Graphics.Rendering.Chart.Plot.Vectors:renderPlotVectors from Chart-1.5.3

Percentage Accurate: 77.9% → 100.0%

Time: 5.7s

Alternatives: 7

Speedup: 1.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x + ((1.0 - x) * (1.0 - y))

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x + ((1.0 - x) * (1.0 - y))

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (1.0 + (y * x)) - y

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.4%

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

   1. sub-neg N/A

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

   2. distribute-rgt-in N/A

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

   3. sub-neg N/A

      \[\leadsto x + \left(1 \cdot \left(1 + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   4. +-commutative N/A

      \[\leadsto x + \left(1 \cdot \left(\left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   5. distribute-lft-in N/A

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

   6. metadata-eval N/A

      \[\leadsto x + \left(\left(1 \cdot \left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   7. associate-+l+ N/A

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

   8. associate-+r+ N/A

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

   9. *-lft-identity N/A

      \[\leadsto \left(x + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   10. neg-mul-1 N/A

       \[\leadsto \left(x + -1 \cdot x\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   11. distribute-rgt1-in N/A

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

   12. metadata-eval N/A

       \[\leadsto 0 \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   13. metadata-eval N/A

       \[\leadsto \left(0 \cdot -1\right) \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   14. associate-*r* N/A

       \[\leadsto 0 \cdot \left(-1 \cdot x\right) + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   15. neg-mul-1 N/A

       \[\leadsto 0 \cdot \left(\mathsf{neg}\left(x\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   16. *-lft-identity N/A

       \[\leadsto 0 \cdot \left(1 \cdot \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   17. mul0-lft N/A

       \[\leadsto 0 + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   18. +-lft-identity N/A

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

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

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

   20. *-commutative N/A

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

   21. neg-mul-1 N/A

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

   22. associate-*r* N/A

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

   23. *-commutative N/A

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

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

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{1 + y \cdot \left(x + -1\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. distribute-rgt-in N/A

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

   2. associate-+r+ N/A

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

   3. mul-1-neg N/A

      \[\leadsto \left(1 + x \cdot y\right) + \left(\mathsf{neg}\left(y\right)\right) \]

   4. unsub-neg N/A

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

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

      \[\leadsto \mathsf{\_.f64}\left(\left(1 + x \cdot y\right), \color{blue}{y}\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(1, \left(x \cdot y\right)\right), y\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(1, \left(y \cdot x\right)\right), y\right) \]

   8. *-lowering-*.f64 100.0%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, x\right)\right), y\right) \]

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\left(1 + y \cdot x\right) - y} \]
7. Add Preprocessing

Alternative 2: 61.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;0 - y\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-56}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+102}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;0 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   (- 0.0 y)
   (if (<= y 3.9e-56) 1.0 (if (<= y 7.5e+102) (* y x) (- 0.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 0.0 - y;
	} else if (y <= 3.9e-56) {
		tmp = 1.0;
	} else if (y <= 7.5e+102) {
		tmp = y * x;
	} else {
		tmp = 0.0 - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.0d0)) then
        tmp = 0.0d0 - y
    else if (y <= 3.9d-56) then
        tmp = 1.0d0
    else if (y <= 7.5d+102) then
        tmp = y * x
    else
        tmp = 0.0d0 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 0.0 - y;
	} else if (y <= 3.9e-56) {
		tmp = 1.0;
	} else if (y <= 7.5e+102) {
		tmp = y * x;
	} else {
		tmp = 0.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 0.0 - y
	elif y <= 3.9e-56:
		tmp = 1.0
	elif y <= 7.5e+102:
		tmp = y * x
	else:
		tmp = 0.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(0.0 - y);
	elseif (y <= 3.9e-56)
		tmp = 1.0;
	elseif (y <= 7.5e+102)
		tmp = Float64(y * x);
	else
		tmp = Float64(0.0 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = 0.0 - y;
	elseif (y <= 3.9e-56)
		tmp = 1.0;
	elseif (y <= 7.5e+102)
		tmp = y * x;
	else
		tmp = 0.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], N[(0.0 - y), $MachinePrecision], If[LessEqual[y, 3.9e-56], 1.0, If[LessEqual[y, 7.5e+102], N[(y * x), $MachinePrecision], N[(0.0 - y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 7.5e102 < y

