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

Percentage Accurate: 84.5% → 96.4%

Time: 5.2s

Alternatives: 7

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: 96.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.1%

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

   1. associate-*r/ 97.0%

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

3. Simplified 97.0%

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

   1. associate-*r/ 81.1%

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

   2. associate-/l* 97.3%

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

5. Applied egg-rr 97.3%

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

6. Final simplification 97.3%

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

Alternative 2: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+104} \lor \neg \left(z \leq -7 \cdot 10^{+81}\right) \land \left(z \leq -3.6 \cdot 10^{-26} \lor \neg \left(z \leq 1.25 \cdot 10^{-55}\right)\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.6e+104)
         (and (not (<= z -7e+81)) (or (<= z -3.6e-26) (not (<= z 1.25e-55)))))
   (* (/ x y) (- z))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.6e+104) || (!(z <= -7e+81) && ((z <= -3.6e-26) || !(z <= 1.25e-55)))) {
		tmp = (x / y) * -z;
	} 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 <= (-2.6d+104)) .or. (.not. (z <= (-7d+81))) .and. (z <= (-3.6d-26)) .or. (.not. (z <= 1.25d-55))) then
        tmp = (x / y) * -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.6e+104) || (!(z <= -7e+81) && ((z <= -3.6e-26) || !(z <= 1.25e-55)))) {
		tmp = (x / y) * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.6e+104) or (not (z <= -7e+81) and ((z <= -3.6e-26) or not (z <= 1.25e-55))):
		tmp = (x / y) * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.6e+104) || (!(z <= -7e+81) && ((z <= -3.6e-26) || !(z <= 1.25e-55))))
		tmp = Float64(Float64(x / y) * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.6e+104) || (~((z <= -7e+81)) && ((z <= -3.6e-26) || ~((z <= 1.25e-55)))))
		tmp = (x / y) * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.6e+104], And[N[Not[LessEqual[z, -7e+81]], $MachinePrecision], Or[LessEqual[z, -3.6e-26], N[Not[LessEqual[z, 1.25e-55]], $MachinePrecision]]]], N[(N[(x / y), $MachinePrecision] * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e104 or -7.0000000000000001e81 < z < -3.6000000000000001e-26 or 1.25e-55 < z

   1. Initial program 87.6%

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

      1. associate-*r/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in y around 0 71.7%

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

      1. mul-1-neg 71.7%

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

      2. associate-*l/ 72.7%

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

      3. distribute-rgt-neg-out 72.7%

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

   6. Simplified 72.7%

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

   if -2.6e104 < z < -7.0000000000000001e81 or -3.6000000000000001e-26 < z < 1.25e-55

   1. Initial program 75.0%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 82.4%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+104} \lor \neg \left(z \leq -7 \cdot 10^{+81}\right) \land \left(z \leq -3.6 \cdot 10^{-26} \lor \neg \left(z \leq 1.25 \cdot 10^{-55}\right)\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 71.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y} \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+104}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-26}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ x y) (- z))))
   (if (<= z -2.6e+104)
     t_0
     (if (<= z -2.1e+81)
       x
       (if (<= z -2.1e-26) t_0 (if (<= z 8.5e-56) x (* x (/ z (- y)))))))))

C

double code(double x, double y, double z) {
	double t_0 = (x / y) * -z;
	double tmp;
	if (z <= -2.6e+104) {
		tmp = t_0;
	} else if (z <= -2.1e+81) {
		tmp = x;
	} else if (z <= -2.1e-26) {
		tmp = t_0;
	} else if (z <= 8.5e-56) {
		tmp = x;
	} else {
		tmp = x * (z / -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
    if (z <= (-2.6d+104)) then
        tmp = t_0
    else if (z <= (-2.1d+81)) then
        tmp = x
    else if (z <= (-2.1d-26)) then
        tmp = t_0
    else if (z <= 8.5d-56) then
        tmp = x
    else
        tmp = x * (z / -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x / y) * -z;
	double tmp;
	if (z <= -2.6e+104) {
		tmp = t_0;
	} else if (z <= -2.1e+81) {
		tmp = x;
	} else if (z <= -2.1e-26) {
		tmp = t_0;
	} else if (z <= 8.5e-56) {
		tmp = x;
	} else {
		tmp = x * (z / -y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x / y) * -z
	tmp = 0
	if z <= -2.6e+104:
		tmp = t_0
	elif z <= -2.1e+81:
		tmp = x
	elif z <= -2.1e-26:
		tmp = t_0
	elif z <= 8.5e-56:
		tmp = x
	else:
		tmp = x * (z / -y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x / y) * Float64(-z))
	tmp = 0.0
	if (z <= -2.6e+104)
		tmp = t_0;
	elseif (z <= -2.1e+81)
		tmp = x;
	elseif (z <= -2.1e-26)
		tmp = t_0;
	elseif (z <= 8.5e-56)
		tmp = x;
	else
		tmp = Float64(x * Float64(z / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x / y) * -z;
	tmp = 0.0;
	if (z <= -2.6e+104)
		tmp = t_0;
	elseif (z <= -2.1e+81)
		tmp = x;
	elseif (z <= -2.1e-26)
		tmp = t_0;
	elseif (z <= 8.5e-56)
		tmp = x;
	else
		tmp = x * (z / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x / y), $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[z, -2.6e+104], t$95$0, If[LessEqual[z, -2.1e+81], x, If[LessEqual[z, -2.1e-26], t$95$0, If[LessEqual[z, 8.5e-56], x, N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6e104 or -2.0999999999999999e81 < z < -2.10000000000000008e-26

