Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2

Percentage Accurate: 99.8% → 99.8%

Time: 8.3s

Alternatives: 6

Speedup: 1.0×

• 33.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 2: 63.8% accurate, 0.9× speedup

Math

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

FPCore

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

C

double code(double x) {
	double tmp;
	if (x <= 1.5) {
		tmp = x * (x * 3.0);
	} else {
		tmp = (x * -4.5) + -6.75;
	}
	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)) + (-6.75d0)
    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) + -6.75;
	}
	return tmp;
}

Python

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

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.5)
		tmp = Float64(x * Float64(x * 3.0));
	else
		tmp = Float64(Float64(x * -4.5) + -6.75);
	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) + -6.75;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if 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. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. flip-- 99.8%

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

      2. clear-num 99.8%

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

      3. associate-*l/ 99.7%

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

      4. *-un-lft-identity 99.7%

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

      5. pow2 99.7%

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

      6. clear-num 99.7%

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

      7. flip-- 99.7%

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

      8. sub-neg 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around 0 76.5%

      \[\leadsto \frac{{x}^{2}}{\color{blue}{0.3333333333333333}} \]
   7. Step-by-step derivation

      1. div-inv 76.6%

         \[\leadsto \color{blue}{{x}^{2} \cdot \frac{1}{0.3333333333333333}} \]

      2. unpow2 76.6%

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

      3. metadata-eval 76.6%

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

      4. associate-*l* 76.6%

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

   8. Applied egg-rr 76.6%

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

   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. *-commutative 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*r* 99.9%

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

      2. flip-- 98.4%

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

      3. associate-*l/ 98.4%

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

      4. associate-*l/ 88.8%

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

      5. *-commutative 88.8%

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

      6. sub-neg 88.8%

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

      7. metadata-eval 88.8%

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

      8. swap-sqr 88.8%

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

      9. distribute-rgt-neg-in 88.8%

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

      10. pow2 88.8%

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

      11. metadata-eval 88.8%

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

      12. metadata-eval 88.8%

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

   5. Applied egg-rr 88.8%

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

   6. Taylor expanded in x around 0 0.4%

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

      1. *-commutative 0.4%

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

   8. Simplified 0.4%

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

   9. Taylor expanded in x around inf 0.4%

      \[\leadsto \color{blue}{4.5 \cdot x - 6.75} \]
   10. Step-by-step derivation

       1. sub-neg 0.4%

          \[\leadsto \color{blue}{4.5 \cdot x + \left(-6.75\right)} \]

       2. add-sqr-sqrt 0.4%

          \[\leadsto 4.5 \cdot \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} + \left(-6.75\right) \]

       3. sqrt-prod 0.4%

          \[\leadsto 4.5 \cdot \color{blue}{\sqrt{x \cdot x}} + \left(-6.75\right) \]

       4. unpow2 0.4%

          \[\leadsto 4.5 \cdot \sqrt{\color{blue}{{x}^{2}}} + \left(-6.75\right) \]

       5. unpow2 0.4%

          \[\leadsto 4.5 \cdot \sqrt{\color{blue}{x \cdot x}} + \left(-6.75\right) \]

       6. sqr-neg 0.4%

          \[\leadsto 4.5 \cdot \sqrt{\color{blue}{\left(-x\right) \cdot \left(-x\right)}} + \left(-6.75\right) \]

       7. sqrt-unprod 0.0%

          \[\leadsto 4.5 \cdot \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} + \left(-6.75\right) \]

       8. add-sqr-sqrt 7.6%

          \[\leadsto 4.5 \cdot \color{blue}{\left(-x\right)} + \left(-6.75\right) \]

       9. distribute-rgt-neg-out 7.6%

          \[\leadsto \color{blue}{\left(-4.5 \cdot x\right)} + \left(-6.75\right) \]

       10. distribute-neg-in 7.6%

           \[\leadsto \color{blue}{-\left(4.5 \cdot x + 6.75\right)} \]

       11. *-un-lft-identity 7.6%

           \[\leadsto -\color{blue}{1 \cdot \left(4.5 \cdot x + 6.75\right)} \]

