Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2

Percentage Accurate: 99.8% → 99.8%

Time: 8.4s

Alternatives: 8

Speedup: 1.0×

• 32.8% 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, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-*l* N/A

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

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

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

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

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

   4. sub-neg N/A

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

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

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

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

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

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

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

   8. metadata-eval 99.8%

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

3. Simplified 99.8%

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

   1. distribute-rgt-in N/A

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

   2. fma-define N/A

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

   3. metadata-eval N/A

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

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

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

   5. distribute-lft-neg-out N/A

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

   6. fmm-undef N/A

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

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

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

   8. *-commutative N/A

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

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

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

   10. *-commutative N/A

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

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

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

   12. *-lowering-*.f64 99.8%

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

6. Applied egg-rr 99.8%

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

Alternative 2: 97.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1.5 or 1.5 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 99.2%

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

   5. Simplified 99.2%

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

   if -1.5 < x < 1.5

   1. Initial program 99.6%

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

      1. associate-*l* N/A

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

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

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

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

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

      4. sub-neg N/A

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

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

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

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

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

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

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

      8. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 97.1%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5:\\ \;\;\;\;\left(x \cdot -2\right) \cdot \left(x \cdot x\right)\\ \mathbf{elif}\;x \leq 1.5:\\ \;\;\;\;x \cdot \left(x \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot -2\right) \cdot \left(x \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{x}{\frac{-0.5}{x}}\\ \mathbf{if}\;x \leq -1.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.5:\\ \;\;\;\;x \cdot \left(x \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* x (/ x (/ -0.5 x)))))
   (if (<= x -1.5) t_0 (if (<= x 1.5) (* x (* x 3.0)) t_0))))

C

double code(double x) {
	double t_0 = x * (x / (-0.5 / x));
	double tmp;
	if (x <= -1.5) {
		tmp = t_0;
	} else if (x <= 1.5) {
		tmp = x * (x * 3.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (x / ((-0.5d0) / x))
    if (x <= (-1.5d0)) then
        tmp = t_0
    else if (x <= 1.5d0) then
        tmp = x * (x * 3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = x * (x / (-0.5 / x));
	double tmp;
	if (x <= -1.5) {
		tmp = t_0;
	} else if (x <= 1.5) {
		tmp = x * (x * 3.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x):
	t_0 = x * (x / (-0.5 / x))
	tmp = 0
	if x <= -1.5:
		tmp = t_0
	elif x <= 1.5:
		tmp = x * (x * 3.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x)
	t_0 = Float64(x * Float64(x / Float64(-0.5 / x)))
	tmp = 0.0
	if (x <= -1.5)
		tmp = t_0;
	elseif (x <= 1.5)
		tmp = Float64(x * Float64(x * 3.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = x * (x / (-0.5 / x));
	tmp = 0.0;
	if (x <= -1.5)
		tmp = t_0;
	elseif (x <= 1.5)
		tmp = x * (x * 3.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(x * N[(x / N[(-0.5 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.5], t$95$0, If[LessEqual[x, 1.5], N[(x * N[(x * 3.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5 or 1.5 < x

   1. Initial program 99.9%

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

      1. associate-*l* N/A

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

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

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

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

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

      4. sub-neg N/A

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

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

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

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

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

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

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. distribute-rgt-in N/A

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

      2. fma-define N/A

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

      3. metadata-eval N/A

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

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

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

      5. distribute-lft-neg-out N/A

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

      6. fmm-undef N/A

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

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

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

      8. *-commutative N/A

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

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

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

      10. *-commutative N/A

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

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

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

      12. *-lowering-*.f64 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. distribute-lft-out-- N/A

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

      2. *-commutative N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-commutative N/A

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

      6. /-rgt-identity N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(x \cdot \frac{3 + x \cdot -2}{\color{blue}{1}}\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(x \cdot \frac{3 + x \cdot -2}{\mathsf{neg}\left(-1\right)}\right)\right) \]

      8. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(x \cdot \frac{1}{\color{blue}{\frac{\mathsf{neg}\left(-1\right)}{3 + x \cdot -2}}}\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(x \cdot \frac{1}{\frac{1}{\color{blue}{3} + x \cdot -2}}\right)\right) \]