   1. Initial program 85.2%

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

      1. associate-*r/ 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in y around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. associate-*l/ 80.8%

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

      3. distribute-rgt-neg-out 80.8%

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

   6. Simplified 80.8%

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

   if -2.6e104 < z < -2.0999999999999999e81 or -2.10000000000000008e-26 < z < 8.49999999999999932e-56

   1. Initial program 75.0%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 82.4%

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

   if 8.49999999999999932e-56 < z

   1. Initial program 89.7%

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

      1. associate-*r/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in y around 0 66.6%

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

      1. mul-1-neg 66.6%

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

      2. *-commutative 66.6%

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

      3. associate-/l* 65.9%

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

      4. associate-/r/ 67.7%

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

      5. distribute-lft-neg-in 67.7%

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

      6. distribute-neg-frac 67.7%

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

      7. neg-mul-1 67.7%

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

      8. remove-double-neg 67.7%

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

      9. neg-mul-1 67.7%

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

      10. times-frac 67.7%

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

      11. metadata-eval 67.7%

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

      12. *-lft-identity 67.7%

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

   6. Simplified 67.7%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \end{array} \]

Alternative 4: 71.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y} \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{+104}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-26}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ x y) (- z))))
   (if (<= z -3e+104)
     t_0
     (if (<= z -5.5e+81)
       x
       (if (<= z -6.6e-26) t_0 (if (<= z 4e-55) x (/ (- x) (/ y z))))))))

C

double code(double x, double y, double z) {
	double t_0 = (x / y) * -z;
	double tmp;
	if (z <= -3e+104) {
		tmp = t_0;
	} else if (z <= -5.5e+81) {
		tmp = x;
	} else if (z <= -6.6e-26) {
		tmp = t_0;
	} else if (z <= 4e-55) {
		tmp = x;
	} else {
		tmp = -x / (y / z);
	}
	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
    if (z <= (-3d+104)) then
        tmp = t_0
    else if (z <= (-5.5d+81)) then
        tmp = x
    else if (z <= (-6.6d-26)) then
        tmp = t_0
    else if (z <= 4d-55) then
        tmp = x
    else
        tmp = -x / (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x / y) * -z;
	double tmp;
	if (z <= -3e+104) {
		tmp = t_0;
	} else if (z <= -5.5e+81) {
		tmp = x;
	} else if (z <= -6.6e-26) {
		tmp = t_0;
	} else if (z <= 4e-55) {
		tmp = x;
	} else {
		tmp = -x / (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x / y) * -z
	tmp = 0
	if z <= -3e+104:
		tmp = t_0
	elif z <= -5.5e+81:
		tmp = x
	elif z <= -6.6e-26:
		tmp = t_0
	elif z <= 4e-55:
		tmp = x
	else:
		tmp = -x / (y / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x / y) * Float64(-z))
	tmp = 0.0
	if (z <= -3e+104)
		tmp = t_0;
	elseif (z <= -5.5e+81)
		tmp = x;
	elseif (z <= -6.6e-26)
		tmp = t_0;
	elseif (z <= 4e-55)
		tmp = x;
	else
		tmp = Float64(Float64(-x) / Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x / y) * -z;
	tmp = 0.0;
	if (z <= -3e+104)
		tmp = t_0;
	elseif (z <= -5.5e+81)
		tmp = x;
	elseif (z <= -6.6e-26)
		tmp = t_0;
	elseif (z <= 4e-55)
		tmp = x;
	else
		tmp = -x / (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x / y), $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[z, -3e+104], t$95$0, If[LessEqual[z, -5.5e+81], x, If[LessEqual[z, -6.6e-26], t$95$0, If[LessEqual[z, 4e-55], x, N[((-x) / N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.99999999999999969e104 or -5.5000000000000003e81 < z < -6.5999999999999997e-26

   1. Initial program 85.2%

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

      1. associate-*r/ 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in y around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. associate-*l/ 80.8%

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

      3. distribute-rgt-neg-out 80.8%

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

   6. Simplified 80.8%

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

   if -2.99999999999999969e104 < z < -5.5000000000000003e81 or -6.5999999999999997e-26 < z < 3.99999999999999998e-55

