Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D

Percentage Accurate: 99.8% → 99.9%

Time: 8.4s

Alternatives: 7

Speedup: 1.4×

• 24.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))

C

double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 * ((((x * 3.0d0) * x) - (x * 4.0d0)) + 1.0d0)
end function

Java

public static double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

Python

def code(x):
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0)

Julia

function code(x)
	return Float64(3.0 * Float64(Float64(Float64(Float64(x * 3.0) * x) - Float64(x * 4.0)) + 1.0))
end

MATLAB

function tmp = code(x)
	tmp = 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
end

Wolfram

code[x_] := N[(3.0 * N[(N[(N[(N[(x * 3.0), $MachinePrecision] * x), $MachinePrecision] - N[(x * 4.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))

C

double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 * ((((x * 3.0d0) * x) - (x * 4.0d0)) + 1.0d0)
end function

Java

public static double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

Python

def code(x):
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0)

Julia

function code(x)
	return Float64(3.0 * Float64(Float64(Float64(Float64(x * 3.0) * x) - Float64(x * 4.0)) + 1.0))
end

MATLAB

function tmp = code(x)
	tmp = 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
end

Wolfram

code[x_] := N[(3.0 * N[(N[(N[(N[(x * 3.0), $MachinePrecision] * x), $MachinePrecision] - N[(x * 4.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ 3 + x \cdot \mathsf{fma}\left(x, 9, -12\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (+ 3.0 (* x (fma x 9.0 -12.0))))

C

double code(double x) {
	return 3.0 + (x * fma(x, 9.0, -12.0));
}

Julia

function code(x)
	return Float64(3.0 + Float64(x * fma(x, 9.0, -12.0)))
end

Wolfram

code[x_] := N[(3.0 + N[(x * N[(x * 9.0 + -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
2. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \cdot \color{blue}{3} \]

   2. distribute-rgt1-in N/A

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

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

      \[\leadsto \mathsf{+.f64}\left(3, \color{blue}{\left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) \cdot 3\right)}\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(3, \left(\left(x \cdot \left(x \cdot 3\right) - x \cdot 4\right) \cdot 3\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(3, \left(\left(x \cdot \left(x \cdot 3 - 4\right)\right) \cdot 3\right)\right) \]

   6. associate-*l* N/A

      \[\leadsto \mathsf{+.f64}\left(3, \left(x \cdot \color{blue}{\left(\left(x \cdot 3 - 4\right) \cdot 3\right)}\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \color{blue}{\left(\left(x \cdot 3 - 4\right) \cdot 3\right)}\right)\right) \]

   8. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \left(3 \cdot \color{blue}{\left(x \cdot 3 - 4\right)}\right)\right)\right) \]

   9. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \left(3 \cdot \left(x \cdot 3 + \color{blue}{\left(\mathsf{neg}\left(4\right)\right)}\right)\right)\right)\right) \]

   10. distribute-lft-in N/A

       \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \left(3 \cdot \left(x \cdot 3\right) + \color{blue}{3 \cdot \left(\mathsf{neg}\left(4\right)\right)}\right)\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(3 \cdot \left(x \cdot 3\right)\right), \color{blue}{\left(3 \cdot \left(\mathsf{neg}\left(4\right)\right)\right)}\right)\right)\right) \]

   12. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(x \cdot 3\right) \cdot 3\right), \left(\color{blue}{3} \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right)\right) \]

   13. associate-*l* N/A

       \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(x \cdot \left(3 \cdot 3\right)\right), \left(\color{blue}{3} \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(3 \cdot 3\right)\right), \left(\color{blue}{3} \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right)\right) \]

   15. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 9\right), \left(3 \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right)\right) \]

   16. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 9\right), \left(3 \cdot -4\right)\right)\right)\right) \]

   17. metadata-eval 99.9%

       \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 9\right), -12\right)\right)\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{3 + x \cdot \left(x \cdot 9 + -12\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. fma-define N/A