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. sub-neg N/A

         \[\leadsto x + \left(1 \cdot \left(1 + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(1 \cdot \left(\left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

         \[\leadsto x + \left(\left(1 \cdot \left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      7. associate-+l+ N/A

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

      8. associate-+r+ N/A

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

      9. *-lft-identity N/A

         \[\leadsto \left(x + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      10. neg-mul-1 N/A

          \[\leadsto \left(x + -1 \cdot x\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      11. distribute-rgt1-in N/A

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

      12. metadata-eval N/A

          \[\leadsto 0 \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \left(0 \cdot -1\right) \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto 0 \cdot \left(-1 \cdot x\right) + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      15. neg-mul-1 N/A

          \[\leadsto 0 \cdot \left(\mathsf{neg}\left(x\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto 0 \cdot \left(1 \cdot \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      17. mul0-lft N/A

          \[\leadsto 0 + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      18. +-lft-identity N/A

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

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

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

      20. *-commutative N/A

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

      21. neg-mul-1 N/A

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

      22. associate-*r* N/A

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

      23. *-commutative N/A

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

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

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + y \cdot \left(x + -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + -1 \cdot y} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto 1 + \left(\mathsf{neg}\left(y\right)\right) \]

      2. unsub-neg N/A

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

      3. --lowering--.f64 63.5%

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{y}\right) \]

   7. Simplified 63.5%

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

   8. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{y} \]

      3. --lowering--.f64 63.3%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{y}\right) \]

   10. Simplified 63.3%

       \[\leadsto \color{blue}{0 - y} \]
   11. Step-by-step derivation

       1. sub0-neg N/A

          \[\leadsto \mathsf{neg}\left(y\right) \]

       2. neg-lowering-neg.f64 63.3%

          \[\leadsto \mathsf{neg.f64}\left(y\right) \]

   12. Applied egg-rr 63.3%

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

   if -1 < y < 3.9e-56

   1. Initial program 59.5%

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. sub-neg N/A

         \[\leadsto x + \left(1 \cdot \left(1 + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(1 \cdot \left(\left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

         \[\leadsto x + \left(\left(1 \cdot \left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      7. associate-+l+ N/A

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

      8. associate-+r+ N/A

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

      9. *-lft-identity N/A

         \[\leadsto \left(x + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      10. neg-mul-1 N/A

          \[\leadsto \left(x + -1 \cdot x\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      11. distribute-rgt1-in N/A

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

      12. metadata-eval N/A

          \[\leadsto 0 \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \left(0 \cdot -1\right) \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto 0 \cdot \left(-1 \cdot x\right) + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      15. neg-mul-1 N/A

          \[\leadsto 0 \cdot \left(\mathsf{neg}\left(x\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto 0 \cdot \left(1 \cdot \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      17. mul0-lft N/A

          \[\leadsto 0 + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      18. +-lft-identity N/A

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

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

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

      20. *-commutative N/A

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

      21. neg-mul-1 N/A

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

      22. associate-*r* N/A

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

      23. *-commutative N/A

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

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

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + y \cdot \left(x + -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0

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

   7. Simplified 78.7%

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

   if 3.9e-56 < y < 7.5e102

   1. Initial program 85.1%

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. sub-neg N/A

         \[\leadsto x + \left(1 \cdot \left(1 + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(1 \cdot \left(\left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

         \[\leadsto x + \left(\left(1 \cdot \left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      7. associate-+l+ N/A

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

      8. associate-+r+ N/A

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

      9. *-lft-identity N/A

         \[\leadsto \left(x + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      10. neg-mul-1 N/A

          \[\leadsto \left(x + -1 \cdot x\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      11. distribute-rgt1-in N/A

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

      12. metadata-eval N/A

          \[\leadsto 0 \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \left(0 \cdot -1\right) \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto 0 \cdot \left(-1 \cdot x\right) + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      15. neg-mul-1 N/A

          \[\leadsto 0 \cdot \left(\mathsf{neg}\left(x\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto 0 \cdot \left(1 \cdot \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      17. mul0-lft N/A

          \[\leadsto 0 + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      18. +-lft-identity N/A