       12. distribute-lft-neg-in 7.6%

           \[\leadsto \color{blue}{\left(-1\right) \cdot \left(4.5 \cdot x + 6.75\right)} \]

       13. metadata-eval 7.6%

           \[\leadsto \color{blue}{-1} \cdot \left(4.5 \cdot x + 6.75\right) \]

       14. *-commutative 7.6%

           \[\leadsto -1 \cdot \left(\color{blue}{x \cdot 4.5} + 6.75\right) \]

       15. fma-def 7.6%

           \[\leadsto -1 \cdot \color{blue}{\mathsf{fma}\left(x, 4.5, 6.75\right)} \]

   11. Applied egg-rr 7.6%

       \[\leadsto \color{blue}{-1 \cdot \mathsf{fma}\left(x, 4.5, 6.75\right)} \]
   12. Step-by-step derivation

       1. fma-udef 7.6%

          \[\leadsto -1 \cdot \color{blue}{\left(x \cdot 4.5 + 6.75\right)} \]

       2. distribute-lft-in 7.6%

          \[\leadsto \color{blue}{-1 \cdot \left(x \cdot 4.5\right) + -1 \cdot 6.75} \]

       3. neg-mul-1 7.6%

          \[\leadsto \color{blue}{\left(-x \cdot 4.5\right)} + -1 \cdot 6.75 \]

       4. distribute-rgt-neg-in 7.6%

          \[\leadsto \color{blue}{x \cdot \left(-4.5\right)} + -1 \cdot 6.75 \]

       5. metadata-eval 7.6%

          \[\leadsto x \cdot \color{blue}{-4.5} + -1 \cdot 6.75 \]

       6. metadata-eval 7.6%

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

   13. Simplified 7.6%

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

4. Final simplification 58.6%

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

Alternative 3: 75.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

double code(double x) {
	double tmp;
	if (x <= 1.5) {
		tmp = x * (x * 3.0);
	} 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) then
        tmp = x * (x * 3.0d0)
    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) {
		tmp = x * (x * 3.0);
	} else {
		tmp = x * (x * -3.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.5:
		tmp = x * (x * 3.0)
	else:
		tmp = x * (x * -3.0)
	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(x * -3.0));
	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 * (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if 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. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. flip-- 99.8%

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

      2. clear-num 99.8%

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

      3. associate-*l/ 99.7%

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

      4. *-un-lft-identity 99.7%

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

      5. pow2 99.7%

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

      6. clear-num 99.7%

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

      7. flip-- 99.7%

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

      8. sub-neg 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around 0 76.5%

      \[\leadsto \frac{{x}^{2}}{\color{blue}{0.3333333333333333}} \]
   7. Step-by-step derivation

      1. div-inv 76.6%

         \[\leadsto \color{blue}{{x}^{2} \cdot \frac{1}{0.3333333333333333}} \]

      2. unpow2 76.6%

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

      3. metadata-eval 76.6%

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

      4. associate-*l* 76.6%

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

   8. Applied egg-rr 76.6%

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

   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. *-commutative 99.9%

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

   3. Simplified 99.9%

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

      1. flip-- 98.4%

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

      2. clear-num 98.3%

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

      3. associate-*l/ 98.3%

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

      4. *-un-lft-identity 98.3%

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

      5. pow2 98.3%

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

      6. clear-num 98.3%

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

      7. flip-- 99.8%

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

      8. sub-neg 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{{x}^{2}}{\frac{1}{3 + x \cdot -2}}} \]
   6. Step-by-step derivation

      1. unpow2 99.8%

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

      2. div-inv 99.8%

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

      3. times-frac 99.9%

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

      4. +-commutative 99.9%

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

      5. fma-def 99.9%

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

   7. Applied egg-rr 99.9%

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

   8. Taylor expanded in x around 0 0.3%

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

      1. frac-2neg 0.3%

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

      2. neg-sub0 0.3%

         \[\leadsto \frac{x}{1} \cdot \frac{\color{blue}{0 - x}}{-0.3333333333333333} \]

      3. div-sub 0.3%

         \[\leadsto \frac{x}{1} \cdot \color{blue}{\left(\frac{0}{-0.3333333333333333} - \frac{x}{-0.3333333333333333}\right)} \]

