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

Percentage Accurate: 84.5% → 96.0%

Time: 9.0s

Alternatives: 5

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: 84.5% 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: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return ((y - z) / y) * 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 = ((y - z) / y) * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.1%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 97.0

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

4. Applied rewrites 97.0%

   \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]
5. Add Preprocessing

Alternative 2: 90.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \leq 0:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (/ (* (- y z) x) y) 0.0) (* (- y z) (/ x y)) (- x (/ (* z x) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((y - z) * x) / y) <= 0.0) {
		tmp = (y - z) * (x / y);
	} else {
		tmp = x - ((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 ((((y - z) * x) / y) <= 0.0d0) then
        tmp = (y - z) * (x / y)
    else
        tmp = x - ((z * x) / y)
    end if
    code = tmp
end function

Java

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

Python

def code(x, y, z):
	tmp = 0
	if (((y - z) * x) / y) <= 0.0:
		tmp = (y - z) * (x / y)
	else:
		tmp = x - ((z * x) / y)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], 0.0], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 84.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 83.1

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

   4. Applied rewrites 83.1%

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

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

   1. Initial program 87.6%

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

   3. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

      3. *-inverses N/A

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

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

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

      5. *-rgt-identity N/A

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

      6. associate-/l* N/A

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

      7. lower--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 95.0

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

   5. Applied rewrites 95.0%

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

4. Final simplification 88.5%

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

Alternative 3: 70.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \leq 0:\\ \;\;\;\;\frac{x}{y} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (/ (* (- y z) x) y) 0.0) (* (/ x y) (- z)) (- x (/ (* z x) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((y - z) * x) / y) <= 0.0) {
		tmp = (x / y) * -z;
	} else {
		tmp = x - ((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 ((((y - z) * x) / y) <= 0.0d0) then
        tmp = (x / y) * -z
    else
        tmp = x - ((z * x) / y)
    end if
    code = tmp
end function

Java

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

Python

def code(x, y, z):
	tmp = 0
	if (((y - z) * x) / y) <= 0.0:
		tmp = (x / y) * -z
	else:
		tmp = x - ((z * x) / y)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], 0.0], N[(N[(x / y), $MachinePrecision] * (-z)), $MachinePrecision], N[(x - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 84.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 97.9

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

   4. Applied rewrites 97.9%

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

   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 54.1

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

   7. Applied rewrites 54.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 51.0

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

   9. Applied rewrites 51.0%

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

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

   1. Initial program 87.6%

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

   3. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

      3. *-inverses N/A

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

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

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

      5. *-rgt-identity N/A

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

      6. associate-/l* N/A

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

      7. lower--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 95.0

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

   5. Applied rewrites 95.0%

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

4. Final simplification 71.0%

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

Alternative 4: 49.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \leq 0:\\ \;\;\;\;\frac{x}{y} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (/ (* (- y z) x) y) 0.0) (* (/ x y) (- z)) (* x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((y - z) * x) / y) <= 0.0) {
		tmp = (x / y) * -z;
	} else {
		tmp = x * 1.0;
	}
	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 ((((y - z) * x) / y) <= 0.0d0) then
        tmp = (x / y) * -z
    else
        tmp = x * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((((y - z) * x) / y) <= 0.0) {
		tmp = (x / y) * -z;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (((y - z) * x) / y) <= 0.0:
		tmp = (x / y) * -z
	else:
		tmp = x * 1.0
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((((y - z) * x) / y) <= 0.0)
		tmp = (x / y) * -z;
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], 0.0], N[(N[(x / y), $MachinePrecision] * (-z)), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 84.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 97.9

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

   4. Applied rewrites 97.9%

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

   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 54.1

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

   7. Applied rewrites 54.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 51.0

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

   9. Applied rewrites 51.0%

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

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

   1. Initial program 87.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 95.9

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

   4. Applied rewrites 95.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 49.0%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \leq 0:\\ \;\;\;\;\frac{x}{y} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.4% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ x \cdot 1 \end{array} \]

FPCore

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

C

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

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 * 1.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.1%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 97.0

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

4. Applied rewrites 97.0%

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

5. Taylor expanded in y around inf

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

7. Applied rewrites 47.3%

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

8. Final simplification 47.3%

   \[\leadsto x \cdot 1 \]
9. Add Preprocessing

Developer Target 1: 96.2% 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 2024238 
(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))