Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3

Percentage Accurate: 84.8% → 96.2%

Time: 9.1s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (- y z)) y))

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return (x * (y - z)) / y

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (- y z)) y))

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return (x * (y - z)) / y

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{z}{-y}, x, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (/ z (- y)) x x))

C

double code(double x, double y, double z) {
	return fma((z / -y), x, x);
}

Julia

function code(x, y, z)
	return fma(Float64(z / Float64(-y)), x, x)
end

Wolfram

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

Derivation

1. Initial program 84.6%

   \[\frac{x \cdot \left(y - z\right)}{y} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. remove-double-neg N/A

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

   4. remove-double-neg N/A

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

   5. lift-*.f64 N/A

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

   6. associate-/l* N/A

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]

   7. *-commutative N/A

      \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]

   8. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]

   9. lower-/.f64 95.8

      \[\leadsto \color{blue}{\frac{y - z}{y}} \cdot x \]

4. Applied rewrites 95.8%

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

   1. lift--.f64 N/A

      \[\leadsto \frac{\color{blue}{y - z}}{y} \cdot x \]

   2. associate-*l/ N/A

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

   3. *-commutative N/A

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

   4. associate-*l/ N/A

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

   5. lift-/.f64 N/A

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

   6. lift--.f64 N/A

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

   7. sub-neg N/A

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

   8. +-commutative N/A

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

   9. distribute-rgt-in N/A

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

   10. lift-/.f64 N/A

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

   11. associate-/l* N/A

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

   12. *-commutative N/A

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

   13. associate-/l* N/A

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

   14. *-inverses N/A

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

   15. *-rgt-identity N/A

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

   16. lift-/.f64 N/A

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

   17. clear-num N/A

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

   18. associate-/r/ N/A

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

   19. lift-/.f64 N/A

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

   20. associate-*r* N/A

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

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

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

   22. lift-/.f64 N/A

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

   23. div-inv N/A

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

   24. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(\frac{z}{y}\right), x, x\right)} \]

6. Applied rewrites 95.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{-y}, x, x\right)} \]
7. Add Preprocessing

Alternative 2: 53.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{if}\;t\_0 \leq 0:\\ \;\;\;\;-x \cdot \frac{z}{y}\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+171}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_0 \leq 10^{+305}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x (- y z)) y)))
   (if (<= t_0 0.0)
     (- (* x (/ z y)))
     (if (<= t_0 2e+171)
       x
       (if (<= t_0 1e+305) (/ (* x (- z)) y) (* y (/ x y)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * (y - z)) / y;
	double tmp;
	if (t_0 <= 0.0) {
		tmp = -(x * (z / y));
	} else if (t_0 <= 2e+171) {
		tmp = x;
	} else if (t_0 <= 1e+305) {
		tmp = (x * -z) / y;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * (y - z)) / y
    if (t_0 <= 0.0d0) then
        tmp = -(x * (z / y))
    else if (t_0 <= 2d+171) then
        tmp = x
    else if (t_0 <= 1d+305) then
        tmp = (x * -z) / y
    else
        tmp = y * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * (y - z)) / y;
	double tmp;
	if (t_0 <= 0.0) {
		tmp = -(x * (z / y));
	} else if (t_0 <= 2e+171) {
		tmp = x;
	} else if (t_0 <= 1e+305) {
		tmp = (x * -z) / y;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * (y - z)) / y
	tmp = 0
	if t_0 <= 0.0:
		tmp = -(x * (z / y))
	elif t_0 <= 2e+171:
		tmp = x
	elif t_0 <= 1e+305:
		tmp = (x * -z) / y
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(y - z)) / y)
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = Float64(-Float64(x * Float64(z / y)));
	elseif (t_0 <= 2e+171)
		tmp = x;
	elseif (t_0 <= 1e+305)
		tmp = Float64(Float64(x * Float64(-z)) / y);
	else
		tmp = Float64(y * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * (y - z)) / y;
	tmp = 0.0;
	if (t_0 <= 0.0)
		tmp = -(x * (z / y));
	elseif (t_0 <= 2e+171)
		tmp = x;
	elseif (t_0 <= 1e+305)
		tmp = (x * -z) / y;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$0, 0.0], (-N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), If[LessEqual[t$95$0, 2e+171], x, If[LessEqual[t$95$0, 1e+305], N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -0.0

