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

Percentage Accurate: 84.7% → 96.3%

Time: 8.0s

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: 84.7% 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: 96.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.8%

   \[\frac{x \cdot \left(y - z\right)}{y} \]
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. clear-num N/A

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

   5. un-div-inv N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 97.7

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

4. Applied rewrites 97.7%

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

6. Applied rewrites 97.7%

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

Alternative 2: 92.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(y - z\right) \cdot x}{y}\\ t_1 := \frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{if}\;t\_0 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 4 \cdot 10^{+306}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* (- y z) x) y)) (t_1 (* (/ x y) (- y z))))
   (if (<= t_0 0.0) t_1 (if (<= t_0 4e+306) (- x (/ (* z x) y)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = ((y - z) * x) / y;
	double t_1 = (x / y) * (y - z);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 4e+306) {
		tmp = x - ((z * x) / y);
	} 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 = ((y - z) * x) / y
    t_1 = (x / y) * (y - z)
    if (t_0 <= 0.0d0) then
        tmp = t_1
    else if (t_0 <= 4d+306) then
        tmp = x - ((z * x) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y - z) * x) / y;
	double t_1 = (x / y) * (y - z);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 4e+306) {
		tmp = x - ((z * x) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y - z) * x) / y
	t_1 = (x / y) * (y - z)
	tmp = 0
	if t_0 <= 0.0:
		tmp = t_1
	elif t_0 <= 4e+306:
		tmp = x - ((z * x) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y - z) * x) / y)
	t_1 = Float64(Float64(x / y) * Float64(y - z))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 4e+306)
		tmp = Float64(x - Float64(Float64(z * x) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y - z) * x) / y;
	t_1 = (x / y) * (y - z);
	tmp = 0.0;
	if (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 4e+306)
		tmp = x - ((z * x) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.0], t$95$1, If[LessEqual[t$95$0, 4e+306], N[(x - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -0.0 or 4.00000000000000007e306 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 76.9%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 86.1

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

   4. Applied rewrites 86.1%

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

   if -0.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < 4.00000000000000007e306

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 99.2

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

   5. Applied rewrites 99.2%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \leq 0:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \leq 4 \cdot 10^{+306}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z):
	tmp = 0
	if (((y - z) * x) / y) <= -math.inf:
		tmp = -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) <= Float64(-Inf))
		tmp = Float64(Float64(-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) <= -Inf)
		tmp = -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], (-Infinity)], N[((-z) * 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) < -inf.0

   1. Initial program 51.6%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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. *-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 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 61.4

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

   7. Applied rewrites 61.4%

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

   if -inf.0 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 89.7%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 94.3

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

   5. Applied rewrites 94.3%

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

4. Final simplification 90.1%

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

Alternative 4: 72.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{1}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+22}:\\ \;\;\;\;\frac{\left(-z\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.2e-69)
   (/ x 1.0)
   (if (<= y 1.2e+22) (/ (* (- z) x) y) (/ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e-69) {
		tmp = x / 1.0;
	} else if (y <= 1.2e+22) {
		tmp = (-z * x) / y;
	} 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 <= (-4.2d-69)) then
        tmp = x / 1.0d0
    else if (y <= 1.2d+22) then
        tmp = (-z * x) / y
    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 <= -4.2e-69) {
		tmp = x / 1.0;
	} else if (y <= 1.2e+22) {
		tmp = (-z * x) / y;
	} else {
		tmp = x / 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.2e-69:
		tmp = x / 1.0
	elif y <= 1.2e+22:
		tmp = (-z * x) / y
	else:
		tmp = x / 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.2e-69)
		tmp = Float64(x / 1.0);
	elseif (y <= 1.2e+22)
		tmp = Float64(Float64(Float64(-z) * x) / y);
	else
		tmp = Float64(x / 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.2e-69)
		tmp = x / 1.0;
	elseif (y <= 1.2e+22)
		tmp = (-z * x) / y;
	else
		tmp = x / 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.2e-69], N[(x / 1.0), $MachinePrecision], If[LessEqual[y, 1.2e+22], N[(N[((-z) * x), $MachinePrecision] / y), $MachinePrecision], N[(x / 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1999999999999999e-69 or 1.2e22 < y

