Logistic function from Lakshay Garg

Percentage Accurate: 54.3% → 99.6%

Time: 8.3s

Alternatives: 6

Speedup: 5.3×

Specification

Math

\[\begin{array}{l} \\ \frac{2}{1 + e^{-2 \cdot x}} - 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))

C

double code(double x, double y) {
	return (2.0 / (1.0 + exp((-2.0 * x)))) - 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (2.0d0 / (1.0d0 + exp(((-2.0d0) * x)))) - 1.0d0
end function

Java

public static double code(double x, double y) {
	return (2.0 / (1.0 + Math.exp((-2.0 * x)))) - 1.0;
}

Python

def code(x, y):
	return (2.0 / (1.0 + math.exp((-2.0 * x)))) - 1.0

Julia

function code(x, y)
	return Float64(Float64(2.0 / Float64(1.0 + exp(Float64(-2.0 * x)))) - 1.0)
end

MATLAB

function tmp = code(x, y)
	tmp = (2.0 / (1.0 + exp((-2.0 * x)))) - 1.0;
end

Wolfram

code[x_, y_] := N[(N[(2.0 / N[(1.0 + N[Exp[N[(-2.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]

Initial Program: 54.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{2}{1 + e^{-2 \cdot x}} - 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))

C

double code(double x, double y) {
	return (2.0 / (1.0 + exp((-2.0 * x)))) - 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (2.0d0 / (1.0d0 + exp(((-2.0d0) * x)))) - 1.0d0
end function

Java

public static double code(double x, double y) {
	return (2.0 / (1.0 + Math.exp((-2.0 * x)))) - 1.0;
}

Python

def code(x, y):
	return (2.0 / (1.0 + math.exp((-2.0 * x)))) - 1.0

Julia

function code(x, y)
	return Float64(Float64(2.0 / Float64(1.0 + exp(Float64(-2.0 * x)))) - 1.0)
end

MATLAB

function tmp = code(x, y)
	tmp = (2.0 / (1.0 + exp((-2.0 * x)))) - 1.0;
end

Wolfram

code[x_, y_] := N[(N[(2.0 / N[(1.0 + N[Exp[N[(-2.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]

Alternative 1: 99.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-2 \cdot x \leq -2:\\ \;\;\;\;\frac{-2 \cdot \mathsf{expm1}\left(-2 \cdot x\right)}{1 - e^{x \cdot -4}} + -1\\ \mathbf{elif}\;-2 \cdot x \leq 0.0002:\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, x \cdot \left(x \cdot x\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* -2.0 x) -2.0)
   (+ (/ (* -2.0 (expm1 (* -2.0 x))) (- 1.0 (exp (* x -4.0)))) -1.0)
   (if (<= (* -2.0 x) 0.0002) (fma -0.3333333333333333 (* x (* x x)) x) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((-2.0 * x) <= -2.0) {
		tmp = ((-2.0 * expm1((-2.0 * x))) / (1.0 - exp((x * -4.0)))) + -1.0;
	} else if ((-2.0 * x) <= 0.0002) {
		tmp = fma(-0.3333333333333333, (x * (x * x)), x);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(-2.0 * x) <= -2.0)
		tmp = Float64(Float64(Float64(-2.0 * expm1(Float64(-2.0 * x))) / Float64(1.0 - exp(Float64(x * -4.0)))) + -1.0);
	elseif (Float64(-2.0 * x) <= 0.0002)
		tmp = fma(-0.3333333333333333, Float64(x * Float64(x * x)), x);
	else
		tmp = -1.0;
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[N[(-2.0 * x), $MachinePrecision], -2.0], N[(N[(N[(-2.0 * N[(Exp[N[(-2.0 * x), $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[Exp[N[(x * -4.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[N[(-2.0 * x), $MachinePrecision], 0.0002], N[(-0.3333333333333333 * N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], -1.0]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 #s(literal -2 binary64) x) < -2

   1. Initial program 100.0%

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip-+ N/A

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

      2. associate-/r/ N/A

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

      3. associate-*l/ N/A

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

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

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

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

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

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

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

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

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

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

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

      9. metadata-eval N/A

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

      10. --lowering--.f64 N/A

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

      11. prod-exp N/A

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

      12. exp-lowering-exp.f64 N/A

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

      13. distribute-rgt-out N/A

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

      14. metadata-eval N/A

          \[\leadsto \frac{2 \cdot \left(1 - e^{-2 \cdot x}\right)}{1 - e^{x \cdot \color{blue}{-4}}} - 1 \]

