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

Percentage Accurate: 99.8% → 99.9%

Time: 7.9s

Alternatives: 8

Speedup: 1.4×

• 25.0% 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, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

Alternative 2: 99.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.58:\\ \;\;\;\;3 \cdot \left(x \cdot \left(-4 + 3 \cdot x\right)\right)\\ \mathbf{elif}\;x \leq 0.6:\\ \;\;\;\;3 \cdot \left(x \cdot -4 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot 9 + -12\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -0.58)
   (* 3.0 (* x (+ -4.0 (* 3.0 x))))
   (if (<= x 0.6) (* 3.0 (+ (* x -4.0) 1.0)) (* x (+ (* x 9.0) -12.0)))))

C

double code(double x) {
	double tmp;
	if (x <= -0.58) {
		tmp = 3.0 * (x * (-4.0 + (3.0 * x)));
	} else if (x <= 0.6) {
		tmp = 3.0 * ((x * -4.0) + 1.0);
	} else {
		tmp = x * ((x * 9.0) + -12.0);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-0.58d0)) then
        tmp = 3.0d0 * (x * ((-4.0d0) + (3.0d0 * x)))
    else if (x <= 0.6d0) then
        tmp = 3.0d0 * ((x * (-4.0d0)) + 1.0d0)
    else
        tmp = x * ((x * 9.0d0) + (-12.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -0.58) {
		tmp = 3.0 * (x * (-4.0 + (3.0 * x)));
	} else if (x <= 0.6) {
		tmp = 3.0 * ((x * -4.0) + 1.0);
	} else {
		tmp = x * ((x * 9.0) + -12.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -0.58:
		tmp = 3.0 * (x * (-4.0 + (3.0 * x)))
	elif x <= 0.6:
		tmp = 3.0 * ((x * -4.0) + 1.0)
	else:
		tmp = x * ((x * 9.0) + -12.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -0.58)
		tmp = Float64(3.0 * Float64(x * Float64(-4.0 + Float64(3.0 * x))));
	elseif (x <= 0.6)
		tmp = Float64(3.0 * Float64(Float64(x * -4.0) + 1.0));
	else
		tmp = Float64(x * Float64(Float64(x * 9.0) + -12.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -0.58)
		tmp = 3.0 * (x * (-4.0 + (3.0 * x)));
	elseif (x <= 0.6)
		tmp = 3.0 * ((x * -4.0) + 1.0);
	else
		tmp = x * ((x * 9.0) + -12.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -0.58], N[(3.0 * N[(x * N[(-4.0 + N[(3.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.6], N[(3.0 * N[(N[(x * -4.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(x * 9.0), $MachinePrecision] + -12.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.57999999999999996

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(3, \color{blue}{\left({x}^{2} \cdot \left(3 - 4 \cdot \frac{1}{x}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(3, \left(\left(x \cdot x\right) \cdot \left(\color{blue}{3} - 4 \cdot \frac{1}{x}\right)\right)\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(3, \left(x \cdot \color{blue}{\left(x \cdot \left(3 - 4 \cdot \frac{1}{x}\right)\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(3, \left(x \cdot \left(\left(3 - 4 \cdot \frac{1}{x}\right) \cdot \color{blue}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x, \color{blue}{\left(\left(3 - 4 \cdot \frac{1}{x}\right) \cdot x\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x, \left(x \cdot \color{blue}{\left(3 - 4 \cdot \frac{1}{x}\right)}\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x, \left(x \cdot \left(3 + \color{blue}{\left(\mathsf{neg}\left(4 \cdot \frac{1}{x}\right)\right)}\right)\right)\right)\right) \]

