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

Percentage Accurate: 84.0% → 95.9%

Time: 4.4s

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: 84.0% 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: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.0%

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

   1. associate-*l/ 87.5%

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

   2. distribute-rgt-out-- 83.8%

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

   3. associate-*r/ 79.7%

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

   4. associate-*l/ 94.6%

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

   5. *-inverses 94.6%

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

   6. *-lft-identity 94.6%

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

3. Simplified 94.6%

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

4. Taylor expanded in z around 0 96.2%

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

   1. associate-/l* 95.1%

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

   2. associate-/r/ 97.7%

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

6. Applied egg-rr 97.7%

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

7. Final simplification 97.7%

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

Alternative 2: 69.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.7 \cdot 10^{-47} \lor \neg \left(z \leq 2.6 \cdot 10^{-14} \lor \neg \left(z \leq 3.1 \cdot 10^{+15}\right) \land z \leq 1.35 \cdot 10^{+116}\right):\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.7e-47)
         (not (or (<= z 2.6e-14) (and (not (<= z 3.1e+15)) (<= z 1.35e+116)))))
   (* (/ z y) (- x))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.7e-47) || !((z <= 2.6e-14) || (!(z <= 3.1e+15) && (z <= 1.35e+116)))) {
		tmp = (z / y) * -x;
	} else {
		tmp = x;
	}
	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 <= (-8.7d-47)) .or. (.not. (z <= 2.6d-14) .or. (.not. (z <= 3.1d+15)) .and. (z <= 1.35d+116))) then
        tmp = (z / y) * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.7e-47) || !((z <= 2.6e-14) || (!(z <= 3.1e+15) && (z <= 1.35e+116)))) {
		tmp = (z / y) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.7e-47) or not ((z <= 2.6e-14) or (not (z <= 3.1e+15) and (z <= 1.35e+116))):
		tmp = (z / y) * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.7e-47) || !((z <= 2.6e-14) || (!(z <= 3.1e+15) && (z <= 1.35e+116))))
		tmp = Float64(Float64(z / y) * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.7e-47) || ~(((z <= 2.6e-14) || (~((z <= 3.1e+15)) && (z <= 1.35e+116)))))
		tmp = (z / y) * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.7e-47], N[Not[Or[LessEqual[z, 2.6e-14], And[N[Not[LessEqual[z, 3.1e+15]], $MachinePrecision], LessEqual[z, 1.35e+116]]]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.7000000000000001e-47 or 2.59999999999999997e-14 < z < 3.1e15 or 1.35e116 < z

   1. Initial program 92.3%

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

   2. Taylor expanded in y around 0 81.7%

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

      1. mul-1-neg 81.7%

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

      2. associate-*l/ 79.3%

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

      3. *-commutative 79.3%

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

      4. distribute-rgt-neg-in 79.3%

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

      5. distribute-frac-neg 79.3%

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

   4. Simplified 79.3%

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

   if -8.7000000000000001e-47 < z < 2.59999999999999997e-14 or 3.1e15 < z < 1.35e116