      4. metadata-eval 0.3%

         \[\leadsto \frac{x}{1} \cdot \left(\frac{0}{\color{blue}{-0.3333333333333333}} - \frac{x}{-0.3333333333333333}\right) \]

      5. metadata-eval 0.3%

         \[\leadsto \frac{x}{1} \cdot \left(\color{blue}{0} - \frac{x}{-0.3333333333333333}\right) \]

      6. add-sqr-sqrt 0.3%

         \[\leadsto \frac{x}{1} \cdot \left(0 - \frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{-0.3333333333333333}\right) \]

      7. sqrt-prod 0.3%

         \[\leadsto \frac{x}{1} \cdot \left(0 - \frac{\color{blue}{\sqrt{x \cdot x}}}{-0.3333333333333333}\right) \]

      8. unpow2 0.3%

         \[\leadsto \frac{x}{1} \cdot \left(0 - \frac{\sqrt{\color{blue}{{x}^{2}}}}{-0.3333333333333333}\right) \]

      9. unpow2 0.3%

         \[\leadsto \frac{x}{1} \cdot \left(0 - \frac{\sqrt{\color{blue}{x \cdot x}}}{-0.3333333333333333}\right) \]

      10. sqr-neg 0.3%

          \[\leadsto \frac{x}{1} \cdot \left(0 - \frac{\sqrt{\color{blue}{\left(-x\right) \cdot \left(-x\right)}}}{-0.3333333333333333}\right) \]

      11. sqrt-unprod 0.0%

          \[\leadsto \frac{x}{1} \cdot \left(0 - \frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{-0.3333333333333333}\right) \]

      12. add-sqr-sqrt 51.6%

          \[\leadsto \frac{x}{1} \cdot \left(0 - \frac{\color{blue}{-x}}{-0.3333333333333333}\right) \]

      13. neg-sub0 51.6%

          \[\leadsto \frac{x}{1} \cdot \left(0 - \frac{\color{blue}{0 - x}}{-0.3333333333333333}\right) \]

      14. div-sub 51.6%

          \[\leadsto \frac{x}{1} \cdot \left(0 - \color{blue}{\left(\frac{0}{-0.3333333333333333} - \frac{x}{-0.3333333333333333}\right)}\right) \]

      15. metadata-eval 51.6%

          \[\leadsto \frac{x}{1} \cdot \left(0 - \left(\frac{0}{\color{blue}{-0.3333333333333333}} - \frac{x}{-0.3333333333333333}\right)\right) \]

      16. metadata-eval 51.6%

          \[\leadsto \frac{x}{1} \cdot \left(0 - \left(\color{blue}{0} - \frac{x}{-0.3333333333333333}\right)\right) \]

      17. add-sqr-sqrt 51.6%

          \[\leadsto \frac{x}{1} \cdot \left(0 - \left(0 - \frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{-0.3333333333333333}\right)\right) \]

      18. sqrt-prod 51.6%

          \[\leadsto \frac{x}{1} \cdot \left(0 - \left(0 - \frac{\color{blue}{\sqrt{x \cdot x}}}{-0.3333333333333333}\right)\right) \]

      19. unpow2 51.6%

          \[\leadsto \frac{x}{1} \cdot \left(0 - \left(0 - \frac{\sqrt{\color{blue}{{x}^{2}}}}{-0.3333333333333333}\right)\right) \]

      20. unpow2 51.6%

          \[\leadsto \frac{x}{1} \cdot \left(0 - \left(0 - \frac{\sqrt{\color{blue}{x \cdot x}}}{-0.3333333333333333}\right)\right) \]

      21. sqr-neg 51.6%

          \[\leadsto \frac{x}{1} \cdot \left(0 - \left(0 - \frac{\sqrt{\color{blue}{\left(-x\right) \cdot \left(-x\right)}}}{-0.3333333333333333}\right)\right) \]

      22. sqrt-unprod 0.0%

          \[\leadsto \frac{x}{1} \cdot \left(0 - \left(0 - \frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{-0.3333333333333333}\right)\right) \]