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

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

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

      20. *-commutative N/A

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

      21. neg-mul-1 N/A

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

      22. associate-*r* N/A

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

      23. *-commutative N/A

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

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

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + y \cdot \left(x + -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 62.0%

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

   7. Simplified 62.0%

      \[\leadsto \color{blue}{y \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;0 - y\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-56}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+102}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;0 - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + y \cdot x\\ \mathbf{if}\;x \leq -290:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-21}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* y x))))
   (if (<= x -290.0) t_0 (if (<= x 5.8e-21) (- 1.0 y) t_0))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (y * x);
	double tmp;
	if (x <= -290.0) {
		tmp = t_0;
	} else if (x <= 5.8e-21) {
		tmp = 1.0 - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + (y * x)
    if (x <= (-290.0d0)) then
        tmp = t_0
    else if (x <= 5.8d-21) then
        tmp = 1.0d0 - y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + (y * x);
	double tmp;
	if (x <= -290.0) {
		tmp = t_0;
	} else if (x <= 5.8e-21) {
		tmp = 1.0 - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (y * x)
	tmp = 0
	if x <= -290.0:
		tmp = t_0
	elif x <= 5.8e-21:
		tmp = 1.0 - y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(y * x))
	tmp = 0.0
	if (x <= -290.0)
		tmp = t_0;
	elseif (x <= 5.8e-21)
		tmp = Float64(1.0 - y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (y * x);
	tmp = 0.0;
	if (x <= -290.0)
		tmp = t_0;
	elseif (x <= 5.8e-21)
		tmp = 1.0 - y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -290.0], t$95$0, If[LessEqual[x, 5.8e-21], N[(1.0 - y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -290 or 5.8e-21 < x

   1. Initial program 49.8%

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. sub-neg N/A

         \[\leadsto x + \left(1 \cdot \left(1 + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(1 \cdot \left(\left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

         \[\leadsto x + \left(\left(1 \cdot \left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      7. associate-+l+ N/A

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

      8. associate-+r+ N/A

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

      9. *-lft-identity N/A

         \[\leadsto \left(x + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      10. neg-mul-1 N/A

          \[\leadsto \left(x + -1 \cdot x\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      11. distribute-rgt1-in N/A

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

      12. metadata-eval N/A

          \[\leadsto 0 \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \left(0 \cdot -1\right) \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto 0 \cdot \left(-1 \cdot x\right) + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      15. neg-mul-1 N/A

          \[\leadsto 0 \cdot \left(\mathsf{neg}\left(x\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto 0 \cdot \left(1 \cdot \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      17. mul0-lft N/A

          \[\leadsto 0 + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      18. +-lft-identity N/A

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

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

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

      20. *-commutative N/A

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

      21. neg-mul-1 N/A

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

      22. associate-*r* N/A

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

      23. *-commutative N/A

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

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

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + y \cdot \left(x + -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 99.5%

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

   7. Simplified 99.5%

      \[\leadsto 1 + \color{blue}{y \cdot x} \]

   if -290 < x < 5.8e-21

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. sub-neg N/A

         \[\leadsto x + \left(1 \cdot \left(1 + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(1 \cdot \left(\left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

         \[\leadsto x + \left(\left(1 \cdot \left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      7. associate-+l+ N/A

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

      8. associate-+r+ N/A

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

      9. *-lft-identity N/A

         \[\leadsto \left(x + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      10. neg-mul-1 N/A

          \[\leadsto \left(x + -1 \cdot x\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      11. distribute-rgt1-in N/A

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

      12. metadata-eval N/A

          \[\leadsto 0 \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \left(0 \cdot -1\right) \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto 0 \cdot \left(-1 \cdot x\right) + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      15. neg-mul-1 N/A

          \[\leadsto 0 \cdot \left(\mathsf{neg}\left(x\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto 0 \cdot \left(1 \cdot \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      17. mul0-lft N/A

          \[\leadsto 0 + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      18. +-lft-identity N/A