   1. Initial program 74.2%

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

   2. Taylor expanded in y around inf 81.2%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.7 \cdot 10^{-47} \lor \neg \left(z \leq 2.6 \cdot 10^{-14} \lor \neg \left(z \leq 3.1 \cdot 10^{+15}\right) \land z \leq 1.35 \cdot 10^{+116}\right):\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 71.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-46} \lor \neg \left(z \leq 4.9 \cdot 10^{-15} \lor \neg \left(z \leq 1.25 \cdot 10^{+15}\right) \land z \leq 1.6 \cdot 10^{+117}\right):\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.35e-46)
         (not (or (<= z 4.9e-15) (and (not (<= z 1.25e+15)) (<= z 1.6e+117)))))
   (* z (/ (- x) y))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e-46) || !((z <= 4.9e-15) || (!(z <= 1.25e+15) && (z <= 1.6e+117)))) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	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 <= (-1.35d-46)) .or. (.not. (z <= 4.9d-15) .or. (.not. (z <= 1.25d+15)) .and. (z <= 1.6d+117))) then
        tmp = z * (-x / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e-46) || !((z <= 4.9e-15) || (!(z <= 1.25e+15) && (z <= 1.6e+117)))) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.35e-46) or not ((z <= 4.9e-15) or (not (z <= 1.25e+15) and (z <= 1.6e+117))):
		tmp = z * (-x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.35e-46) || !((z <= 4.9e-15) || (!(z <= 1.25e+15) && (z <= 1.6e+117))))
		tmp = Float64(z * Float64(Float64(-x) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.35e-46) || ~(((z <= 4.9e-15) || (~((z <= 1.25e+15)) && (z <= 1.6e+117)))))
		tmp = z * (-x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.35e-46], N[Not[Or[LessEqual[z, 4.9e-15], And[N[Not[LessEqual[z, 1.25e+15]], $MachinePrecision], LessEqual[z, 1.6e+117]]]], $MachinePrecision]], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e-46 or 4.8999999999999999e-15 < z < 1.25e15 or 1.60000000000000002e117 < z

   1. Initial program 92.3%

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

   2. Taylor expanded in y around 0 81.7%

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

      1. mul-1-neg 81.7%

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

      2. associate-*r/ 81.2%

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

      3. *-commutative 81.2%

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

      4. distribute-rgt-neg-in 81.2%

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

   4. Simplified 81.2%

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

   if -1.35e-46 < z < 4.8999999999999999e-15 or 1.25e15 < z < 1.60000000000000002e117

   1. Initial program 74.2%

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

   2. Taylor expanded in y around inf 81.2%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-46} \lor \neg \left(z \leq 4.9 \cdot 10^{-15} \lor \neg \left(z \leq 1.25 \cdot 10^{+15}\right) \land z \leq 1.6 \cdot 10^{+117}\right):\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 71.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{\frac{-y}{x}}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{-46}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+15}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+116}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ z (/ (- y) x))))
   (if (<= z -1.45e-46)
     t_0
     (if (<= z 1.65e-14)
       x
       (if (<= z 1.6e+15) (* z (/ (- x) y)) (if (<= z 4.6e+116) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z / (-y / x);
	double tmp;
	if (z <= -1.45e-46) {
		tmp = t_0;
	} else if (z <= 1.65e-14) {
		tmp = x;
	} else if (z <= 1.6e+15) {
		tmp = z * (-x / y);
	} else if (z <= 4.6e+116) {
		tmp = x;
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = z / (-y / x)
    if (z <= (-1.45d-46)) then
        tmp = t_0
    else if (z <= 1.65d-14) then
        tmp = x
    else if (z <= 1.6d+15) then
        tmp = z * (-x / y)
    else if (z <= 4.6d+116) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z / (-y / x);
	double tmp;
	if (z <= -1.45e-46) {
		tmp = t_0;
	} else if (z <= 1.65e-14) {
		tmp = x;
	} else if (z <= 1.6e+15) {
		tmp = z * (-x / y);
	} else if (z <= 4.6e+116) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z / (-y / x)
	tmp = 0
	if z <= -1.45e-46:
		tmp = t_0
	elif z <= 1.65e-14:
		tmp = x
	elif z <= 1.6e+15:
		tmp = z * (-x / y)
	elif z <= 4.6e+116:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z / Float64(Float64(-y) / x))
	tmp = 0.0
	if (z <= -1.45e-46)
		tmp = t_0;
	elseif (z <= 1.65e-14)
		tmp = x;
	elseif (z <= 1.6e+15)
		tmp = Float64(z * Float64(Float64(-x) / y));
	elseif (z <= 4.6e+116)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z / (-y / x);
	tmp = 0.0;
	if (z <= -1.45e-46)
		tmp = t_0;
	elseif (z <= 1.65e-14)
		tmp = x;
	elseif (z <= 1.6e+15)
		tmp = z * (-x / y);
	elseif (z <= 4.6e+116)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z / N[((-y) / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e-46], t$95$0, If[LessEqual[z, 1.65e-14], x, If[LessEqual[z, 1.6e+15], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+116], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45000000000000002e-46 or 4.5999999999999999e116 < z

