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

Percentage Accurate: 84.7% → 95.8%

Time: 7.6s

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: 95.8% 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 84.6%

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

   1. *-commutative 84.6%

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

   2. associate-/l* 84.0%

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

   3. div-sub 79.2%

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

   4. associate-/r/ 78.1%

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

   5. associate-/r/ 95.8%

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

   6. *-inverses 95.8%

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

   7. *-lft-identity 95.8%

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

   8. *-commutative 95.8%

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

3. Simplified 95.8%

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

4. Final simplification 95.8%

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

Alternative 2: 68.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{-z}{y}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-188} \lor \neg \left(z \leq 820000\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ (- z) y))))
   (if (<= z -3.5e-14)
     t_0
     (if (<= z -7e-133)
       (* y (/ x y))
       (if (or (<= z -1.05e-188) (not (<= z 820000.0))) t_0 x)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-z / y);
	double tmp;
	if (z <= -3.5e-14) {
		tmp = t_0;
	} else if (z <= -7e-133) {
		tmp = y * (x / y);
	} else if ((z <= -1.05e-188) || !(z <= 820000.0)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x * (-z / y)
    if (z <= (-3.5d-14)) then
        tmp = t_0
    else if (z <= (-7d-133)) then
        tmp = y * (x / y)
    else if ((z <= (-1.05d-188)) .or. (.not. (z <= 820000.0d0))) then
        tmp = t_0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-z / y);
	double tmp;
	if (z <= -3.5e-14) {
		tmp = t_0;
	} else if (z <= -7e-133) {
		tmp = y * (x / y);
	} else if ((z <= -1.05e-188) || !(z <= 820000.0)) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-z / y)
	tmp = 0
	if z <= -3.5e-14:
		tmp = t_0
	elif z <= -7e-133:
		tmp = y * (x / y)
	elif (z <= -1.05e-188) or not (z <= 820000.0):
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(-z) / y))
	tmp = 0.0
	if (z <= -3.5e-14)
		tmp = t_0;
	elseif (z <= -7e-133)
		tmp = Float64(y * Float64(x / y));
	elseif ((z <= -1.05e-188) || !(z <= 820000.0))
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-z / y);
	tmp = 0.0;
	if (z <= -3.5e-14)
		tmp = t_0;
	elseif (z <= -7e-133)
		tmp = y * (x / y);
	elseif ((z <= -1.05e-188) || ~((z <= 820000.0)))
		tmp = t_0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e-14], t$95$0, If[LessEqual[z, -7e-133], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.05e-188], N[Not[LessEqual[z, 820000.0]], $MachinePrecision]], t$95$0, x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5000000000000002e-14 or -7.00000000000000006e-133 < z < -1.05e-188 or 8.2e5 < z

   1. Initial program 88.2%

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

      1. associate-*l/ 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in y around 0 75.8%

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

      1. associate-*r/ 75.8%

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

      2. mul-1-neg 75.8%

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

      3. distribute-rgt-neg-out 75.8%

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

      4. associate-*r/ 71.9%

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

   6. Simplified 71.9%

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

   if -3.5000000000000002e-14 < z < -7.00000000000000006e-133

   1. Initial program 90.9%

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

   2. Taylor expanded in y around inf 53.5%

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

      1. associate-*l/ 75.8%

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

   4. Applied egg-rr 75.8%

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

   if -1.05e-188 < z < 8.2e5

   1. Initial program 78.2%

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

      1. associate-*l/ 80.9%

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

   3. Simplified 80.9%

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

   4. Taylor expanded in y around inf 78.9%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-188} \lor \neg \left(z \leq 820000\right):\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 73.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-14} \lor \neg \left(z \leq 3600000\right):\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.8e-14) (not (<= z 3600000.0))) (* z (/ x (- y))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.8e-14) || !(z <= 3600000.0)) {
		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 <= (-3.8d-14)) .or. (.not. (z <= 3600000.0d0))) 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 <= -3.8e-14) || !(z <= 3600000.0)) {
		tmp = z * (x / -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.8e-14) or not (z <= 3600000.0):
		tmp = z * (x / -y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.8e-14) || !(z <= 3600000.0))
		tmp = Float64(z * Float64(x / Float64(-y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.8e-14) || ~((z <= 3600000.0)))
		tmp = z * (x / -y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.8e-14], N[Not[LessEqual[z, 3600000.0]], $MachinePrecision]], N[(z * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.8000000000000002e-14 or 3.6e6 < z

   1. Initial program 88.2%

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

      1. associate-/l* 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in y around 0 72.4%