      \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \left(\mathsf{fma}\left(x, \color{blue}{9}, -12\right)\right)\right)\right) \]

   2. fma-lowering-fma.f64 99.9%

      \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{fma.f64}\left(x, \color{blue}{9}, -12\right)\right)\right) \]

6. Applied egg-rr 99.9%

   \[\leadsto 3 + x \cdot \color{blue}{\mathsf{fma}\left(x, 9, -12\right)} \]
7. Add Preprocessing

Alternative 2: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-12 + x \cdot 9\right)\\ \mathbf{if}\;x \leq -0.58:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.58:\\ \;\;\;\;3 + x \cdot -12\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* x (+ -12.0 (* x 9.0)))))
   (if (<= x -0.58) t_0 (if (<= x 0.58) (+ 3.0 (* x -12.0)) t_0))))

C

double code(double x) {
	double t_0 = x * (-12.0 + (x * 9.0));
	double tmp;
	if (x <= -0.58) {
		tmp = t_0;
	} else if (x <= 0.58) {
		tmp = 3.0 + (x * -12.0);
	} 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 * ((-12.0d0) + (x * 9.0d0))
    if (x <= (-0.58d0)) then
        tmp = t_0
    else if (x <= 0.58d0) then
        tmp = 3.0d0 + (x * (-12.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = x * (-12.0 + (x * 9.0));
	double tmp;
	if (x <= -0.58) {
		tmp = t_0;
	} else if (x <= 0.58) {
		tmp = 3.0 + (x * -12.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x):
	t_0 = x * (-12.0 + (x * 9.0))
	tmp = 0
	if x <= -0.58:
		tmp = t_0
	elif x <= 0.58:
		tmp = 3.0 + (x * -12.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x)
	t_0 = Float64(x * Float64(-12.0 + Float64(x * 9.0)))
	tmp = 0.0
	if (x <= -0.58)
		tmp = t_0;
	elseif (x <= 0.58)
		tmp = Float64(3.0 + Float64(x * -12.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = x * (-12.0 + (x * 9.0));
	tmp = 0.0;
	if (x <= -0.58)
		tmp = t_0;
	elseif (x <= 0.58)
		tmp = 3.0 + (x * -12.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(x * N[(-12.0 + N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.58], t$95$0, If[LessEqual[x, 0.58], N[(3.0 + N[(x * -12.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.57999999999999996 or 0.57999999999999996 < x

   1. Initial program 99.8%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{{x}^{2} \cdot \left(9 - 12 \cdot \frac{1}{x}\right)} \]
   4. Step-by-step derivation

      1. unpow2 N/A

         \[\leadsto \left(x \cdot x\right) \cdot \left(\color{blue}{9} - 12 \cdot \frac{1}{x}\right) \]

      2. associate-*l* N/A

         \[\leadsto x \cdot \color{blue}{\left(x \cdot \left(9 - 12 \cdot \frac{1}{x}\right)\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(x \cdot \left(9 - 12 \cdot \frac{1}{x}\right)\right)}\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(x \cdot \left(9 + \color{blue}{\left(\mathsf{neg}\left(12 \cdot \frac{1}{x}\right)\right)}\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(x \cdot \left(\left(\mathsf{neg}\left(12 \cdot \frac{1}{x}\right)\right) + \color{blue}{9}\right)\right)\right) \]

      6. distribute-rgt-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(12 \cdot \frac{1}{x}\right)\right) \cdot x + \color{blue}{9 \cdot x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(12 \cdot \frac{1}{x}\right) \cdot x\right)\right) + \color{blue}{9} \cdot x\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(12 \cdot \left(\frac{1}{x} \cdot x\right)\right)\right) + 9 \cdot x\right)\right) \]

      9. fnmadd-define N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fnmadd}\left(12, \color{blue}{\left(\frac{1}{x} \cdot x\right)}, \left(9 \cdot x\right)\right)\right) \]

