

Alternatives: 7

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

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

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%

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

   2. sub-neg 99.9%

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

   3. distribute-rgt-neg-in 99.9%

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

   4. metadata-eval 99.9%

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

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 2: 97.7% 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 99.8%

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

      1. associate-*l* 99.8%

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

      2. sub-neg 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. metadata-eval 99.8%

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

   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 inf 96.6%

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

      1. *-commutative 96.6%

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

      2. unpow2 96.6%

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

      3. associate-*r* 96.6%

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

   6. Simplified 96.6%

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

   if -1.5 < x < 1.5

   1. Initial program 99.8%

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

      1. associate-*l* 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. metadata-eval 99.9%

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

   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 98.8%

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

4. Final simplification 97.6%

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

Alternative 3: 98.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \lor \neg \left(x \leq 1.5\right):\\ \;\;\;\;x \cdot \left(x \cdot \left(x \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{0.3333333333333333}{x} + 0.2222222222222222}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= x -1.12) (not (<= x 1.5)))
   (* x (* x (* x -2.0)))
   (/ x (+ (/ 0.3333333333333333 x) 0.2222222222222222))))

C

double code(double x) {
	double tmp;
	if ((x <= -1.12) || !(x <= 1.5)) {
		tmp = x * (x * (x * -2.0));
	} else {
		tmp = x / ((0.3333333333333333 / x) + 0.2222222222222222);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-1.12d0)) .or. (.not. (x <= 1.5d0))) then
        tmp = x * (x * (x * (-2.0d0)))
    else
        tmp = x / ((0.3333333333333333d0 / x) + 0.2222222222222222d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x <= -1.12) || !(x <= 1.5)) {
		tmp = x * (x * (x * -2.0));
	} else {
		tmp = x / ((0.3333333333333333 / x) + 0.2222222222222222);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x <= -1.12) or not (x <= 1.5):
		tmp = x * (x * (x * -2.0))
	else:
		tmp = x / ((0.3333333333333333 / x) + 0.2222222222222222)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((x <= -1.12) || !(x <= 1.5))
		tmp = Float64(x * Float64(x * Float64(x * -2.0)));
	else
		tmp = Float64(x / Float64(Float64(0.3333333333333333 / x) + 0.2222222222222222));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x <= -1.12) || ~((x <= 1.5)))
		tmp = x * (x * (x * -2.0));
	else
		tmp = x / ((0.3333333333333333 / x) + 0.2222222222222222);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[x, -1.12], N[Not[LessEqual[x, 1.5]], $MachinePrecision]], N[(x * N[(x * N[(x * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(0.3333333333333333 / x), $MachinePrecision] + 0.2222222222222222), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1200000000000001 or 1.5 < x

   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%

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

      2. sub-neg 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. metadata-eval 99.8%

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

   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 inf 96.6%

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

      1. *-commutative 96.6%

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

      2. unpow2 96.6%

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

      3. associate-*r* 96.6%

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

   6. Simplified 96.6%

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

   if -1.1200000000000001 < x < 1.5

   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%

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

      2. sub-neg 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. metadata-eval 99.9%

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

   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. distribute-lft-in 99.9%

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

      2. +-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. distribute-lft-out 99.9%

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

      2. fma-udef 99.9%

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

      3. associate-*r* 99.8%

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

      4. remove-double-div 99.8%

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

      5. /-rgt-identity 99.8%

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

      6. associate-/l* 99.7%

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

      7. frac-2neg 99.7%

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

      8. clear-num 99.7%

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

      9. frac-times 99.8%

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

      10. fma-udef 99.8%

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

      11. distribute-neg-in 99.8%

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

      12. +-commutative 99.8%

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

      13. metadata-eval 99.8%

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

      14. distribute-rgt-neg-in 99.8%

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

      15. metadata-eval 99.8%

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

      16. metadata-eval 99.8%

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

   7. Applied egg-rr 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.8%

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

      3. associate-*r/ 99.8%

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

      4. metadata-eval 99.8%

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

   9. Simplified 99.8%

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

   10. Taylor expanded in x around 0 99.3%

       \[\leadsto \frac{x}{\color{blue}{0.2222222222222222 + 0.3333333333333333 \cdot \frac{1}{x}}} \]
   11. Step-by-step derivation

       1. +-commutative 99.3%

          \[\leadsto \frac{x}{\color{blue}{0.3333333333333333 \cdot \frac{1}{x} + 0.2222222222222222}} \]

       2. associate-*r/ 99.4%

          \[\leadsto \frac{x}{\color{blue}{\frac{0.3333333333333333 \cdot 1}{x}} + 0.2222222222222222} \]

       3. metadata-eval 99.4%

          \[\leadsto \frac{x}{\frac{\color{blue}{0.3333333333333333}}{x} + 0.2222222222222222} \]