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

      1. associate-*r/ 72.4%

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

      2. neg-mul-1 72.4%

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

   6. Simplified 72.4%

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

      1. associate-/r/ 75.9%

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

   8. Applied egg-rr 75.9%

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

   if -3.8000000000000002e-14 < z < 3.6e6

   1. Initial program 80.9%

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

      1. associate-*l/ 80.0%

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

   3. Simplified 80.0%

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

   4. Taylor expanded in y around inf 73.7%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-14} \lor \neg \left(z \leq 3600000\right):\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 73.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-14} \lor \neg \left(z \leq 1200000\right):\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.8e-14) (not (<= z 1200000.0))) (/ (* x (- z)) y) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e-14) || !(z <= 1200000.0)) {
		tmp = (x * -z) / 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 <= (-4.8d-14)) .or. (.not. (z <= 1200000.0d0))) then
        tmp = (x * -z) / 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 <= -4.8e-14) || !(z <= 1200000.0)) {
		tmp = (x * -z) / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.8e-14) or not (z <= 1200000.0):
		tmp = (x * -z) / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.8e-14) || !(z <= 1200000.0))
		tmp = Float64(Float64(x * Float64(-z)) / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.8e-14) || ~((z <= 1200000.0)))
		tmp = (x * -z) / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.8e-14], N[Not[LessEqual[z, 1200000.0]], $MachinePrecision]], N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e-14 or 1.2e6 < z

   1. Initial program 88.2%

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

   2. Taylor expanded in y around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. distribute-rgt-neg-out 77.3%

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

   4. Simplified 77.3%

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

   if -4.8e-14 < z < 1.2e6

   1. Initial program 80.9%

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

      1. associate-*l/ 80.0%

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

   3. Simplified 80.0%

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

   4. Taylor expanded in y around inf 73.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-14} \lor \neg \left(z \leq 1200000\right):\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 73.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{elif}\;z \leq 52000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2e-14) (* z (/ x (- y))) (if (<= z 52000.0) x (/ (- z) (/ y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e-14) {
		tmp = z * (x / -y);
	} else if (z <= 52000.0) {
		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 <= (-2d-14)) then
        tmp = z * (x / -y)
    else if (z <= 52000.0d0) 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 <= -2e-14) {
		tmp = z * (x / -y);
	} else if (z <= 52000.0) {
		tmp = x;
	} else {
		tmp = -z / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2e-14:
		tmp = z * (x / -y)
	elif z <= 52000.0:
		tmp = x
	else:
		tmp = -z / (y / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2e-14)
		tmp = Float64(z * Float64(x / Float64(-y)));
	elseif (z <= 52000.0)
		tmp = x;
	else
		tmp = Float64(Float64(-z) / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2e-14)
		tmp = z * (x / -y);
	elseif (z <= 52000.0)
		tmp = x;
	else
		tmp = -z / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2e-14], N[(z * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 52000.0], x, N[((-z) / N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2e-14

   1. Initial program 88.4%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in y around 0 71.6%

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

      1. associate-*r/ 71.6%

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

      2. neg-mul-1 71.6%

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

   6. Simplified 71.6%

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

      1. associate-/r/ 75.8%

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

   8. Applied egg-rr 75.8%

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

   if -2e-14 < z < 52000

   1. Initial program 80.9%

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

      1. associate-*l/ 80.0%

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

   3. Simplified 80.0%

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

   4. Taylor expanded in y around inf 73.7%

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

   if 52000 < z

   1. Initial program 88.0%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in y around 0 76.1%

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

      1. associate-*r/ 76.1%

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

      2. mul-1-neg 76.1%

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

      3. distribute-rgt-neg-out 76.1%

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

      4. associate-*r/ 73.3%

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

   6. Simplified 73.3%

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

      1. *-commutative 73.3%

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

      2. associate-/r/ 76.0%

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

   8. Applied egg-rr 76.0%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{elif}\;z \leq 52000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \end{array} \]

Alternative 6: 87.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.4 \cdot 10^{+166}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 5.4e+166) (* (/ x y) (- y z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 5.4e+166) {
		tmp = (x / y) * (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 (y <= 5.4d+166) then
        tmp = (x / y) * (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 (y <= 5.4e+166) {
		tmp = (x / y) * (y - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 5.4e+166:
		tmp = (x / y) * (y - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 5.4e+166)
		tmp = Float64(Float64(x / y) * Float64(y - z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 5.4e+166)
		tmp = (x / y) * (y - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 5.4e+166], N[(N[(x / y), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < 5.40000000000000023e166

   1. Initial program 86.5%

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

      1. associate-*l/ 87.0%

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

   3. Simplified 87.0%

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

   if 5.40000000000000023e166 < y

   1. Initial program 69.5%

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

      1. associate-*l/ 63.7%

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

   3. Simplified 63.7%

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

   4. Taylor expanded in y around inf 86.0%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.4 \cdot 10^{+166}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 50.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+107}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -1.6e+107) (* y (/ x y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.6e+107) {
		tmp = y * (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 (x <= (-1.6d+107)) then
        tmp = y * (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 (x <= -1.6e+107) {
		tmp = y * (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.6e+107:
		tmp = y * (x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.6e+107)
		tmp = Float64(y * Float64(x / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.6e+107)
		tmp = y * (x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.6e+107], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if x < -1.60000000000000015e107

   1. Initial program 80.6%

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

   2. Taylor expanded in y around inf 23.8%

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

      1. associate-*l/ 54.5%

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

   4. Applied egg-rr 54.5%

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

   if -1.60000000000000015e107 < x

   1. Initial program 85.6%

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

      1. associate-*l/ 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in y around inf 48.5%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+107}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 49.9% 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 84.6%

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

   1. associate-*l/ 84.5%

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

3. Simplified 84.5%

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

4. Taylor expanded in y around inf 46.3%

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

5. Final simplification 46.3%

   \[\leadsto x \]

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 2023297 
(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))