      10. lft-mult-inverse N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fnmadd}\left(12, 1, \left(9 \cdot x\right)\right)\right) \]

      11. fnmadd-undefine N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(12 \cdot 1\right)\right) + \color{blue}{9 \cdot x}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(12\right)\right) + 9 \cdot x\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-12 + \color{blue}{9} \cdot x\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-12, \color{blue}{\left(9 \cdot x\right)}\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-12, \left(x \cdot \color{blue}{9}\right)\right)\right) \]

      16. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-12, \mathsf{*.f64}\left(x, \color{blue}{9}\right)\right)\right) \]

   5. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \left(-12 + x \cdot 9\right)} \]

   if -0.57999999999999996 < x < 0.57999999999999996

   1. Initial program 100.0%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \cdot \color{blue}{3} \]

      2. distribute-rgt1-in N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(3, \color{blue}{\left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) \cdot 3\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(3, \left(\left(x \cdot \left(x \cdot 3\right) - x \cdot 4\right) \cdot 3\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(3, \left(\left(x \cdot \left(x \cdot 3 - 4\right)\right) \cdot 3\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(3, \left(x \cdot \color{blue}{\left(\left(x \cdot 3 - 4\right) \cdot 3\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \color{blue}{\left(\left(x \cdot 3 - 4\right) \cdot 3\right)}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \left(3 \cdot \color{blue}{\left(x \cdot 3 - 4\right)}\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \left(3 \cdot \left(x \cdot 3 + \color{blue}{\left(\mathsf{neg}\left(4\right)\right)}\right)\right)\right)\right) \]

      10. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \left(3 \cdot \left(x \cdot 3\right) + \color{blue}{3 \cdot \left(\mathsf{neg}\left(4\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(3 \cdot \left(x \cdot 3\right)\right), \color{blue}{\left(3 \cdot \left(\mathsf{neg}\left(4\right)\right)\right)}\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(x \cdot 3\right) \cdot 3\right), \left(\color{blue}{3} \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(x \cdot \left(3 \cdot 3\right)\right), \left(\color{blue}{3} \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(3 \cdot 3\right)\right), \left(\color{blue}{3} \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 9\right), \left(3 \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 9\right), \left(3 \cdot -4\right)\right)\right)\right) \]

      17. metadata-eval 100.0%

          \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 9\right), -12\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{3 + x \cdot \left(x \cdot 9 + -12\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \color{blue}{-12}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 98.4%

      \[\leadsto 3 + x \cdot \color{blue}{-12} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55:\\ \;\;\;\;x \cdot \left(x \cdot 9\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;3 + x \cdot -12\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -1.55)
   (* x (* x 9.0))
   (if (<= x 1.0) (+ 3.0 (* x -12.0)) (* 9.0 (* x x)))))

C

double code(double x) {
	double tmp;
	if (x <= -1.55) {
		tmp = x * (x * 9.0);
	} else if (x <= 1.0) {
		tmp = 3.0 + (x * -12.0);
	} else {
		tmp = 9.0 * (x * x);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-1.55d0)) then
        tmp = x * (x * 9.0d0)
    else if (x <= 1.0d0) then
        tmp = 3.0d0 + (x * (-12.0d0))
    else
        tmp = 9.0d0 * (x * x)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -1.55) {
		tmp = x * (x * 9.0);
	} else if (x <= 1.0) {
		tmp = 3.0 + (x * -12.0);
	} else {
		tmp = 9.0 * (x * x);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -1.55:
		tmp = x * (x * 9.0)
	elif x <= 1.0:
		tmp = 3.0 + (x * -12.0)
	else:
		tmp = 9.0 * (x * x)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -1.55)
		tmp = Float64(x * Float64(x * 9.0));
	elseif (x <= 1.0)
		tmp = Float64(3.0 + Float64(x * -12.0));
	else
		tmp = Float64(9.0 * Float64(x * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -1.55)
		tmp = x * (x * 9.0);
	elseif (x <= 1.0)
		tmp = 3.0 + (x * -12.0);
	else
		tmp = 9.0 * (x * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -1.55], N[(x * N[(x * 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], N[(3.0 + N[(x * -12.0), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(x * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55000000000000004