   1. Initial program 92.3%

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

   2. Taylor expanded in y around 0 81.8%

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

      1. mul-1-neg 81.8%

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

      2. associate-*l/ 78.7%

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

      3. *-commutative 78.7%

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

      4. distribute-rgt-neg-in 78.7%

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

      5. distribute-frac-neg 78.7%

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

   4. Simplified 78.7%

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

      1. *-commutative 78.7%

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

      2. associate-*l/ 81.8%

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

      3. associate-*r/ 80.7%

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

      4. add-sqr-sqrt 46.1%

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

      5. sqrt-unprod 38.4%

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

      6. sqr-neg 38.4%

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

      7. sqrt-unprod 0.7%

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

      8. add-sqr-sqrt 1.5%

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

      9. clear-num 1.5%

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

      10. div-inv 1.5%

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

      11. frac-2neg 1.5%

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

      12. add-sqr-sqrt 0.8%

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

      13. sqrt-unprod 18.8%

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

      14. sqr-neg 18.8%

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

      15. sqrt-unprod 34.3%

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

      16. add-sqr-sqrt 80.8%

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

   6. Applied egg-rr 80.8%

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

   if -1.45000000000000002e-46 < z < 1.6499999999999999e-14 or 1.6e15 < z < 4.5999999999999999e116

   1. Initial program 74.2%

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

   2. Taylor expanded in y around inf 81.2%

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

   if 1.6499999999999999e-14 < z < 1.6e15

   1. Initial program 91.6%

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

   2. Taylor expanded in y around 0 79.9%

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

      1. mul-1-neg 79.9%

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

      2. associate-*r/ 88.0%

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

      3. *-commutative 88.0%

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

      4. distribute-rgt-neg-in 88.0%

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

   4. Simplified 88.0%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-46}:\\ \;\;\;\;\frac{z}{\frac{-y}{x}}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+15}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+116}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{-y}{x}}\\ \end{array} \]

Alternative 5: 71.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-46}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 21500000000000:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+116}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{-y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.45e-46)
   (/ (* x (- z)) y)
   (if (<= z 5.1e-16)
     x
     (if (<= z 21500000000000.0)
       (* z (/ (- x) y))
       (if (<= z 1.35e+116) x (/ z (/ (- y) x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.45e-46) {
		tmp = (x * -z) / y;
	} else if (z <= 5.1e-16) {
		tmp = x;
	} else if (z <= 21500000000000.0) {
		tmp = z * (-x / y);
	} else if (z <= 1.35e+116) {
		tmp = x;
	} else {
		tmp = z / (-y / x);
	}
	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 <= (-1.45d-46)) then
        tmp = (x * -z) / y
    else if (z <= 5.1d-16) then
        tmp = x
    else if (z <= 21500000000000.0d0) then
        tmp = z * (-x / y)
    else if (z <= 1.35d+116) then
        tmp = x
    else
        tmp = z / (-y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.45e-46) {
		tmp = (x * -z) / y;
	} else if (z <= 5.1e-16) {
		tmp = x;
	} else if (z <= 21500000000000.0) {
		tmp = z * (-x / y);
	} else if (z <= 1.35e+116) {
		tmp = x;
	} else {
		tmp = z / (-y / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.45e-46:
		tmp = (x * -z) / y
	elif z <= 5.1e-16:
		tmp = x
	elif z <= 21500000000000.0:
		tmp = z * (-x / y)
	elif z <= 1.35e+116:
		tmp = x
	else:
		tmp = z / (-y / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.45e-46)
		tmp = Float64(Float64(x * Float64(-z)) / y);
	elseif (z <= 5.1e-16)
		tmp = x;
	elseif (z <= 21500000000000.0)
		tmp = Float64(z * Float64(Float64(-x) / y));
	elseif (z <= 1.35e+116)
		tmp = x;
	else
		tmp = Float64(z / Float64(Float64(-y) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.45e-46)
		tmp = (x * -z) / y;
	elseif (z <= 5.1e-16)
		tmp = x;
	elseif (z <= 21500000000000.0)
		tmp = z * (-x / y);
	elseif (z <= 1.35e+116)
		tmp = x;
	else
		tmp = z / (-y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.45e-46], N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 5.1e-16], x, If[LessEqual[z, 21500000000000.0], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+116], x, N[(z / N[((-y) / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.45000000000000002e-46