   12. Simplified 99.4%

       \[\leadsto \frac{x}{\color{blue}{\frac{0.3333333333333333}{x} + 0.2222222222222222}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \lor \neg \left(x \leq 1.5\right):\\ \;\;\;\;x \cdot \left(x \cdot \left(x \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{0.3333333333333333}{x} + 0.2222222222222222}\\ \end{array} \]

Alternative 4: 98.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12:\\ \;\;\;\;\frac{x}{\frac{-0.5}{x \cdot x}}\\ \mathbf{elif}\;x \leq 1.5:\\ \;\;\;\;\frac{x}{\frac{0.3333333333333333}{x} + 0.2222222222222222}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \left(x \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -1.12)
   (/ x (/ -0.5 (* x x)))
   (if (<= x 1.5)
     (/ x (+ (/ 0.3333333333333333 x) 0.2222222222222222))
     (* x (* x (* x -2.0))))))

C

double code(double x) {
	double tmp;
	if (x <= -1.12) {
		tmp = x / (-0.5 / (x * x));
	} else if (x <= 1.5) {
		tmp = x / ((0.3333333333333333 / x) + 0.2222222222222222);
	} else {
		tmp = x * (x * (x * -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-1.12d0)) then
        tmp = x / ((-0.5d0) / (x * x))
    else if (x <= 1.5d0) then
        tmp = x / ((0.3333333333333333d0 / x) + 0.2222222222222222d0)
    else
        tmp = x * (x * (x * (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -1.12) {
		tmp = x / (-0.5 / (x * x));
	} else if (x <= 1.5) {
		tmp = x / ((0.3333333333333333 / x) + 0.2222222222222222);
	} else {
		tmp = x * (x * (x * -2.0));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -1.12:
		tmp = x / (-0.5 / (x * x))
	elif x <= 1.5:
		tmp = x / ((0.3333333333333333 / x) + 0.2222222222222222)
	else:
		tmp = x * (x * (x * -2.0))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -1.12)
		tmp = Float64(x / Float64(-0.5 / Float64(x * x)));
	elseif (x <= 1.5)
		tmp = Float64(x / Float64(Float64(0.3333333333333333 / x) + 0.2222222222222222));
	else
		tmp = Float64(x * Float64(x * Float64(x * -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -1.12)
		tmp = x / (-0.5 / (x * x));
	elseif (x <= 1.5)
		tmp = x / ((0.3333333333333333 / x) + 0.2222222222222222);
	else
		tmp = x * (x * (x * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -1.12], N[(x / N[(-0.5 / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5], N[(x / N[(N[(0.3333333333333333 / x), $MachinePrecision] + 0.2222222222222222), $MachinePrecision]), $MachinePrecision], N[(x * N[(x * N[(x * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1200000000000001

   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%

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

      2. sub-neg 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. metadata-eval 99.9%

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

   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. distribute-lft-in 99.9%

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

      2. +-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. distribute-lft-out 99.9%

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

      2. fma-udef 99.9%

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

      3. associate-*r* 99.9%

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

      4. remove-double-div 99.9%

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

      5. /-rgt-identity 99.9%

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

      6. associate-/l* 99.8%

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

      7. frac-2neg 99.8%

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

      8. clear-num 99.9%

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

      9. frac-times 99.8%

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

      10. fma-udef 99.8%

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

      11. distribute-neg-in 99.8%

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

      12. +-commutative 99.8%

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

      13. metadata-eval 99.8%

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

      14. distribute-rgt-neg-in 99.8%

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

      15. metadata-eval 99.8%

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

      16. metadata-eval 99.8%

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

   7. Applied egg-rr 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 100.0%

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

      3. associate-*r/ 100.0%

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

      4. metadata-eval 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in x around inf 97.9%

       \[\leadsto \frac{x}{\color{blue}{\frac{-0.5}{{x}^{2}}}} \]
   11. Step-by-step derivation

       1. unpow2 97.9%

          \[\leadsto \frac{x}{\frac{-0.5}{\color{blue}{x \cdot x}}} \]

   12. Simplified 97.9%

       \[\leadsto \frac{x}{\color{blue}{\frac{-0.5}{x \cdot x}}} \]

   if -1.1200000000000001 < x < 1.5

   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%

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

      2. sub-neg 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. metadata-eval 99.9%

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

   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. distribute-lft-in 99.9%

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

      2. +-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. distribute-lft-out 99.9%

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

      2. fma-udef 99.9%

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

      3. associate-*r* 99.8%

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

      4. remove-double-div 99.8%

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

      5. /-rgt-identity 99.8%

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

      6. associate-/l* 99.7%

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

      7. frac-2neg 99.7%

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

      8. clear-num 99.7%

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

      9. frac-times 99.8%

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

      10. fma-udef 99.8%

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

      11. distribute-neg-in 99.8%

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

      12. +-commutative 99.8%

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

      13. metadata-eval 99.8%

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

      14. distribute-rgt-neg-in 99.8%

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

      15. metadata-eval 99.8%

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

      16. metadata-eval 99.8%

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

   7. Applied egg-rr 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.8%

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

      3. associate-*r/ 99.8%

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

      4. metadata-eval 99.8%

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

   9. Simplified 99.8%

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

   10. Taylor expanded in x around 0 99.3%

       \[\leadsto \frac{x}{\color{blue}{0.2222222222222222 + 0.3333333333333333 \cdot \frac{1}{x}}} \]
   11. Step-by-step derivation