   1. Initial program 99.7%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{{x}^{2} \cdot \left(9 - 12 \cdot \frac{1}{x}\right)} \]
   4. Step-by-step derivation

      1. unpow2 N/A

         \[\leadsto \left(x \cdot x\right) \cdot \left(\color{blue}{9} - 12 \cdot \frac{1}{x}\right) \]

      2. associate-*l* N/A

         \[\leadsto x \cdot \color{blue}{\left(x \cdot \left(9 - 12 \cdot \frac{1}{x}\right)\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(x \cdot \left(9 - 12 \cdot \frac{1}{x}\right)\right)}\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(x \cdot \left(9 + \color{blue}{\left(\mathsf{neg}\left(12 \cdot \frac{1}{x}\right)\right)}\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(x \cdot \left(\left(\mathsf{neg}\left(12 \cdot \frac{1}{x}\right)\right) + \color{blue}{9}\right)\right)\right) \]

      6. distribute-rgt-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(12 \cdot \frac{1}{x}\right)\right) \cdot x + \color{blue}{9 \cdot x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(12 \cdot \frac{1}{x}\right) \cdot x\right)\right) + \color{blue}{9} \cdot x\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(12 \cdot \left(\frac{1}{x} \cdot x\right)\right)\right) + 9 \cdot x\right)\right) \]

      9. fnmadd-define N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fnmadd}\left(12, \color{blue}{\left(\frac{1}{x} \cdot x\right)}, \left(9 \cdot x\right)\right)\right) \]

      10. lft-mult-inverse N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fnmadd}\left(12, 1, \left(9 \cdot x\right)\right)\right) \]

      11. fnmadd-undefine N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(12 \cdot 1\right)\right) + \color{blue}{9 \cdot x}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(12\right)\right) + 9 \cdot x\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-12 + \color{blue}{9} \cdot x\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-12, \color{blue}{\left(9 \cdot x\right)}\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-12, \left(x \cdot \color{blue}{9}\right)\right)\right) \]

      16. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-12, \mathsf{*.f64}\left(x, \color{blue}{9}\right)\right)\right) \]

   5. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \left(-12 + x \cdot 9\right)} \]

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 99.2%

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

   8. Simplified 99.2%

      \[\leadsto x \cdot \color{blue}{\left(x \cdot 9\right)} \]

   if -1.55000000000000004 < x < 1

   1. Initial program 100.0%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \cdot \color{blue}{3} \]

      2. distribute-rgt1-in N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(3, \color{blue}{\left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) \cdot 3\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(3, \left(\left(x \cdot \left(x \cdot 3\right) - x \cdot 4\right) \cdot 3\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(3, \left(\left(x \cdot \left(x \cdot 3 - 4\right)\right) \cdot 3\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(3, \left(x \cdot \color{blue}{\left(\left(x \cdot 3 - 4\right) \cdot 3\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \color{blue}{\left(\left(x \cdot 3 - 4\right) \cdot 3\right)}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \left(3 \cdot \color{blue}{\left(x \cdot 3 - 4\right)}\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \left(3 \cdot \left(x \cdot 3 + \color{blue}{\left(\mathsf{neg}\left(4\right)\right)}\right)\right)\right)\right) \]

      10. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \left(3 \cdot \left(x \cdot 3\right) + \color{blue}{3 \cdot \left(\mathsf{neg}\left(4\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(3 \cdot \left(x \cdot 3\right)\right), \color{blue}{\left(3 \cdot \left(\mathsf{neg}\left(4\right)\right)\right)}\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(x \cdot 3\right) \cdot 3\right), \left(\color{blue}{3} \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(x \cdot \left(3 \cdot 3\right)\right), \left(\color{blue}{3} \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(3 \cdot 3\right)\right), \left(\color{blue}{3} \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 9\right), \left(3 \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 9\right), \left(3 \cdot -4\right)\right)\right)\right) \]