      10. un-div-inv N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{x}{\color{blue}{\frac{1}{3 + x \cdot -2}}}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{3 + x \cdot -2}\right)}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(x, \left(\frac{\mathsf{neg}\left(-1\right)}{\color{blue}{3} + x \cdot -2}\right)\right)\right) \]

      13. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(x, \left(\frac{\mathsf{neg}\left(-1\right)}{\mathsf{neg}\left(\left(\mathsf{neg}\left(\left(3 + x \cdot -2\right)\right)\right)\right)}\right)\right)\right) \]

      14. frac-2neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(x, \left(\frac{-1}{\color{blue}{\mathsf{neg}\left(\left(3 + x \cdot -2\right)\right)}}\right)\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(-1, \color{blue}{\left(\mathsf{neg}\left(\left(3 + x \cdot -2\right)\right)\right)}\right)\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(-1, \left(\mathsf{neg}\left(\left(x \cdot -2 + 3\right)\right)\right)\right)\right)\right) \]

      17. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(-1, \left(\left(\mathsf{neg}\left(x \cdot -2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right)\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(-1, \left(\left(\mathsf{neg}\left(x \cdot \left(\mathsf{neg}\left(2\right)\right)\right)\right) + \left(\mathsf{neg}\left(3\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(-1, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x \cdot 2\right)\right)\right)\right) + \left(\mathsf{neg}\left(3\right)\right)\right)\right)\right)\right) \]

      20. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(-1, \left(x \cdot 2 + \left(\mathsf{neg}\left(\color{blue}{3}\right)\right)\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(-1, \left(x \cdot 2 + -3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(\left(x \cdot 2\right), \color{blue}{-3}\right)\right)\right)\right) \]

      23. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), -3\right)\right)\right)\right) \]

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{\frac{-1}{2}}{x}\right)}\right)\right) \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 99.2%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\frac{-1}{2}, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 99.2%

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

   if -1.5 < x < 1.5

   1. Initial program 99.6%

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

      1. associate-*l* N/A

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

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

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

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

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

      4. sub-neg N/A

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

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

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

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

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

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

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

      8. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 97.1%

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

Alternative 4: 75.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.5:\\ \;\;\;\;x \cdot \left(x \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-0.3333333333333333}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 1.5) (* x (* x 3.0)) (/ x (/ -0.3333333333333333 x))))

C

double code(double x) {
	double tmp;
	if (x <= 1.5) {
		tmp = x * (x * 3.0);
	} else {
		tmp = x / (-0.3333333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 1.5d0) then
        tmp = x * (x * 3.0d0)
    else
        tmp = x / ((-0.3333333333333333d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 1.5) {
		tmp = x * (x * 3.0);
	} else {
		tmp = x / (-0.3333333333333333 / x);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.5:
		tmp = x * (x * 3.0)
	else:
		tmp = x / (-0.3333333333333333 / x)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.5)
		tmp = Float64(x * Float64(x * 3.0));
	else
		tmp = Float64(x / Float64(-0.3333333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 1.5)
		tmp = x * (x * 3.0);
	else
		tmp = x / (-0.3333333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 1.5], N[(x * N[(x * 3.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(-0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if 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* N/A

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

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

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

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

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

      4. sub-neg N/A

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

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

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

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

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

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

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 85.0%

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

   if 1.5 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 0.2%

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

      1. metadata-eval N/A

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

      2. div-inv N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

         \[\leadsto \frac{x}{\color{blue}{\frac{\frac{1}{3}}{x}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{\frac{1}{3}}{x}\right)}\right) \]

      7. /-lowering-/.f64 0.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\frac{1}{3}, \color{blue}{x}\right)\right) \]

   7. Applied egg-rr 0.2%

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

      1. frac-2neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{\mathsf{neg}\left(\frac{1}{3}\right)}{\color{blue}{\mathsf{neg}\left(x\right)}}\right)\right) \]

      2. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \color{blue}{\frac{1}{\mathsf{neg}\left(x\right)}}\right)\right) \]