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

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

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

      20. *-commutative N/A

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

      21. neg-mul-1 N/A

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

      22. associate-*r* N/A

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

      23. *-commutative N/A

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

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

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + y \cdot \left(x + -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + -1 \cdot y} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto 1 + \left(\mathsf{neg}\left(y\right)\right) \]

      2. unsub-neg N/A

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

      3. --lowering--.f64 99.1%

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{y}\right) \]

   7. Simplified 99.1%

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

Alternative 4: 87.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+35}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 10^{+15}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -8.2e+35) (* y x) (if (<= x 1e+15) (- 1.0 y) (* y x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -8.2e+35) {
		tmp = y * x;
	} else if (x <= 1e+15) {
		tmp = 1.0 - y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-8.2d+35)) then
        tmp = y * x
    else if (x <= 1d+15) then
        tmp = 1.0d0 - y
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -8.2e+35) {
		tmp = y * x;
	} else if (x <= 1e+15) {
		tmp = 1.0 - y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -8.2e+35:
		tmp = y * x
	elif x <= 1e+15:
		tmp = 1.0 - y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -8.2e+35)
		tmp = Float64(y * x);
	elseif (x <= 1e+15)
		tmp = Float64(1.0 - y);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -8.2e+35)
		tmp = y * x;
	elseif (x <= 1e+15)
		tmp = 1.0 - y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -8.2e+35], N[(y * x), $MachinePrecision], If[LessEqual[x, 1e+15], N[(1.0 - y), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.1999999999999997e35 or 1e15 < x

   1. Initial program 48.8%

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. sub-neg N/A

         \[\leadsto x + \left(1 \cdot \left(1 + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(1 \cdot \left(\left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

         \[\leadsto x + \left(\left(1 \cdot \left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      7. associate-+l+ N/A

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

      8. associate-+r+ N/A

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

      9. *-lft-identity N/A

         \[\leadsto \left(x + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      10. neg-mul-1 N/A

          \[\leadsto \left(x + -1 \cdot x\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      11. distribute-rgt1-in N/A

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

      12. metadata-eval N/A

          \[\leadsto 0 \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \left(0 \cdot -1\right) \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto 0 \cdot \left(-1 \cdot x\right) + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      15. neg-mul-1 N/A

          \[\leadsto 0 \cdot \left(\mathsf{neg}\left(x\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto 0 \cdot \left(1 \cdot \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      17. mul0-lft N/A

          \[\leadsto 0 + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      18. +-lft-identity N/A

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

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

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

      20. *-commutative N/A

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

      21. neg-mul-1 N/A

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

      22. associate-*r* N/A

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

      23. *-commutative N/A

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

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

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + y \cdot \left(x + -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 76.0%

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

   7. Simplified 76.0%

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

   if -8.1999999999999997e35 < x < 1e15

   1. Initial program 98.0%

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. sub-neg N/A

         \[\leadsto x + \left(1 \cdot \left(1 + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(1 \cdot \left(\left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

         \[\leadsto x + \left(\left(1 \cdot \left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      7. associate-+l+ N/A

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

      8. associate-+r+ N/A

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

      9. *-lft-identity N/A

         \[\leadsto \left(x + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      10. neg-mul-1 N/A

          \[\leadsto \left(x + -1 \cdot x\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      11. distribute-rgt1-in N/A

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

      12. metadata-eval N/A

          \[\leadsto 0 \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \left(0 \cdot -1\right) \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto 0 \cdot \left(-1 \cdot x\right) + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      15. neg-mul-1 N/A

          \[\leadsto 0 \cdot \left(\mathsf{neg}\left(x\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto 0 \cdot \left(1 \cdot \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      17. mul0-lft N/A

          \[\leadsto 0 + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      18. +-lft-identity N/A

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

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

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

      20. *-commutative N/A

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

      21. neg-mul-1 N/A

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

      22. associate-*r* N/A

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

      23. *-commutative N/A

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

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

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + y \cdot \left(x + -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + -1 \cdot y} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto 1 + \left(\mathsf{neg}\left(y\right)\right) \]