   1. Initial program 75.0%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 82.4%

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

   if 3.99999999999999998e-55 < z

   1. Initial program 89.7%

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

      1. associate-*r/ 97.2%

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

   3. Simplified 97.2%

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

      1. associate-*r/ 89.7%

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

      2. associate-/l* 97.3%

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

   5. Applied egg-rr 97.3%

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

   6. Taylor expanded in y around 0 66.6%

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

      1. mul-1-neg 66.6%

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

      2. associate-/l* 67.8%

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

      3. distribute-neg-frac 67.8%

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

   8. Simplified 67.8%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{y}{z}}\\ \end{array} \]

Alternative 5: 71.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-26}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.4e+104)
   (* (/ x y) (- z))
   (if (<= z -7e+81)
     x
     (if (<= z -2.3e-26)
       (/ (* z (- x)) y)
       (if (<= z 2.7e-55) x (/ (- x) (/ y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.4e+104) {
		tmp = (x / y) * -z;
	} else if (z <= -7e+81) {
		tmp = x;
	} else if (z <= -2.3e-26) {
		tmp = (z * -x) / y;
	} else if (z <= 2.7e-55) {
		tmp = x;
	} else {
		tmp = -x / (y / z);
	}
	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 <= (-3.4d+104)) then
        tmp = (x / y) * -z
    else if (z <= (-7d+81)) then
        tmp = x
    else if (z <= (-2.3d-26)) then
        tmp = (z * -x) / y
    else if (z <= 2.7d-55) then
        tmp = x
    else
        tmp = -x / (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.4e+104) {
		tmp = (x / y) * -z;
	} else if (z <= -7e+81) {
		tmp = x;
	} else if (z <= -2.3e-26) {
		tmp = (z * -x) / y;
	} else if (z <= 2.7e-55) {
		tmp = x;
	} else {
		tmp = -x / (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.4e+104:
		tmp = (x / y) * -z
	elif z <= -7e+81:
		tmp = x
	elif z <= -2.3e-26:
		tmp = (z * -x) / y
	elif z <= 2.7e-55:
		tmp = x
	else:
		tmp = -x / (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.4e+104)
		tmp = Float64(Float64(x / y) * Float64(-z));
	elseif (z <= -7e+81)
		tmp = x;
	elseif (z <= -2.3e-26)
		tmp = Float64(Float64(z * Float64(-x)) / y);
	elseif (z <= 2.7e-55)
		tmp = x;
	else
		tmp = Float64(Float64(-x) / Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.4e+104)
		tmp = (x / y) * -z;
	elseif (z <= -7e+81)
		tmp = x;
	elseif (z <= -2.3e-26)
		tmp = (z * -x) / y;
	elseif (z <= 2.7e-55)
		tmp = x;
	else
		tmp = -x / (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.4e+104], N[(N[(x / y), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[z, -7e+81], x, If[LessEqual[z, -2.3e-26], N[(N[(z * (-x)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 2.7e-55], x, N[((-x) / N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.3999999999999997e104

   1. Initial program 83.1%

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

      1. associate-*r/ 85.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in y around 0 80.1%

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

      1. mul-1-neg 80.1%

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

      2. associate-*l/ 85.5%

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

      3. distribute-rgt-neg-out 85.5%

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

   6. Simplified 85.5%

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

   if -3.3999999999999997e104 < z < -7.0000000000000001e81 or -2.30000000000000009e-26 < z < 2.70000000000000004e-55

   1. Initial program 75.0%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 82.4%

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

   if -7.0000000000000001e81 < z < -2.30000000000000009e-26

   1. Initial program 88.1%

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

   2. Taylor expanded in y around 0 74.3%

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

      1. mul-1-neg 74.3%

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

      2. distribute-rgt-neg-out 74.3%

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

   4. Simplified 74.3%

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

   if 2.70000000000000004e-55 < z

   1. Initial program 89.7%

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

      1. associate-*r/ 97.2%

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

   3. Simplified 97.2%

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

      1. associate-*r/ 89.7%

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

      2. associate-/l* 97.3%

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

   5. Applied egg-rr 97.3%

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

   6. Taylor expanded in y around 0 66.6%

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

      1. mul-1-neg 66.6%

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

      2. associate-/l* 67.8%

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

      3. distribute-neg-frac 67.8%

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

   8. Simplified 67.8%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-26}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{y}{z}}\\ \end{array} \]

Alternative 6: 96.1% 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 81.1%

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

   1. associate-*r/ 97.0%

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

3. Simplified 97.0%

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

4. Final simplification 97.0%

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

Alternative 7: 50.4% 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 81.1%

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

   1. associate-*r/ 97.0%

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

3. Simplified 97.0%

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

4. Taylor expanded in y around inf 53.8%

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

5. Final simplification 53.8%

   \[\leadsto x \]

Developer target: 96.1% 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 2023320 
(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))