      3. inv-pow N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot {\left(\mathsf{neg}\left(x\right)\right)}^{\color{blue}{-1}}\right)\right) \]

      4. sqr-pow N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \left({\left(\mathsf{neg}\left(x\right)\right)}^{\left(\frac{-1}{2}\right)} \cdot \color{blue}{{\left(\mathsf{neg}\left(x\right)\right)}^{\left(\frac{-1}{2}\right)}}\right)\right)\right) \]

      5. pow-prod-down N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot {\left(\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(x\right)\right)\right)}^{\color{blue}{\left(\frac{-1}{2}\right)}}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot {\left(\mathsf{neg}\left(x \cdot \left(\mathsf{neg}\left(x\right)\right)\right)\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot {\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x \cdot x\right)\right)\right)\right)}^{\left(\frac{-1}{2}\right)}\right)\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot {\left(x \cdot x\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)}\right)\right) \]

      9. pow-prod-down N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \left({x}^{\left(\frac{-1}{2}\right)} \cdot \color{blue}{{x}^{\left(\frac{-1}{2}\right)}}\right)\right)\right) \]

      10. sqr-pow N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot {x}^{\color{blue}{-1}}\right)\right) \]

      11. inv-pow N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \frac{1}{\color{blue}{x}}\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \frac{1}{\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)}\right)\right) \]

      13. div-inv N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{\mathsf{neg}\left(\frac{1}{3}\right)}{\color{blue}{\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)}}\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{\mathsf{neg}\left(\frac{1}{3}\right)}{x}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right), \color{blue}{x}\right)\right) \]

      16. metadata-eval 61.8%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\frac{-1}{3}, x\right)\right) \]

   9. Applied egg-rr 61.8%

      \[\leadsto \frac{x}{\color{blue}{\frac{-0.3333333333333333}{x}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 64.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.5:\\ \;\;\;\;x \cdot \left(x \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;-6.75 - x \cdot 4.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 1.5) (* x (* x 3.0)) (- -6.75 (* x 4.5))))

C

double code(double x) {
	double tmp;
	if (x <= 1.5) {
		tmp = x * (x * 3.0);
	} else {
		tmp = -6.75 - (x * 4.5);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 1.5d0) then
        tmp = x * (x * 3.0d0)
    else
        tmp = (-6.75d0) - (x * 4.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 1.5) {
		tmp = x * (x * 3.0);
	} else {
		tmp = -6.75 - (x * 4.5);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.5:
		tmp = x * (x * 3.0)
	else:
		tmp = -6.75 - (x * 4.5)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.5)
		tmp = Float64(x * Float64(x * 3.0));
	else
		tmp = Float64(-6.75 - Float64(x * 4.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 1.5)
		tmp = x * (x * 3.0);
	else
		tmp = -6.75 - (x * 4.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 1.5], N[(x * N[(x * 3.0), $MachinePrecision]), $MachinePrecision], N[(-6.75 - N[(x * 4.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if 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* N/A

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

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

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

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

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

      4. sub-neg N/A

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

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

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

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

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

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

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 85.0%

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

   if 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* N/A

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

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

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

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

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

      4. sub-neg N/A

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

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

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

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

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

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

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   6. Applied egg-rr 0.2%

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

   7. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 60.7%

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

   9. Simplified 60.7%

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

   10. Taylor expanded in x around inf

       \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\frac{9}{2} + \frac{27}{4} \cdot \frac{1}{x}\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(x \cdot \left(\frac{9}{2} + \frac{27}{4} \cdot \frac{1}{x}\right)\right) \]

       2. distribute-rgt-in N/A

          \[\leadsto \mathsf{neg}\left(\left(\frac{9}{2} \cdot x + \left(\frac{27}{4} \cdot \frac{1}{x}\right) \cdot x\right)\right) \]

       3. distribute-neg-in N/A

          \[\leadsto \left(\mathsf{neg}\left(\frac{9}{2} \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\frac{27}{4} \cdot \frac{1}{x}\right) \cdot x\right)\right)} \]