      2. unsub-neg N/A

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

      3. --lowering--.f64 97.9%

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{y}\right) \]

   7. Simplified 97.9%

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

Alternative 5: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;0 - y\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) (- 0.0 y) (if (<= y 1.8e-7) 1.0 (- 0.0 y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 0.0 - y;
	} else if (y <= 1.8e-7) {
		tmp = 1.0;
	} else {
		tmp = 0.0 - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.0d0)) then
        tmp = 0.0d0 - y
    else if (y <= 1.8d-7) then
        tmp = 1.0d0
    else
        tmp = 0.0d0 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 0.0 - y;
	} else if (y <= 1.8e-7) {
		tmp = 1.0;
	} else {
		tmp = 0.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 0.0 - y
	elif y <= 1.8e-7:
		tmp = 1.0
	else:
		tmp = 0.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(0.0 - y);
	elseif (y <= 1.8e-7)
		tmp = 1.0;
	else
		tmp = Float64(0.0 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = 0.0 - y;
	elseif (y <= 1.8e-7)
		tmp = 1.0;
	else
		tmp = 0.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], N[(0.0 - y), $MachinePrecision], If[LessEqual[y, 1.8e-7], 1.0, N[(0.0 - y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.79999999999999997e-7 < y

   1. Initial program 99.7%

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. sub-neg N/A

         \[\leadsto x + \left(1 \cdot \left(1 + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(1 \cdot \left(\left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

         \[\leadsto x + \left(\left(1 \cdot \left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      7. associate-+l+ N/A

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

      8. associate-+r+ N/A

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

      9. *-lft-identity N/A

         \[\leadsto \left(x + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      10. neg-mul-1 N/A

          \[\leadsto \left(x + -1 \cdot x\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      11. distribute-rgt1-in N/A

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

      12. metadata-eval N/A

          \[\leadsto 0 \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \left(0 \cdot -1\right) \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto 0 \cdot \left(-1 \cdot x\right) + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      15. neg-mul-1 N/A

          \[\leadsto 0 \cdot \left(\mathsf{neg}\left(x\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto 0 \cdot \left(1 \cdot \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      17. mul0-lft N/A

          \[\leadsto 0 + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      18. +-lft-identity N/A

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

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

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

      20. *-commutative N/A

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

      21. neg-mul-1 N/A

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

      22. associate-*r* N/A

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

      23. *-commutative N/A

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

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

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + y \cdot \left(x + -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + -1 \cdot y} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto 1 + \left(\mathsf{neg}\left(y\right)\right) \]

      2. unsub-neg N/A

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

      3. --lowering--.f64 57.3%

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{y}\right) \]

   7. Simplified 57.3%

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

   8. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{y} \]

      3. --lowering--.f64 56.4%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{y}\right) \]

   10. Simplified 56.4%

       \[\leadsto \color{blue}{0 - y} \]
   11. Step-by-step derivation

       1. sub0-neg N/A

          \[\leadsto \mathsf{neg}\left(y\right) \]

       2. neg-lowering-neg.f64 56.4%

          \[\leadsto \mathsf{neg.f64}\left(y\right) \]

   12. Applied egg-rr 56.4%

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

   if -1 < y < 1.79999999999999997e-7

   1. Initial program 58.4%

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. sub-neg N/A

         \[\leadsto x + \left(1 \cdot \left(1 + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(1 \cdot \left(\left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

         \[\leadsto x + \left(\left(1 \cdot \left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      7. associate-+l+ N/A

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

      8. associate-+r+ N/A

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

      9. *-lft-identity N/A

         \[\leadsto \left(x + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      10. neg-mul-1 N/A

          \[\leadsto \left(x + -1 \cdot x\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      11. distribute-rgt1-in N/A

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

      12. metadata-eval N/A

          \[\leadsto 0 \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \left(0 \cdot -1\right) \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto 0 \cdot \left(-1 \cdot x\right) + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      15. neg-mul-1 N/A

          \[\leadsto 0 \cdot \left(\mathsf{neg}\left(x\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto 0 \cdot \left(1 \cdot \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      17. mul0-lft N/A

          \[\leadsto 0 + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

      18. +-lft-identity N/A

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

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

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

      20. *-commutative N/A

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

      21. neg-mul-1 N/A

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

      22. associate-*r* N/A

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

      23. *-commutative N/A

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

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

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + y \cdot \left(x + -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0