   1. Initial program 79.3%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. remove-double-neg N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]

      7. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]

      9. lower-/.f64 97.6

         \[\leadsto \color{blue}{\frac{y - z}{y}} \cdot x \]

   4. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(z\right)}}{y} \cdot x \]

      2. lower-neg.f64 49.1

         \[\leadsto \frac{\color{blue}{-z}}{y} \cdot x \]

   7. Applied rewrites 49.1%

      \[\leadsto \frac{\color{blue}{-z}}{y} \cdot x \]

   if -0.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < 1.99999999999999991e171

   1. Initial program 99.7%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 65.7

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

   5. Applied rewrites 65.7%

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

      1. associate-/l* N/A

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

      2. *-inverses N/A

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

      3. *-rgt-identity 65.9

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

   7. Applied rewrites 65.9%

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

   if 1.99999999999999991e171 < (/.f64 (*.f64 x (-.f64 y z)) y) < 9.9999999999999994e304

   1. Initial program 99.5%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

         \[\leadsto \frac{z \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}}{y} \]

      7. lower-neg.f64 84.9

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

   5. Applied rewrites 84.9%

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

   if 9.9999999999999994e304 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 59.9%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 5.6

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

   5. Applied rewrites 5.6%

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

      1. associate-*l/ N/A

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

      2. lift-/.f64 N/A

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

      3. lower-*.f64 61.5

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

   7. Applied rewrites 61.5%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq 0:\\ \;\;\;\;-x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 2 \cdot 10^{+171}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 10^{+305}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ t_1 := -x \cdot \frac{z}{y}\\ \mathbf{if}\;t\_0 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+171}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_0 \leq 10^{+305}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x (- y z)) y)) (t_1 (- (* x (/ z y)))))
   (if (<= t_0 0.0)
     t_1
     (if (<= t_0 2e+171) x (if (<= t_0 1e+305) t_1 (* y (/ x y)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * (y - z)) / y;
	double t_1 = -(x * (z / y));
	double tmp;
	if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 2e+171) {
		tmp = x;
	} else if (t_0 <= 1e+305) {
		tmp = t_1;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x * (y - z)) / y
    t_1 = -(x * (z / y))
    if (t_0 <= 0.0d0) then
        tmp = t_1
    else if (t_0 <= 2d+171) then
        tmp = x
    else if (t_0 <= 1d+305) then
        tmp = t_1
    else
        tmp = y * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * (y - z)) / y;
	double t_1 = -(x * (z / y));
	double tmp;
	if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 2e+171) {
		tmp = x;
	} else if (t_0 <= 1e+305) {
		tmp = t_1;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * (y - z)) / y
	t_1 = -(x * (z / y))
	tmp = 0
	if t_0 <= 0.0:
		tmp = t_1
	elif t_0 <= 2e+171:
		tmp = x
	elif t_0 <= 1e+305:
		tmp = t_1
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(y - z)) / y)
	t_1 = Float64(-Float64(x * Float64(z / y)))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 2e+171)
		tmp = x;
	elseif (t_0 <= 1e+305)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * (y - z)) / y;
	t_1 = -(x * (z / y));
	tmp = 0.0;
	if (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 2e+171)
		tmp = x;
	elseif (t_0 <= 1e+305)
		tmp = t_1;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = (-N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[t$95$0, 0.0], t$95$1, If[LessEqual[t$95$0, 2e+171], x, If[LessEqual[t$95$0, 1e+305], t$95$1, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -0.0 or 1.99999999999999991e171 < (/.f64 (*.f64 x (-.f64 y z)) y) < 9.9999999999999994e304

   1. Initial program 82.4%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. remove-double-neg N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]

      7. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]

      9. lower-/.f64 93.6

         \[\leadsto \color{blue}{\frac{y - z}{y}} \cdot x \]

   4. Applied rewrites 93.6%

      \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(z\right)}}{y} \cdot x \]

      2. lower-neg.f64 50.3

         \[\leadsto \frac{\color{blue}{-z}}{y} \cdot x \]

   7. Applied rewrites 50.3%

      \[\leadsto \frac{\color{blue}{-z}}{y} \cdot x \]

   if -0.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < 1.99999999999999991e171