      15. metadata-eval N/A

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

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

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

      17. metadata-eval 100.0

          \[\leadsto \frac{2 \cdot \left(1 - e^{-2 \cdot x}\right)}{1 - e^{x \cdot \color{blue}{-4}}} - 1 \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{2 \cdot \left(1 - e^{-2 \cdot x}\right)}{1 - e^{x \cdot -4}}} - 1 \]

   5. Taylor expanded in x around inf

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. neg-sub0 N/A

         \[\leadsto \frac{2 \cdot \left(\color{blue}{\left(0 - e^{-2 \cdot x}\right)} + 1\right)}{1 - e^{x \cdot -4}} - 1 \]

      4. associate-+l- N/A

         \[\leadsto \frac{2 \cdot \color{blue}{\left(0 - \left(e^{-2 \cdot x} - 1\right)\right)}}{1 - e^{x \cdot -4}} - 1 \]

      5. sub0-neg N/A

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

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

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

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

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

      8. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{-2} \cdot \left(e^{-2 \cdot x} - 1\right)}{1 - e^{x \cdot -4}} - 1 \]

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. /-rgt-identity N/A

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

      12. metadata-eval N/A

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

      13. metadata-eval N/A

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

      14. distribute-neg-frac2 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. metadata-eval N/A

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

      18. metadata-eval N/A

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

      19. div-sub N/A

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

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

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

      21. div-sub N/A

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

   7. Simplified 100.0%

      \[\leadsto \frac{\color{blue}{-2 \cdot \mathsf{expm1}\left(x \cdot -2\right)}}{1 - e^{x \cdot -4}} - 1 \]

   if -2 < (*.f64 #s(literal -2 binary64) x) < 2.0000000000000001e-4

   1. Initial program 10.1%

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. distribute-lft-in N/A

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

      2. *-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

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

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

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

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

      9. unpow2 N/A

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

      10. *-lowering-*.f64 100.0

          \[\leadsto \mathsf{fma}\left(-0.3333333333333333, x \cdot \color{blue}{\left(x \cdot x\right)}, x\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, x \cdot \left(x \cdot x\right), x\right)} \]

   if 2.0000000000000001e-4 < (*.f64 #s(literal -2 binary64) x)

   1. Initial program 100.0%

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. metadata-eval N/A

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

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

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

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

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

      4. count-2 N/A

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

      5. +-lowering-+.f64 95.7

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

   5. Simplified 95.7%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1} \]
   7. Step-by-step derivation

   8. Simplified 100.0%

      \[\leadsto \color{blue}{-1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-2 \cdot x \leq -2:\\ \;\;\;\;\frac{-2 \cdot \mathsf{expm1}\left(-2 \cdot x\right)}{1 - e^{x \cdot -4}} + -1\\ \mathbf{elif}\;-2 \cdot x \leq 0.0002:\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, x \cdot \left(x \cdot x\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-2 \cdot x \leq -2:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} + -1\\ \mathbf{elif}\;-2 \cdot x \leq 0.0002:\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, x \cdot \left(x \cdot x\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* -2.0 x) -2.0)
   (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) -1.0)
   (if (<= (* -2.0 x) 0.0002) (fma -0.3333333333333333 (* x (* x x)) x) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((-2.0 * x) <= -2.0) {
		tmp = (2.0 / (1.0 + exp((-2.0 * x)))) + -1.0;
	} else if ((-2.0 * x) <= 0.0002) {
		tmp = fma(-0.3333333333333333, (x * (x * x)), x);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(-2.0 * x) <= -2.0)
		tmp = Float64(Float64(2.0 / Float64(1.0 + exp(Float64(-2.0 * x)))) + -1.0);
	elseif (Float64(-2.0 * x) <= 0.0002)
		tmp = fma(-0.3333333333333333, Float64(x * Float64(x * x)), x);
	else
		tmp = -1.0;
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[N[(-2.0 * x), $MachinePrecision], -2.0], N[(N[(2.0 / N[(1.0 + N[Exp[N[(-2.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[N[(-2.0 * x), $MachinePrecision], 0.0002], N[(-0.3333333333333333 * N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], -1.0]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 #s(literal -2 binary64) x) < -2

   1. Initial program 100.0%

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1 \]
   2. Add Preprocessing

   if -2 < (*.f64 #s(literal -2 binary64) x) < 2.0000000000000001e-4

   1. Initial program 10.1%

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. distribute-lft-in N/A

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

      2. *-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

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

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

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

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

      9. unpow2 N/A

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

      10. *-lowering-*.f64 100.0

          \[\leadsto \mathsf{fma}\left(-0.3333333333333333, x \cdot \color{blue}{\left(x \cdot x\right)}, x\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, x \cdot \left(x \cdot x\right), x\right)} \]

   if 2.0000000000000001e-4 < (*.f64 #s(literal -2 binary64) x)