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

   7. Simplified 75.7%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;0 - y\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0 - y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0 + (y * (x + -1.0))

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.4%

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

   1. sub-neg N/A

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

   2. distribute-rgt-in N/A

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

   3. sub-neg N/A

      \[\leadsto x + \left(1 \cdot \left(1 + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   4. +-commutative N/A

      \[\leadsto x + \left(1 \cdot \left(\left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   5. distribute-lft-in N/A

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

   6. metadata-eval N/A

      \[\leadsto x + \left(\left(1 \cdot \left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   7. associate-+l+ N/A

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

   8. associate-+r+ N/A

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

   9. *-lft-identity N/A

      \[\leadsto \left(x + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   10. neg-mul-1 N/A

       \[\leadsto \left(x + -1 \cdot x\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   11. distribute-rgt1-in N/A

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

   12. metadata-eval N/A

       \[\leadsto 0 \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   13. metadata-eval N/A

       \[\leadsto \left(0 \cdot -1\right) \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   14. associate-*r* N/A

       \[\leadsto 0 \cdot \left(-1 \cdot x\right) + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   15. neg-mul-1 N/A

       \[\leadsto 0 \cdot \left(\mathsf{neg}\left(x\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   16. *-lft-identity N/A

       \[\leadsto 0 \cdot \left(1 \cdot \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   17. mul0-lft N/A

       \[\leadsto 0 + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   18. +-lft-identity N/A

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

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

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

   20. *-commutative N/A

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

   21. neg-mul-1 N/A

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

   22. associate-*r* N/A

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

   23. *-commutative N/A

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

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

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{1 + y \cdot \left(x + -1\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 7: 39.3% accurate, 9.0× 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 77.4%

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

   1. sub-neg N/A

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

   2. distribute-rgt-in N/A

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

   3. sub-neg N/A

      \[\leadsto x + \left(1 \cdot \left(1 + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   4. +-commutative N/A

      \[\leadsto x + \left(1 \cdot \left(\left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   5. distribute-lft-in N/A

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

   6. metadata-eval N/A

      \[\leadsto x + \left(\left(1 \cdot \left(\mathsf{neg}\left(x\right)\right) + 1\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   7. associate-+l+ N/A

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

   8. associate-+r+ N/A

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

   9. *-lft-identity N/A

      \[\leadsto \left(x + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   10. neg-mul-1 N/A

       \[\leadsto \left(x + -1 \cdot x\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   11. distribute-rgt1-in N/A

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

   12. metadata-eval N/A

       \[\leadsto 0 \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   13. metadata-eval N/A

       \[\leadsto \left(0 \cdot -1\right) \cdot x + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   14. associate-*r* N/A

       \[\leadsto 0 \cdot \left(-1 \cdot x\right) + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   15. neg-mul-1 N/A

       \[\leadsto 0 \cdot \left(\mathsf{neg}\left(x\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   16. *-lft-identity N/A

       \[\leadsto 0 \cdot \left(1 \cdot \left(\mathsf{neg}\left(x\right)\right)\right) + \left(1 + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   17. mul0-lft N/A

       \[\leadsto 0 + \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right) \cdot \left(1 - x\right)\right) \]

   18. +-lft-identity N/A

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

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

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

   20. *-commutative N/A

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

   21. neg-mul-1 N/A

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

   22. associate-*r* N/A

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

   23. *-commutative N/A

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

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

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{1 + y \cdot \left(x + -1\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0

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

7. Simplified 42.0%

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

Developer Target 1: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (y * x) - (y - 1.0)

Julia

function code(x, y)
	return Float64(Float64(y * x) - Float64(y - 1.0))
end

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(y * x), $MachinePrecision] - N[(y - 1.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024160 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.Vectors:renderPlotVectors from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- (* y x) (- y 1)))

  (+ x (* (- 1.0 x) (- 1.0 y))))