      17. metadata-eval 100.0%

          \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 9\right), -12\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{3 + x \cdot \left(x \cdot 9 + -12\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \color{blue}{-12}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 98.4%

      \[\leadsto 3 + x \cdot \color{blue}{-12} \]

   if 1 < x

   1. Initial program 99.8%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

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

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

      2. unpow2 N/A

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

      3. *-lowering-*.f64 99.2%

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

   5. Simplified 99.2%

      \[\leadsto \color{blue}{9 \cdot \left(x \cdot x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 97.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.58:\\ \;\;\;\;x \cdot \left(x \cdot 9\right)\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;3\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -0.58) (* x (* x 9.0)) (if (<= x 1.7) 3.0 (* 9.0 (* x x)))))

C

double code(double x) {
	double tmp;
	if (x <= -0.58) {
		tmp = x * (x * 9.0);
	} else if (x <= 1.7) {
		tmp = 3.0;
	} else {
		tmp = 9.0 * (x * x);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-0.58d0)) then
        tmp = x * (x * 9.0d0)
    else if (x <= 1.7d0) then
        tmp = 3.0d0
    else
        tmp = 9.0d0 * (x * x)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -0.58) {
		tmp = x * (x * 9.0);
	} else if (x <= 1.7) {
		tmp = 3.0;
	} else {
		tmp = 9.0 * (x * x);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -0.58:
		tmp = x * (x * 9.0)
	elif x <= 1.7:
		tmp = 3.0
	else:
		tmp = 9.0 * (x * x)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -0.58)
		tmp = Float64(x * Float64(x * 9.0));
	elseif (x <= 1.7)
		tmp = 3.0;
	else
		tmp = Float64(9.0 * Float64(x * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -0.58)
		tmp = x * (x * 9.0);
	elseif (x <= 1.7)
		tmp = 3.0;
	else
		tmp = 9.0 * (x * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -0.58], N[(x * N[(x * 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7], 3.0, N[(9.0 * N[(x * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.57999999999999996

   1. Initial program 99.7%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{{x}^{2} \cdot \left(9 - 12 \cdot \frac{1}{x}\right)} \]
   4. Step-by-step derivation

      1. unpow2 N/A

         \[\leadsto \left(x \cdot x\right) \cdot \left(\color{blue}{9} - 12 \cdot \frac{1}{x}\right) \]

      2. associate-*l* N/A

         \[\leadsto x \cdot \color{blue}{\left(x \cdot \left(9 - 12 \cdot \frac{1}{x}\right)\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(x \cdot \left(9 - 12 \cdot \frac{1}{x}\right)\right)}\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(x \cdot \left(9 + \color{blue}{\left(\mathsf{neg}\left(12 \cdot \frac{1}{x}\right)\right)}\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(x \cdot \left(\left(\mathsf{neg}\left(12 \cdot \frac{1}{x}\right)\right) + \color{blue}{9}\right)\right)\right) \]

      6. distribute-rgt-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(12 \cdot \frac{1}{x}\right)\right) \cdot x + \color{blue}{9 \cdot x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(12 \cdot \frac{1}{x}\right) \cdot x\right)\right) + \color{blue}{9} \cdot x\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(12 \cdot \left(\frac{1}{x} \cdot x\right)\right)\right) + 9 \cdot x\right)\right) \]

      9. fnmadd-define N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fnmadd}\left(12, \color{blue}{\left(\frac{1}{x} \cdot x\right)}, \left(9 \cdot x\right)\right)\right) \]

      10. lft-mult-inverse N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{fnmadd}\left(12, 1, \left(9 \cdot x\right)\right)\right) \]

      11. fnmadd-undefine N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(12 \cdot 1\right)\right) + \color{blue}{9 \cdot x}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(12\right)\right) + 9 \cdot x\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-12 + \color{blue}{9} \cdot x\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-12, \color{blue}{\left(9 \cdot x\right)}\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-12, \left(x \cdot \color{blue}{9}\right)\right)\right) \]