   1. Initial program 99.7%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 65.7

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

   5. Applied rewrites 65.7%

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

      1. associate-/l* N/A

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

      2. *-inverses N/A

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

      3. *-rgt-identity 65.9

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

   7. Applied rewrites 65.9%

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

   if 9.9999999999999994e304 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 59.9%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 5.6

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

   5. Applied rewrites 5.6%

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

      1. associate-*l/ N/A

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

      2. lift-/.f64 N/A

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

      3. lower-*.f64 61.5

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

   7. Applied rewrites 61.5%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq 0:\\ \;\;\;\;-x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 2 \cdot 10^{+171}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 10^{+305}:\\ \;\;\;\;-x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ t_1 := \left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{if}\;t\_0 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x (- y z)) y)) (t_1 (* (- y z) (/ x y))))
   (if (<= t_0 0.0) t_1 (if (<= t_0 1e-39) x t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (x * (y - z)) / y;
	double t_1 = (y - z) * (x / y);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 1e-39) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x * (y - z)) / y
    t_1 = (y - z) * (x / y)
    if (t_0 <= 0.0d0) then
        tmp = t_1
    else if (t_0 <= 1d-39) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * (y - z)) / y;
	double t_1 = (y - z) * (x / y);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 1e-39) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * (y - z)) / y
	t_1 = (y - z) * (x / y)
	tmp = 0
	if t_0 <= 0.0:
		tmp = t_1
	elif t_0 <= 1e-39:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(y - z)) / y)
	t_1 = Float64(Float64(y - z) * Float64(x / y))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 1e-39)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * (y - z)) / y;
	t_1 = (y - z) * (x / y);
	tmp = 0.0;
	if (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 1e-39)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.0], t$95$1, If[LessEqual[t$95$0, 1e-39], x, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -0.0 or 9.99999999999999929e-40 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 81.0%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. remove-double-neg N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 84.4

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

   4. Applied rewrites 84.4%

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

   if -0.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < 9.99999999999999929e-40

   1. Initial program 99.7%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 71.8

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

   5. Applied rewrites 71.8%

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

      1. associate-/l* N/A

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

      2. *-inverses N/A

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

      3. *-rgt-identity 72.0

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

   7. Applied rewrites 72.0%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq 0:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{if}\;t\_0 \leq 0:\\ \;\;\;\;\frac{x}{y} \cdot \left(-z\right)\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+275}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x (- y z)) y)))
   (if (<= t_0 0.0) (* (/ x y) (- z)) (if (<= t_0 5e+275) x (* y (/ x y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * (y - z)) / y;
	double tmp;
	if (t_0 <= 0.0) {
		tmp = (x / y) * -z;
	} else if (t_0 <= 5e+275) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * (y - z)) / y
    if (t_0 <= 0.0d0) then
        tmp = (x / y) * -z
    else if (t_0 <= 5d+275) then
        tmp = x
    else
        tmp = y * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * (y - z)) / y;
	double tmp;
	if (t_0 <= 0.0) {
		tmp = (x / y) * -z;
	} else if (t_0 <= 5e+275) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * (y - z)) / y
	tmp = 0
	if t_0 <= 0.0:
		tmp = (x / y) * -z
	elif t_0 <= 5e+275:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(y - z)) / y)
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = Float64(Float64(x / y) * Float64(-z));
	elseif (t_0 <= 5e+275)
		tmp = x;
	else
		tmp = Float64(y * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * (y - z)) / y;
	tmp = 0.0;
	if (t_0 <= 0.0)
		tmp = (x / y) * -z;
	elseif (t_0 <= 5e+275)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$0, 0.0], N[(N[(x / y), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[t$95$0, 5e+275], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -0.0

   1. Initial program 79.3%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

         \[\leadsto \frac{z \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}}{y} \]

      7. lower-neg.f64 44.9

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

   5. Applied rewrites 44.9%

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

      1. lift-neg.f64 N/A

         \[\leadsto \frac{z \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}}{y} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot z}}{y} \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(x\right)}{y} \cdot z} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(x\right)}{y} \cdot z} \]

      5. remove-double-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(x\right)}{\color{blue}{\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)}} \cdot z \]

      6. lift-neg.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(x\right)}}{\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)} \cdot z \]

      7. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{x}{\mathsf{neg}\left(y\right)}} \cdot z \]

      8. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{\mathsf{neg}\left(y\right)}} \cdot z \]

      9. lower-neg.f64 46.8

         \[\leadsto \frac{x}{\color{blue}{-y}} \cdot z \]