       4. +-commutative N/A

          \[\leadsto \left(\mathsf{neg}\left(\left(\frac{27}{4} \cdot \frac{1}{x}\right) \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{9}{2} \cdot x\right)\right)} \]

       5. sub-neg N/A

          \[\leadsto \left(\mathsf{neg}\left(\left(\frac{27}{4} \cdot \frac{1}{x}\right) \cdot x\right)\right) - \color{blue}{\frac{9}{2} \cdot x} \]

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

          \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(\frac{27}{4} \cdot \frac{1}{x}\right) \cdot x\right)\right), \color{blue}{\left(\frac{9}{2} \cdot x\right)}\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\frac{27}{4} \cdot \left(\frac{1}{x} \cdot x\right)\right)\right), \left(\frac{9}{2} \cdot x\right)\right) \]

       8. lft-mult-inverse N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\frac{27}{4} \cdot 1\right)\right), \left(\frac{9}{2} \cdot x\right)\right) \]

       9. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\frac{27}{4}\right)\right), \left(\frac{9}{2} \cdot x\right)\right) \]

       10. metadata-eval N/A

           \[\leadsto \mathsf{\_.f64}\left(\frac{-27}{4}, \left(\color{blue}{\frac{9}{2}} \cdot x\right)\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{\_.f64}\left(\frac{-27}{4}, \left(x \cdot \color{blue}{\frac{9}{2}}\right)\right) \]

       12. *-lowering-*.f64 6.8%

           \[\leadsto \mathsf{\_.f64}\left(\frac{-27}{4}, \mathsf{*.f64}\left(x, \color{blue}{\frac{9}{2}}\right)\right) \]

   12. Simplified 6.8%

       \[\leadsto \color{blue}{-6.75 - x \cdot 4.5} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 64.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.5:\\ \;\;\;\;x \cdot \left(x \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -4.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= x 1.5) (* x (* x 3.0)) (* x -4.5)))

C

double code(double x) {
	double tmp;
	if (x <= 1.5) {
		tmp = x * (x * 3.0);
	} else {
		tmp = x * -4.5;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 1.5d0) then
        tmp = x * (x * 3.0d0)
    else
        tmp = x * (-4.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 1.5) {
		tmp = x * (x * 3.0);
	} else {
		tmp = x * -4.5;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.5:
		tmp = x * (x * 3.0)
	else:
		tmp = x * -4.5
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.5)
		tmp = Float64(x * Float64(x * 3.0));
	else
		tmp = Float64(x * -4.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 1.5)
		tmp = x * (x * 3.0);
	else
		tmp = x * -4.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 1.5], N[(x * N[(x * 3.0), $MachinePrecision]), $MachinePrecision], N[(x * -4.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if 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* N/A

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

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

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

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

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

      4. sub-neg N/A

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

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

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

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

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

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

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 85.0%

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

   if 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* N/A

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

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

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

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

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

      4. sub-neg N/A

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

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

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

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

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

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

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   6. Applied egg-rr 0.2%

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

   7. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 60.7%

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

   9. Simplified 60.7%

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

   10. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. *-lowering-*.f64 6.8%

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

   12. Simplified 6.8%

       \[\leadsto \color{blue}{x \cdot -4.5} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-*l* N/A

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

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

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

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

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

   4. sub-neg N/A

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

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

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

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

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

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

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

   8. metadata-eval 99.8%

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

3. Simplified 99.8%

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

Alternative 8: 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* N/A

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

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

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

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

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

   4. sub-neg N/A

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

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

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

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

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

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

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

   8. metadata-eval 99.8%

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

3. Simplified 99.8%

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

6. Applied egg-rr 48.6%

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

7. Taylor expanded in x around 0

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

   1. *-commutative N/A

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

   2. *-lowering-*.f64 78.5%

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

9. Simplified 78.5%

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

10. Taylor expanded in x around inf

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

    1. *-commutative N/A

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

    2. *-lowering-*.f64 6.2%

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

12. Simplified 6.2%

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

Developer Target 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024160 
(FPCore (x)
  :name "Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2"
  :precision binary64

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

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