      7. distribute-rgt-in N/A

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x, \left(3 \cdot x + \color{blue}{\left(\mathsf{neg}\left(4 \cdot \frac{1}{x}\right)\right) \cdot x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x, \left(3 \cdot x + \left(\left(\mathsf{neg}\left(4\right)\right) \cdot \frac{1}{x}\right) \cdot x\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x, \left(3 \cdot x + \left(-4 \cdot \frac{1}{x}\right) \cdot x\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x, \left(3 \cdot x + -4 \cdot \color{blue}{\left(\frac{1}{x} \cdot x\right)}\right)\right)\right) \]

      11. lft-mult-inverse N/A

          \[\leadsto \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x, \left(3 \cdot x + -4 \cdot 1\right)\right)\right) \]

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

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

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

      15. *-lowering-*.f64 99.7%

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

   5. Simplified 99.7%

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

   if -0.57999999999999996 < x < 0.599999999999999978

   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

      \[\leadsto \mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\color{blue}{\left(-4 \cdot x\right)}, 1\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\left(x \cdot -4\right), 1\right)\right) \]

      2. *-lowering-*.f64 99.0%

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, -4\right), 1\right)\right) \]

   5. Simplified 99.0%

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

   if 0.599999999999999978 < x

   1. Initial program 98.1%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   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. distribute-rgt-in N/A

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

      6. +-commutative 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-in N/A

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

      8. metadata-eval N/A

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

      9. associate-*l* N/A

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

      10. fma-define N/A

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

      11. lft-mult-inverse N/A

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

      12. fma-undefine N/A

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

      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 99.3%

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

   5. Simplified 99.3%

      \[\leadsto \color{blue}{x \cdot \left(-12 + x \cdot 9\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.58:\\ \;\;\;\;3 \cdot \left(x \cdot \left(-4 + 3 \cdot x\right)\right)\\ \mathbf{elif}\;x \leq 0.6:\\ \;\;\;\;3 \cdot \left(x \cdot -4 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot 9 + -12\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot 9 + -12\right)\\ \mathbf{if}\;x \leq -0.58:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.6:\\ \;\;\;\;3 \cdot \left(x \cdot -4 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* x (+ (* x 9.0) -12.0))))
   (if (<= x -0.58) t_0 (if (<= x 0.6) (* 3.0 (+ (* x -4.0) 1.0)) t_0))))

C

double code(double x) {
	double t_0 = x * ((x * 9.0) + -12.0);
	double tmp;
	if (x <= -0.58) {
		tmp = t_0;
	} else if (x <= 0.6) {
		tmp = 3.0 * ((x * -4.0) + 1.0);
	} 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 * 9.0d0) + (-12.0d0))
    if (x <= (-0.58d0)) then
        tmp = t_0
    else if (x <= 0.6d0) then
        tmp = 3.0d0 * ((x * (-4.0d0)) + 1.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = x * ((x * 9.0) + -12.0);
	double tmp;
	if (x <= -0.58) {
		tmp = t_0;
	} else if (x <= 0.6) {
		tmp = 3.0 * ((x * -4.0) + 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x):
	t_0 = x * ((x * 9.0) + -12.0)
	tmp = 0
	if x <= -0.58:
		tmp = t_0
	elif x <= 0.6:
		tmp = 3.0 * ((x * -4.0) + 1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x)
	t_0 = Float64(x * Float64(Float64(x * 9.0) + -12.0))
	tmp = 0.0
	if (x <= -0.58)
		tmp = t_0;
	elseif (x <= 0.6)
		tmp = Float64(3.0 * Float64(Float64(x * -4.0) + 1.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = x * ((x * 9.0) + -12.0);
	tmp = 0.0;
	if (x <= -0.58)
		tmp = t_0;
	elseif (x <= 0.6)
		tmp = 3.0 * ((x * -4.0) + 1.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(x * N[(N[(x * 9.0), $MachinePrecision] + -12.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.58], t$95$0, If[LessEqual[x, 0.6], N[(3.0 * N[(N[(x * -4.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.57999999999999996 or 0.599999999999999978 < x

   1. Initial program 98.8%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   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. distribute-rgt-in N/A