   1. Initial program 77.6%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 73.1%

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

   if -4.1999999999999999e-69 < y < 1.2e22

   1. Initial program 92.5%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 78.9

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

   5. Applied rewrites 78.9%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{1}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+22}:\\ \;\;\;\;\frac{\left(-z\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{1}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+22}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.2e-69)
   (/ x 1.0)
   (if (<= y 1.2e+22) (* (- z) (/ x y)) (/ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e-69) {
		tmp = x / 1.0;
	} else if (y <= 1.2e+22) {
		tmp = -z * (x / y);
	} 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 <= (-4.2d-69)) then
        tmp = x / 1.0d0
    else if (y <= 1.2d+22) then
        tmp = -z * (x / y)
    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 <= -4.2e-69) {
		tmp = x / 1.0;
	} else if (y <= 1.2e+22) {
		tmp = -z * (x / y);
	} else {
		tmp = x / 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.2e-69:
		tmp = x / 1.0
	elif y <= 1.2e+22:
		tmp = -z * (x / y)
	else:
		tmp = x / 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.2e-69)
		tmp = Float64(x / 1.0);
	elseif (y <= 1.2e+22)
		tmp = Float64(Float64(-z) * Float64(x / y));
	else
		tmp = Float64(x / 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.2e-69)
		tmp = x / 1.0;
	elseif (y <= 1.2e+22)
		tmp = -z * (x / y);
	else
		tmp = x / 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.2e-69], N[(x / 1.0), $MachinePrecision], If[LessEqual[y, 1.2e+22], N[((-z) * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1999999999999999e-69 or 1.2e22 < y

   1. Initial program 77.6%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 73.1%

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

   if -4.1999999999999999e-69 < y < 1.2e22

   1. Initial program 92.5%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 93.8

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

   4. Applied rewrites 93.8%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 78.4

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

   7. Applied rewrites 78.4%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{1}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+22}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{1}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+22}:\\ \;\;\;\;\frac{-z}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.2e-69)
   (/ x 1.0)
   (if (<= y 1.2e+22) (* (/ (- z) y) x) (/ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e-69) {
		tmp = x / 1.0;
	} else if (y <= 1.2e+22) {
		tmp = (-z / y) * x;
	} 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 <= (-4.2d-69)) then
        tmp = x / 1.0d0
    else if (y <= 1.2d+22) then
        tmp = (-z / y) * x
    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 <= -4.2e-69) {
		tmp = x / 1.0;
	} else if (y <= 1.2e+22) {
		tmp = (-z / y) * x;
	} else {
		tmp = x / 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.2e-69:
		tmp = x / 1.0
	elif y <= 1.2e+22:
		tmp = (-z / y) * x
	else:
		tmp = x / 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.2e-69)
		tmp = Float64(x / 1.0);
	elseif (y <= 1.2e+22)
		tmp = Float64(Float64(Float64(-z) / y) * x);
	else
		tmp = Float64(x / 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.2e-69)
		tmp = x / 1.0;
	elseif (y <= 1.2e+22)
		tmp = (-z / y) * x;
	else
		tmp = x / 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.2e-69], N[(x / 1.0), $MachinePrecision], If[LessEqual[y, 1.2e+22], N[(N[((-z) / y), $MachinePrecision] * x), $MachinePrecision], N[(x / 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1999999999999999e-69 or 1.2e22 < y

   1. Initial program 77.6%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 73.1%

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

   if -4.1999999999999999e-69 < y < 1.2e22

   1. Initial program 92.5%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 78.4

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

   5. Applied rewrites 78.4%

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

Alternative 7: 96.3% 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 84.8%

   \[\frac{x \cdot \left(y - z\right)}{y} \]
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 97.6

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

4. Applied rewrites 97.6%

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

Alternative 8: 50.3% accurate, 1.7× speedup

Math

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

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 84.8%

   \[\frac{x \cdot \left(y - z\right)}{y} \]
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. clear-num N/A

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

   5. un-div-inv N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 97.7

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

4. Applied rewrites 97.7%

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

5. Taylor expanded in z around 0

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

7. Applied rewrites 46.9%

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

Developer Target 1: 96.1% 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 2024257 
(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))