      16. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-12, \mathsf{*.f64}\left(x, \color{blue}{9}\right)\right)\right) \]

   5. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \left(-12 + x \cdot 9\right)} \]

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 99.2%

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

   8. Simplified 99.2%

      \[\leadsto x \cdot \color{blue}{\left(x \cdot 9\right)} \]

   if -0.57999999999999996 < x < 1.69999999999999996

   1. Initial program 100.0%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{3} \]
   4. Step-by-step derivation

   5. Simplified 97.1%

      \[\leadsto \color{blue}{3} \]

   if 1.69999999999999996 < x

   1. Initial program 99.8%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

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

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

      2. unpow2 N/A

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

      3. *-lowering-*.f64 99.2%

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

   5. Simplified 99.2%

      \[\leadsto \color{blue}{9 \cdot \left(x \cdot x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 97.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 9 \cdot \left(x \cdot x\right)\\ \mathbf{if}\;x \leq -0.58:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* 9.0 (* x x)))) (if (<= x -0.58) t_0 (if (<= x 1.7) 3.0 t_0))))

C

double code(double x) {
	double t_0 = 9.0 * (x * x);
	double tmp;
	if (x <= -0.58) {
		tmp = t_0;
	} else if (x <= 1.7) {
		tmp = 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 = 9.0d0 * (x * x)
    if (x <= (-0.58d0)) then
        tmp = t_0
    else if (x <= 1.7d0) then
        tmp = 3.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = 9.0 * (x * x);
	double tmp;
	if (x <= -0.58) {
		tmp = t_0;
	} else if (x <= 1.7) {
		tmp = 3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x):
	t_0 = 9.0 * (x * x)
	tmp = 0
	if x <= -0.58:
		tmp = t_0
	elif x <= 1.7:
		tmp = 3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x)
	t_0 = Float64(9.0 * Float64(x * x))
	tmp = 0.0
	if (x <= -0.58)
		tmp = t_0;
	elseif (x <= 1.7)
		tmp = 3.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = 9.0 * (x * x);
	tmp = 0.0;
	if (x <= -0.58)
		tmp = t_0;
	elseif (x <= 1.7)
		tmp = 3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(9.0 * N[(x * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.58], t$95$0, If[LessEqual[x, 1.7], 3.0, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.57999999999999996 or 1.69999999999999996 < x

   1. Initial program 99.8%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

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

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

      2. unpow2 N/A

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

      3. *-lowering-*.f64 99.2%

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

   5. Simplified 99.2%

      \[\leadsto \color{blue}{9 \cdot \left(x \cdot x\right)} \]

   if -0.57999999999999996 < x < 1.69999999999999996

   1. Initial program 100.0%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{3} \]
   4. Step-by-step derivation

   5. Simplified 97.1%

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

Alternative 6: 99.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ 3 + x \cdot \left(-12 + x \cdot 9\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (+ 3.0 (* x (+ -12.0 (* x 9.0)))))

C

double code(double x) {
	return 3.0 + (x * (-12.0 + (x * 9.0)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 + (x * ((-12.0d0) + (x * 9.0d0)))
end function

Java

public static double code(double x) {
	return 3.0 + (x * (-12.0 + (x * 9.0)));
}

Python

def code(x):
	return 3.0 + (x * (-12.0 + (x * 9.0)))

Julia

function code(x)
	return Float64(3.0 + Float64(x * Float64(-12.0 + Float64(x * 9.0))))
end

MATLAB

function tmp = code(x)
	tmp = 3.0 + (x * (-12.0 + (x * 9.0)));
end

Wolfram

code[x_] := N[(3.0 + N[(x * N[(-12.0 + N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
2. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \cdot \color{blue}{3} \]