   1. Initial program 100.0%

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. metadata-eval N/A

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

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

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

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

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

      4. count-2 N/A

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

      5. +-lowering-+.f64 95.7

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

   5. Simplified 95.7%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1} \]
   7. Step-by-step derivation

   8. Simplified 100.0%

      \[\leadsto \color{blue}{-1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-2 \cdot x \leq -2:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} + -1\\ \mathbf{elif}\;-2 \cdot x \leq 0.0002:\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, x \cdot \left(x \cdot x\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-2 \cdot x \leq -2:\\ \;\;\;\;1\\ \mathbf{elif}\;-2 \cdot x \leq 0.0002:\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, x \cdot \left(x \cdot x\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* -2.0 x) -2.0)
   1.0
   (if (<= (* -2.0 x) 0.0002) (fma -0.3333333333333333 (* x (* x x)) x) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((-2.0 * x) <= -2.0) {
		tmp = 1.0;
	} else if ((-2.0 * x) <= 0.0002) {
		tmp = fma(-0.3333333333333333, (x * (x * x)), x);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(-2.0 * x) <= -2.0)
		tmp = 1.0;
	elseif (Float64(-2.0 * x) <= 0.0002)
		tmp = fma(-0.3333333333333333, Float64(x * Float64(x * x)), x);
	else
		tmp = -1.0;
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[N[(-2.0 * x), $MachinePrecision], -2.0], 1.0, If[LessEqual[N[(-2.0 * x), $MachinePrecision], 0.0002], N[(-0.3333333333333333 * N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], -1.0]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 #s(literal -2 binary64) x) < -2

   1. Initial program 100.0%

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. metadata-eval N/A

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

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

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

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

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

      4. count-2 N/A

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

      5. +-lowering-+.f64 1.6

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

   5. Simplified 1.6%

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

   7. Applied egg-rr 98.8%

      \[\leadsto \frac{2}{2 - \color{blue}{\frac{x + x}{x + x}}} - 1 \]
   8. Step-by-step derivation

      1. div-inv N/A

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

      2. *-inverses N/A

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

      3. metadata-eval N/A

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

      4. *-inverses N/A

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

      5. clear-num N/A

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

      6. *-inverses N/A

         \[\leadsto 2 \cdot \color{blue}{1} - 1 \]

      7. metadata-eval N/A

         \[\leadsto \color{blue}{2} - 1 \]

      8. metadata-eval 98.8

         \[\leadsto \color{blue}{1} \]

   9. Applied egg-rr 98.8%

      \[\leadsto \color{blue}{1} \]

   if -2 < (*.f64 #s(literal -2 binary64) x) < 2.0000000000000001e-4

   1. Initial program 10.1%

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. distribute-lft-in N/A

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

      2. *-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

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

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

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

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

      9. unpow2 N/A

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

      10. *-lowering-*.f64 100.0

          \[\leadsto \mathsf{fma}\left(-0.3333333333333333, x \cdot \color{blue}{\left(x \cdot x\right)}, x\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, x \cdot \left(x \cdot x\right), x\right)} \]

   if 2.0000000000000001e-4 < (*.f64 #s(literal -2 binary64) x)

   1. Initial program 100.0%

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. metadata-eval N/A

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

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

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

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

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

      4. count-2 N/A

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

      5. +-lowering-+.f64 95.7

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

   5. Simplified 95.7%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1} \]
   7. Step-by-step derivation

   8. Simplified 100.0%

      \[\leadsto \color{blue}{-1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 99.3% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-2 \cdot x \leq -2:\\ \;\;\;\;1\\ \mathbf{elif}\;-2 \cdot x \leq 0.0002:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* -2.0 x) -2.0) 1.0 (if (<= (* -2.0 x) 0.0002) x -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((-2.0 * x) <= -2.0) {
		tmp = 1.0;
	} else if ((-2.0 * x) <= 0.0002) {
		tmp = x;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (((-2.0d0) * x) <= (-2.0d0)) then
        tmp = 1.0d0
    else if (((-2.0d0) * x) <= 0.0002d0) then
        tmp = x
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((-2.0 * x) <= -2.0) {
		tmp = 1.0;
	} else if ((-2.0 * x) <= 0.0002) {
		tmp = x;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (-2.0 * x) <= -2.0:
		tmp = 1.0
	elif (-2.0 * x) <= 0.0002:
		tmp = x
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(-2.0 * x) <= -2.0)
		tmp = 1.0;
	elseif (Float64(-2.0 * x) <= 0.0002)
		tmp = x;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((-2.0 * x) <= -2.0)
		tmp = 1.0;
	elseif ((-2.0 * x) <= 0.0002)
		tmp = x;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(-2.0 * x), $MachinePrecision], -2.0], 1.0, If[LessEqual[N[(-2.0 * x), $MachinePrecision], 0.0002], x, -1.0]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 #s(literal -2 binary64) x) < -2