       1. +-commutative 99.3%

          \[\leadsto \frac{x}{\color{blue}{0.3333333333333333 \cdot \frac{1}{x} + 0.2222222222222222}} \]

       2. associate-*r/ 99.4%

          \[\leadsto \frac{x}{\color{blue}{\frac{0.3333333333333333 \cdot 1}{x}} + 0.2222222222222222} \]

       3. metadata-eval 99.4%

          \[\leadsto \frac{x}{\frac{\color{blue}{0.3333333333333333}}{x} + 0.2222222222222222} \]

   12. Simplified 99.4%

       \[\leadsto \frac{x}{\color{blue}{\frac{0.3333333333333333}{x} + 0.2222222222222222}} \]

   if 1.5 < x

   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%

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

      2. sub-neg 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. metadata-eval 99.8%

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

   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 inf 95.5%

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

      1. *-commutative 95.5%

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

      2. unpow2 95.5%

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

      3. associate-*r* 95.5%

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

   6. Simplified 95.5%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12:\\ \;\;\;\;\frac{x}{\frac{-0.5}{x \cdot x}}\\ \mathbf{elif}\;x \leq 1.5:\\ \;\;\;\;\frac{x}{\frac{0.3333333333333333}{x} + 0.2222222222222222}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \left(x \cdot -2\right)\right)\\ \end{array} \]

Alternative 5: 62.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   2. sub-neg 99.9%

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

   3. distribute-rgt-neg-in 99.9%

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

   4. metadata-eval 99.9%

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

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 58.5%

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

   1. unpow2 58.5%

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

6. Simplified 58.5%

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

7. Final simplification 58.5%

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

Alternative 6: 62.5% 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%

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

   2. sub-neg 99.9%

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

   3. distribute-rgt-neg-in 99.9%

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

   4. metadata-eval 99.9%

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

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 58.5%

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

5. Final simplification 58.5%

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

Alternative 7: 3.2% 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* 99.9%

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

   2. sub-neg 99.9%

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

   3. distribute-rgt-neg-in 99.9%

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

   4. metadata-eval 99.9%

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

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. distribute-lft-in 99.8%

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

   2. +-commutative 99.8%

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

5. Applied egg-rr 99.8%

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

   1. distribute-lft-out 99.9%

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

   2. fma-udef 99.9%

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

   3. associate-*r* 99.8%

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

   4. remove-double-div 99.8%

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

   5. /-rgt-identity 99.8%

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

   6. associate-/l* 99.7%

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

   7. frac-2neg 99.7%

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

   8. clear-num 99.7%

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

   9. frac-times 99.8%

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

   10. fma-udef 99.8%

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

   11. distribute-neg-in 99.8%

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

   12. +-commutative 99.8%

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

   13. metadata-eval 99.8%

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

   14. distribute-rgt-neg-in 99.8%

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

   15. metadata-eval 99.8%

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

   16. metadata-eval 99.8%

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

7. Applied egg-rr 99.8%

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

   1. *-commutative 99.8%

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

   2. associate-/l* 99.8%

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

   3. associate-*r/ 99.8%

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

   4. metadata-eval 99.8%

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

9. Simplified 99.8%

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

10. Taylor expanded in x around 0 46.0%

    \[\leadsto \frac{x}{\color{blue}{0.2222222222222222 + 0.3333333333333333 \cdot \frac{1}{x}}} \]
11. Step-by-step derivation

    1. +-commutative 46.0%

       \[\leadsto \frac{x}{\color{blue}{0.3333333333333333 \cdot \frac{1}{x} + 0.2222222222222222}} \]

    2. associate-*r/ 46.1%

       \[\leadsto \frac{x}{\color{blue}{\frac{0.3333333333333333 \cdot 1}{x}} + 0.2222222222222222} \]

    3. metadata-eval 46.1%

       \[\leadsto \frac{x}{\frac{\color{blue}{0.3333333333333333}}{x} + 0.2222222222222222} \]

12. Simplified 46.1%

    \[\leadsto \frac{x}{\color{blue}{\frac{0.3333333333333333}{x} + 0.2222222222222222}} \]

13. Taylor expanded in x around inf 3.1%

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

    1. *-commutative 3.1%

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

15. Simplified 3.1%

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

16. Final simplification 3.1%

    \[\leadsto x \cdot 4.5 \]

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 2023297 
(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))))