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

      6. +-commutative 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-in N/A

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

      8. metadata-eval N/A

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

      9. associate-*l* N/A

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

      10. fma-define N/A

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

      11. lft-mult-inverse N/A

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

      12. fma-undefine N/A

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

      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 99.4%

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

   5. Simplified 99.4%

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

   if -0.57999999999999996 < x < 0.599999999999999978

   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

      \[\leadsto \mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\color{blue}{\left(-4 \cdot x\right)}, 1\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\left(x \cdot -4\right), 1\right)\right) \]

      2. *-lowering-*.f64 99.0%

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, -4\right), 1\right)\right) \]

   5. Simplified 99.0%

      \[\leadsto 3 \cdot \left(\color{blue}{x \cdot -4} + 1\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.58:\\ \;\;\;\;x \cdot \left(x \cdot 9 + -12\right)\\ \mathbf{elif}\;x \leq 0.6:\\ \;\;\;\;3 \cdot \left(x \cdot -4 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot 9 + -12\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 9 \cdot \left(x \cdot x\right)\\ \mathbf{if}\;x \leq -1.55:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;3 \cdot \left(x \cdot -4 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* 9.0 (* x x))))
   (if (<= x -1.55) t_0 (if (<= x 1.0) (* 3.0 (+ (* x -4.0) 1.0)) t_0))))

C

double code(double x) {
	double t_0 = 9.0 * (x * x);
	double tmp;
	if (x <= -1.55) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = 3.0 * ((x * -4.0) + 1.0);
	} 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 <= (-1.55d0)) then
        tmp = t_0
    else if (x <= 1.0d0) then
        tmp = 3.0d0 * ((x * (-4.0d0)) + 1.0d0)
    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 <= -1.55) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = 3.0 * ((x * -4.0) + 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x):
	t_0 = 9.0 * (x * x)
	tmp = 0
	if x <= -1.55:
		tmp = t_0
	elif x <= 1.0:
		tmp = 3.0 * ((x * -4.0) + 1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x)
	t_0 = Float64(9.0 * Float64(x * x))
	tmp = 0.0
	if (x <= -1.55)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = Float64(3.0 * Float64(Float64(x * -4.0) + 1.0));
	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 <= -1.55)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = 3.0 * ((x * -4.0) + 1.0);
	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, -1.55], t$95$0, If[LessEqual[x, 1.0], N[(3.0 * N[(N[(x * -4.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55000000000000004 or 1 < x

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf

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

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

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

      2. unpow2 N/A

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

      3. *-lowering-*.f64 98.2%

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

   5. Simplified 98.2%

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

      1. associate-*r* N/A

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

      2. metadata-eval N/A

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 98.3%

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

   7. Applied egg-rr 98.3%

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

   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. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\color{blue}{\left(-4 \cdot x\right)}, 1\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\left(x \cdot -4\right), 1\right)\right) \]

      2. *-lowering-*.f64 99.0%

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, -4\right), 1\right)\right) \]

   5. Simplified 99.0%

      \[\leadsto 3 \cdot \left(\color{blue}{x \cdot -4} + 1\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55:\\ \;\;\;\;9 \cdot \left(x \cdot x\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;3 \cdot \left(x \cdot -4 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 9 \cdot \left(x \cdot x\right)\\ \mathbf{if}\;x \leq -1.55:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;3 + x \cdot -12\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* 9.0 (* x x))))
   (if (<= x -1.55) t_0 (if (<= x 1.0) (+ 3.0 (* x -12.0)) t_0))))