      23. add-sqr-sqrt 0.3%

          \[\leadsto \frac{x}{1} \cdot \left(0 - \left(0 - \frac{\color{blue}{-x}}{-0.3333333333333333}\right)\right) \]

      24. frac-2neg 0.3%

          \[\leadsto \frac{x}{1} \cdot \left(0 - \left(0 - \color{blue}{\frac{x}{0.3333333333333333}}\right)\right) \]

   10. Applied egg-rr 51.6%

       \[\leadsto \frac{x}{1} \cdot \color{blue}{\left(0 + x \cdot -3\right)} \]
   11. Step-by-step derivation

       1. +-lft-identity 51.6%

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

   12. Simplified 51.6%

       \[\leadsto \frac{x}{1} \cdot \color{blue}{\left(x \cdot -3\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.1%

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

Alternative 4: 62.2% 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. *-commutative 99.8%

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

3. Simplified 99.8%

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

   1. flip-- 99.4%

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

   2. clear-num 99.4%

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

   3. associate-*l/ 99.3%

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

   4. *-un-lft-identity 99.3%

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

   5. pow2 99.3%

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

   6. clear-num 99.3%

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

   7. flip-- 99.7%

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

   8. sub-neg 99.7%

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

   9. distribute-rgt-neg-in 99.7%

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

   10. metadata-eval 99.7%

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

5. Applied egg-rr 99.7%

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

6. Taylor expanded in x around 0 56.6%

   \[\leadsto \frac{{x}^{2}}{\color{blue}{0.3333333333333333}} \]
7. Step-by-step derivation

   1. div-inv 56.6%

      \[\leadsto \color{blue}{{x}^{2} \cdot \frac{1}{0.3333333333333333}} \]

   2. unpow2 56.6%

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

   3. metadata-eval 56.6%

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

   4. associate-*l* 56.6%

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

8. Applied egg-rr 56.6%

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

9. Final simplification 56.6%

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

Alternative 5: 3.1% 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. *-commutative 99.8%

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

3. Simplified 99.8%

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

   1. associate-*r* 99.8%

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

   2. flip-- 99.4%

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

   3. associate-*l/ 99.4%

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

   4. associate-*l/ 93.4%

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

   5. *-commutative 93.4%

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

   6. sub-neg 93.4%

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

   7. metadata-eval 93.4%

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

   8. swap-sqr 93.4%

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

   9. distribute-rgt-neg-in 93.4%

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

   10. pow2 93.4%

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

   11. metadata-eval 93.4%

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

   12. metadata-eval 93.4%

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

5. Applied egg-rr 93.4%

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

6. Taylor expanded in x around 0 43.2%

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

   1. *-commutative 43.2%

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

8. Simplified 43.2%

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

9. Taylor expanded in x around inf 2.9%

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

    1. *-commutative 2.9%

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

11. Simplified 2.9%

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

12. Final simplification 2.9%

    \[\leadsto x \cdot 4.5 \]

Alternative 6: 2.5% accurate, 9.0× speedup

Math

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

FPCore

(FPCore (x) :precision binary64 -6.75)

C

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

Fortran

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

Java

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

Python

def code(x):
	return -6.75

Julia

function code(x)
	return -6.75
end

MATLAB

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

Wolfram

code[x_] := -6.75

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

3. Simplified 99.8%

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

   1. associate-*r* 99.8%

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

   2. flip-- 99.4%

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

   3. associate-*l/ 99.4%

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

   4. associate-*l/ 93.4%

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

   5. *-commutative 93.4%

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

   6. sub-neg 93.4%

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

   7. metadata-eval 93.4%

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

   8. swap-sqr 93.4%

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

   9. distribute-rgt-neg-in 93.4%

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

   10. pow2 93.4%

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

   11. metadata-eval 93.4%

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

   12. metadata-eval 93.4%

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

5. Applied egg-rr 93.4%

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

6. Taylor expanded in x around 0 43.2%

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

   1. *-commutative 43.2%

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

8. Simplified 43.2%

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

9. Taylor expanded in x around inf 1.4%

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

10. Taylor expanded in x around 0 2.4%

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

11. Final simplification 2.4%

    \[\leadsto -6.75 \]

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023336 
(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))))