   1. Initial program 100.0%

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. metadata-eval N/A

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

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

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

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

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

      4. count-2 N/A

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

      5. +-lowering-+.f64 1.6

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

   5. Simplified 1.6%

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

   7. Applied egg-rr 98.8%

      \[\leadsto \frac{2}{2 - \color{blue}{\frac{x + x}{x + x}}} - 1 \]
   8. Step-by-step derivation

      1. div-inv N/A

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

      2. *-inverses N/A

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

      3. metadata-eval N/A

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

      4. *-inverses N/A

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

      5. clear-num N/A

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

      6. *-inverses N/A

         \[\leadsto 2 \cdot \color{blue}{1} - 1 \]

      7. metadata-eval N/A

         \[\leadsto \color{blue}{2} - 1 \]

      8. metadata-eval 98.8

         \[\leadsto \color{blue}{1} \]

   9. Applied egg-rr 98.8%

      \[\leadsto \color{blue}{1} \]

   if -2 < (*.f64 #s(literal -2 binary64) x) < 2.0000000000000001e-4

   1. Initial program 10.1%

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 99.2%

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

   if 2.0000000000000001e-4 < (*.f64 #s(literal -2 binary64) x)

   1. Initial program 100.0%

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. metadata-eval N/A

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

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

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

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

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

      4. count-2 N/A

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

      5. +-lowering-+.f64 95.7

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

   5. Simplified 95.7%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1} \]
   7. Step-by-step derivation

   8. Simplified 100.0%

      \[\leadsto \color{blue}{-1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 52.7% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-310}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -1e-310) -1.0 1.0))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1e-310) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1d-310)) then
        tmp = -1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1e-310) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1e-310:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1e-310)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1e-310)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1e-310], -1.0, 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -9.999999999999969e-311

   1. Initial program 55.2%

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. metadata-eval N/A

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

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

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

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

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

      4. count-2 N/A

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

      5. +-lowering-+.f64 52.2

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

   5. Simplified 52.2%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1} \]
   7. Step-by-step derivation

   8. Simplified 52.9%

      \[\leadsto \color{blue}{-1} \]

   if -9.999999999999969e-311 < x

   1. Initial program 51.7%

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. metadata-eval N/A

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

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

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

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

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

      4. count-2 N/A

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

      5. +-lowering-+.f64 5.8

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

   5. Simplified 5.8%

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

   7. Applied egg-rr 48.8%

      \[\leadsto \frac{2}{2 - \color{blue}{\frac{x + x}{x + x}}} - 1 \]
   8. Step-by-step derivation

      1. div-inv N/A

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

      2. *-inverses N/A

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

      3. metadata-eval N/A

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

      4. *-inverses N/A

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

      5. clear-num N/A

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

      6. *-inverses N/A

         \[\leadsto 2 \cdot \color{blue}{1} - 1 \]

      7. metadata-eval N/A

         \[\leadsto \color{blue}{2} - 1 \]

      8. metadata-eval 48.8

         \[\leadsto \color{blue}{1} \]

   9. Applied egg-rr 48.8%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 27.8% accurate, 123.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 -1.0)

C

double code(double x, double y) {
	return -1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -1.0d0
end function

Java

public static double code(double x, double y) {
	return -1.0;
}

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

function tmp = code(x, y)
	tmp = -1.0;
end

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 53.3%

   \[\frac{2}{1 + e^{-2 \cdot x}} - 1 \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

   1. metadata-eval N/A

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

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

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

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

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

   4. count-2 N/A

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

   5. +-lowering-+.f64 26.8

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

5. Simplified 26.8%

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

6. Taylor expanded in x around inf

   \[\leadsto \color{blue}{-1} \]
7. Step-by-step derivation

8. Simplified 25.0%

   \[\leadsto \color{blue}{-1} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024198 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  :precision binary64
  (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))