   2. distribute-rgt1-in N/A

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

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

      \[\leadsto \mathsf{+.f64}\left(3, \color{blue}{\left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) \cdot 3\right)}\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(3, \left(\left(x \cdot \left(x \cdot 3\right) - x \cdot 4\right) \cdot 3\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(3, \left(\left(x \cdot \left(x \cdot 3 - 4\right)\right) \cdot 3\right)\right) \]

   6. associate-*l* N/A

      \[\leadsto \mathsf{+.f64}\left(3, \left(x \cdot \color{blue}{\left(\left(x \cdot 3 - 4\right) \cdot 3\right)}\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \color{blue}{\left(\left(x \cdot 3 - 4\right) \cdot 3\right)}\right)\right) \]

   8. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \left(3 \cdot \color{blue}{\left(x \cdot 3 - 4\right)}\right)\right)\right) \]

   9. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \left(3 \cdot \left(x \cdot 3 + \color{blue}{\left(\mathsf{neg}\left(4\right)\right)}\right)\right)\right)\right) \]

   10. distribute-lft-in N/A

       \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \left(3 \cdot \left(x \cdot 3\right) + \color{blue}{3 \cdot \left(\mathsf{neg}\left(4\right)\right)}\right)\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(3 \cdot \left(x \cdot 3\right)\right), \color{blue}{\left(3 \cdot \left(\mathsf{neg}\left(4\right)\right)\right)}\right)\right)\right) \]

   12. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(x \cdot 3\right) \cdot 3\right), \left(\color{blue}{3} \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right)\right) \]

   13. associate-*l* N/A

       \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(x \cdot \left(3 \cdot 3\right)\right), \left(\color{blue}{3} \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(3 \cdot 3\right)\right), \left(\color{blue}{3} \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right)\right) \]

   15. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 9\right), \left(3 \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right)\right) \]

   16. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 9\right), \left(3 \cdot -4\right)\right)\right)\right) \]

   17. metadata-eval 99.9%

       \[\leadsto \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 9\right), -12\right)\right)\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{3 + x \cdot \left(x \cdot 9 + -12\right)} \]
4. Add Preprocessing

5. Final simplification 99.9%

   \[\leadsto 3 + x \cdot \left(-12 + x \cdot 9\right) \]
6. Add Preprocessing

Alternative 7: 51.5% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 3 \end{array} \]

FPCore

(FPCore (x) :precision binary64 3.0)

C

double code(double x) {
	return 3.0;
}

Fortran

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

Java

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

Python

def code(x):
	return 3.0

Julia

function code(x)
	return 3.0
end

MATLAB

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

Wolfram

code[x_] := 3.0

Derivation

1. Initial program 99.9%

   \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{3} \]
4. Step-by-step derivation

5. Simplified 50.5%

   \[\leadsto \color{blue}{3} \]
6. Add Preprocessing

Developer Target 1: 99.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ 3 + \left(\left(9 \cdot x\right) \cdot x - 12 \cdot x\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (+ 3.0 (- (* (* 9.0 x) x) (* 12.0 x))))

C

double code(double x) {
	return 3.0 + (((9.0 * x) * x) - (12.0 * x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 + (((9.0d0 * x) * x) - (12.0d0 * x))
end function

Java

public static double code(double x) {
	return 3.0 + (((9.0 * x) * x) - (12.0 * x));
}

Python

def code(x):
	return 3.0 + (((9.0 * x) * x) - (12.0 * x))

Julia

function code(x)
	return Float64(3.0 + Float64(Float64(Float64(9.0 * x) * x) - Float64(12.0 * x)))
end

MATLAB

function tmp = code(x)
	tmp = 3.0 + (((9.0 * x) * x) - (12.0 * x));
end

Wolfram

code[x_] := N[(3.0 + N[(N[(N[(9.0 * x), $MachinePrecision] * x), $MachinePrecision] - N[(12.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024160 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :alt
  (! :herbie-platform default (+ 3 (- (* (* 9 x) x) (* 12 x))))

  (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))