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0 86.3%

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

      1. associate-*r/ 86.3%

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

      2. neg-mul-1 86.3%

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

      3. distribute-rgt-neg-in 86.3%

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

   4. Simplified 86.3%

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

   if -1.45000000000000002e-46 < z < 5.1e-16 or 2.15e13 < z < 1.35e116

   1. Initial program 74.2%

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

   2. Taylor expanded in y around inf 81.2%

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

   if 5.1e-16 < z < 2.15e13

   1. Initial program 91.6%

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

   2. Taylor expanded in y around 0 79.9%

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

      1. mul-1-neg 79.9%

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

      2. associate-*r/ 88.0%

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

      3. *-commutative 88.0%

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

      4. distribute-rgt-neg-in 88.0%

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

   4. Simplified 88.0%

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

   if 1.35e116 < z

   1. Initial program 88.6%

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

   2. Taylor expanded in y around 0 76.1%

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

      1. mul-1-neg 76.1%

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

      2. associate-*l/ 74.5%

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

      3. *-commutative 74.5%

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

      4. distribute-rgt-neg-in 74.5%

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

      5. distribute-frac-neg 74.5%

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

   4. Simplified 74.5%

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

      1. *-commutative 74.5%

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

      2. associate-*l/ 76.1%

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

      3. associate-*r/ 78.2%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 0.9%

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

      6. sqr-neg 0.9%

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

      7. sqrt-unprod 1.6%

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

      8. add-sqr-sqrt 1.6%

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

      9. clear-num 1.6%

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

      10. div-inv 1.6%

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

      11. frac-2neg 1.6%

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

      12. add-sqr-sqrt 0.0%

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

      13. sqrt-unprod 41.4%

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

      14. sqr-neg 41.4%

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

      15. sqrt-unprod 77.9%

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

      16. add-sqr-sqrt 78.2%

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

   6. Applied egg-rr 78.2%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-46}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 21500000000000:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+116}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{-y}{x}}\\ \end{array} \]

Alternative 6: 51.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6.1 \cdot 10^{+184}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 6.1e+184) x (* y (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 6.1e+184) {
		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 <= 6.1d+184) 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 <= 6.1e+184) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 6.1e+184:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 6.1e+184)
		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 <= 6.1e+184)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 6.1e+184], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.10000000000000009e184

   1. Initial program 83.9%

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

   2. Taylor expanded in y around inf 50.1%

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

   if 6.10000000000000009e184 < x

   1. Initial program 73.8%

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

   2. Taylor expanded in y around inf 29.6%

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

      1. associate-/l* 76.1%

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

      2. div-inv 77.3%

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

      3. clear-num 77.5%

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

   4. Applied egg-rr 77.5%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6.1 \cdot 10^{+184}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]

Alternative 7: 94.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.0%

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

   1. associate-*l/ 87.5%

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

   2. distribute-rgt-out-- 83.8%

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

   3. associate-*r/ 79.7%

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

   4. associate-*l/ 94.6%

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

   5. *-inverses 94.6%

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

   6. *-lft-identity 94.6%

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

3. Simplified 94.6%

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

4. Final simplification 94.6%

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

Alternative 8: 51.4% accurate, 7.0× 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 83.0%

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

2. Taylor expanded in y around inf 50.7%

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

3. Final simplification 50.7%

   \[\leadsto x \]

Developer target: 96.2% accurate, 0.6× 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 2023238 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

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