C

double code(double x) {
	double t_0 = 9.0 * (x * x);
	double tmp;
	if (x <= -1.55) {
		tmp = t_0;
	} else if (x <= 1.0) {
		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 = 9.0d0 * (x * x)
    if (x <= (-1.55d0)) then
        tmp = t_0
    else if (x <= 1.0d0) 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 = 9.0 * (x * x);
	double tmp;
	if (x <= -1.55) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = 3.0 + (x * -12.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x):
	t_0 = 9.0 * (x * x)
	tmp = 0
	if x <= -1.55:
		tmp = t_0
	elif x <= 1.0:
		tmp = 3.0 + (x * -12.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x)
	t_0 = Float64(9.0 * Float64(x * x))
	tmp = 0.0
	if (x <= -1.55)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = Float64(3.0 + Float64(x * -12.0));
	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 <= -1.55)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = 3.0 + (x * -12.0);
	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, -1.55], t$95$0, If[LessEqual[x, 1.0], N[(3.0 + N[(x * -12.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55000000000000004 or 1 < x

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf

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

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

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

      2. unpow2 N/A

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

      3. *-lowering-*.f64 98.2%

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

   5. Simplified 98.2%

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

      1. associate-*r* N/A

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

      2. metadata-eval N/A

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 98.3%

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

   7. Applied egg-rr 98.3%

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

   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 99.0%

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

4. Final simplification 98.7%

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

Alternative 6: 97.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 9 \cdot \left(x \cdot x\right)\\ \mathbf{if}\;x \leq -0.58:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.2:\\ \;\;\;\;3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* 9.0 (* x x)))) (if (<= x -0.58) t_0 (if (<= x 0.2) 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 <= 0.2) {
		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 <= 0.2d0) 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 <= 0.2) {
		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 <= 0.2:
		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 <= 0.2)
		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 <= 0.2)
		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, 0.2], 3.0, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.57999999999999996 or 0.20000000000000001 < x

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf

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

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

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

      2. unpow2 N/A

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

      3. *-lowering-*.f64 98.2%

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

   5. Simplified 98.2%

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

      1. associate-*r* N/A

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

      2. metadata-eval N/A

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 98.3%

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

   7. Applied egg-rr 98.3%

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

   if -0.57999999999999996 < x < 0.20000000000000001

   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 98.0%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.58:\\ \;\;\;\;9 \cdot \left(x \cdot x\right)\\ \mathbf{elif}\;x \leq 0.2:\\ \;\;\;\;3\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;x \leq -0.58:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.2:\\ \;\;\;\;3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* x (* x 9.0)))) (if (<= x -0.58) t_0 (if (<= x 0.2) 3.0 t_0))))

C

double code(double x) {
	double t_0 = x * (x * 9.0);
	double tmp;
	if (x <= -0.58) {
		tmp = t_0;
	} else if (x <= 0.2) {
		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 = x * (x * 9.0d0)
    if (x <= (-0.58d0)) then
        tmp = t_0
    else if (x <= 0.2d0) then
        tmp = 3.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = x * (x * 9.0);
	double tmp;
	if (x <= -0.58) {
		tmp = t_0;
	} else if (x <= 0.2) {
		tmp = 3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x):
	t_0 = x * (x * 9.0)
	tmp = 0
	if x <= -0.58:
		tmp = t_0
	elif x <= 0.2:
		tmp = 3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x)
	t_0 = Float64(x * Float64(x * 9.0))
	tmp = 0.0
	if (x <= -0.58)
		tmp = t_0;
	elseif (x <= 0.2)
		tmp = 3.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = x * (x * 9.0);
	tmp = 0.0;
	if (x <= -0.58)
		tmp = t_0;
	elseif (x <= 0.2)
		tmp = 3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(x * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.58], t$95$0, If[LessEqual[x, 0.2], 3.0, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.57999999999999996 or 0.20000000000000001 < x

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf

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

      1. unpow2 N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 98.2%

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

   5. Simplified 98.2%

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

   if -0.57999999999999996 < x < 0.20000000000000001

   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 98.0%

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

Alternative 8: 51.0% 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 99.4%

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

3. Taylor expanded in x around 0

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

5. Simplified 53.6%

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

Developer Target 1: 99.8% 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 2024149 
(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)))