   7. Applied rewrites 46.8%

      \[\leadsto \color{blue}{\frac{x}{-y} \cdot z} \]

   if -0.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < 5.0000000000000003e275

   1. Initial program 99.6%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 56.6

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

   5. Applied rewrites 56.6%

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

      1. associate-/l* N/A

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

      2. *-inverses N/A

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

      3. *-rgt-identity 56.8

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

   7. Applied rewrites 56.8%

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

   if 5.0000000000000003e275 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 65.2%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 5.4

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

   5. Applied rewrites 5.4%

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

      1. associate-*l/ N/A

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

      2. lift-/.f64 N/A

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

      3. lower-*.f64 53.9

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

   7. Applied rewrites 53.9%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq 0:\\ \;\;\;\;\frac{x}{y} \cdot \left(-z\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 5 \cdot 10^{+275}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq 5 \cdot 10^{+275}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (/ (* x (- y z)) y) 5e+275) x (* y (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x * (y - z)) / y) <= 5e+275) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((x * (y - z)) / y) <= 5d+275) then
        tmp = x
    else
        tmp = y * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((x * (y - z)) / y) <= 5e+275) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x * (y - z)) / y) <= 5e+275:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(x * Float64(y - z)) / y) <= 5e+275)
		tmp = x;
	else
		tmp = Float64(y * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((x * (y - z)) / y) <= 5e+275)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], 5e+275], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < 5.0000000000000003e275

   1. Initial program 87.8%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 45.3

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

   5. Applied rewrites 45.3%

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

      1. associate-/l* N/A

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

      2. *-inverses N/A

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

      3. *-rgt-identity 53.3

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

   7. Applied rewrites 53.3%

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

   if 5.0000000000000003e275 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 65.2%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 5.4

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

   5. Applied rewrites 5.4%

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

      1. associate-*l/ N/A

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

      2. lift-/.f64 N/A

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

      3. lower-*.f64 53.9

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

   7. Applied rewrites 53.9%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq 5 \cdot 10^{+275}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 96.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{y - z}{y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (/ (- y z) y)))

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return x * ((y - z) / y)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.6%

   \[\frac{x \cdot \left(y - z\right)}{y} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. remove-double-neg N/A

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

   4. remove-double-neg N/A

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

   5. lift-*.f64 N/A

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

   6. associate-/l* N/A

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]

   7. *-commutative N/A

      \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]

   8. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]

   9. lower-/.f64 95.8

      \[\leadsto \color{blue}{\frac{y - z}{y}} \cdot x \]

4. Applied rewrites 95.8%

   \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]

5. Final simplification 95.8%

   \[\leadsto x \cdot \frac{y - z}{y} \]
6. Add Preprocessing

Alternative 8: 50.8% accurate, 20.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 84.6%

   \[\frac{x \cdot \left(y - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

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

   1. lower-*.f64 39.6

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

5. Applied rewrites 39.6%

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

   1. associate-/l* N/A

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

   2. *-inverses N/A

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

   3. *-rgt-identity 50.5

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

7. Applied rewrites 50.5%

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

Developer Target 1: 95.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< z -2.060202331921739e+104)
   (- x (/ (* z x) y))
   (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z < (-2.060202331921739d+104)) then
        tmp = x - ((z * x) / y)
    else if (z < 1.6939766013828526d+213) then
        tmp = x / (y / (y - z))
    else
        tmp = (y - z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z < -2.060202331921739e+104:
		tmp = x - ((z * x) / y)
	elif z < 1.6939766013828526e+213:
		tmp = x / (y / (y - z))
	else:
		tmp = (y - z) * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z < -2.060202331921739e+104)
		tmp = Float64(x - Float64(Float64(z * x) / y));
	elseif (z < 1.6939766013828526e+213)
		tmp = Float64(x / Float64(y / Float64(y - z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z < -2.060202331921739e+104)
		tmp = x - ((z * x) / y);
	elseif (z < 1.6939766013828526e+213)
		tmp = x / (y / (y - z));
	else
		tmp = (y - z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[z, -2.060202331921739e+104], N[(x - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Less[z, 1.6939766013828526e+213], N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024219 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -206020233192173900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- x (/ (* z x) y)) (if (< z 1693976601382852600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))

  (/ (* x (- y z)) y))