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

Percentage Accurate: 85.1% → 96.0%

Time: 4.7s

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: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{y} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (y - z)) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.0% accurate, 1.0× speedup

Math

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

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 78.4%

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

   1. associate-*r/ 96.9%

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

   2. div-sub 96.9%

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

   3. *-inverses 96.9%

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

3. Simplified 96.9%

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

   1. sub-neg 96.9%

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

   2. distribute-rgt-in 96.9%

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

   3. *-un-lft-identity 96.9%

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

   4. distribute-neg-frac 96.9%

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

5. Applied egg-rr 96.9%

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

6. Final simplification 96.9%

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

Alternative 2: 70.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-15} \lor \neg \left(z \leq 4.3 \cdot 10^{+99}\right):\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.6e-15) (not (<= z 4.3e+99))) (* x (/ (- z) y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.6e-15) || !(z <= 4.3e+99)) {
		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 <= (-4.6d-15)) .or. (.not. (z <= 4.3d+99))) 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 <= -4.6e-15) || !(z <= 4.3e+99)) {
		tmp = x * (-z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.6e-15) or not (z <= 4.3e+99):
		tmp = x * (-z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.6e-15) || !(z <= 4.3e+99))
		tmp = Float64(x * Float64(Float64(-z) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.6e-15) || ~((z <= 4.3e+99)))
		tmp = x * (-z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.6e-15], N[Not[LessEqual[z, 4.3e+99]], $MachinePrecision]], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.59999999999999981e-15 or 4.3000000000000001e99 < z

   1. Initial program 86.5%

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

      1. associate-*r/ 92.3%

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

      2. div-sub 92.3%

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

      3. *-inverses 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in z around inf 77.2%

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

      1. associate-*r/ 77.2%

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

      2. mul-1-neg 77.2%

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

      3. distribute-rgt-neg-out 77.2%

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

      4. associate-*r/ 75.4%

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

   6. Simplified 75.4%

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

   if -4.59999999999999981e-15 < z < 4.3000000000000001e99

   1. Initial program 73.2%

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

      1. associate-*r/ 99.8%

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

      2. div-sub 99.9%

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

      3. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 77.5%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-15} \lor \neg \left(z \leq 4.3 \cdot 10^{+99}\right):\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 73.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -600000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -600000000.0) x (if (<= y 4.7e-21) (* z (/ (- x) y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -600000000.0) {
		tmp = x;
	} else if (y <= 4.7e-21) {
		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 (y <= (-600000000.0d0)) then
        tmp = x
    else if (y <= 4.7d-21) 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 (y <= -600000000.0) {
		tmp = x;
	} else if (y <= 4.7e-21) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -600000000.0:
		tmp = x
	elif y <= 4.7e-21:
		tmp = z * (-x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -600000000.0)
		tmp = x;
	elseif (y <= 4.7e-21)
		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 (y <= -600000000.0)
		tmp = x;
	elseif (y <= 4.7e-21)
		tmp = z * (-x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -600000000.0], x, If[LessEqual[y, 4.7e-21], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -6e8 or 4.7000000000000003e-21 < y

   1. Initial program 71.8%

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

      1. associate-*r/ 99.9%

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

      2. div-sub 99.9%

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

      3. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 78.4%

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

   if -6e8 < y < 4.7000000000000003e-21

   1. Initial program 86.9%

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

      1. associate-*r/ 93.1%

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

      2. div-sub 93.1%

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

      3. *-inverses 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in z around inf 69.7%

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

      1. mul-1-neg 69.7%

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

      2. *-commutative 69.7%

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

      3. associate-*r/ 76.4%

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

      4. distribute-lft-neg-out 76.4%

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

   6. Simplified 76.4%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -600000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 71.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+95}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.32e-14)
   (* z (/ (- x) y))
   (if (<= z 1.35e+95) x (/ (* x (- z)) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.32e-14) {
		tmp = z * (-x / y);
	} else if (z <= 1.35e+95) {
		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) :: tmp
    if (z <= (-1.32d-14)) then
        tmp = z * (-x / y)
    else if (z <= 1.35d+95) 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 tmp;
	if (z <= -1.32e-14) {
		tmp = z * (-x / y);
	} else if (z <= 1.35e+95) {
		tmp = x;
	} else {
		tmp = (x * -z) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.32e-14:
		tmp = z * (-x / y)
	elif z <= 1.35e+95:
		tmp = x
	else:
		tmp = (x * -z) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.32e-14)
		tmp = Float64(z * Float64(Float64(-x) / y));
	elseif (z <= 1.35e+95)
		tmp = x;
	else
		tmp = Float64(Float64(x * Float64(-z)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.32e-14)
		tmp = z * (-x / y);
	elseif (z <= 1.35e+95)
		tmp = x;
	else
		tmp = (x * -z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.32e-14], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+95], x, N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.32e-14

   1. Initial program 84.1%

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

      1. associate-*r/ 95.2%

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

      2. div-sub 95.2%

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

      3. *-inverses 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around inf 73.2%

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

      1. mul-1-neg 73.2%

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

      2. *-commutative 73.2%

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

      3. associate-*r/ 76.5%

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

      4. distribute-lft-neg-out 76.5%

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

   6. Simplified 76.5%

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

   if -1.32e-14 < z < 1.35e95

   1. Initial program 73.2%

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

      1. associate-*r/ 99.8%

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

      2. div-sub 99.9%

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

      3. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 77.5%

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

   if 1.35e95 < z

   1. Initial program 90.2%

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

   2. Taylor expanded in y around 0 83.1%

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

      1. mul-1-neg 83.1%

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

      2. distribute-rgt-neg-out 83.1%

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

   4. Simplified 83.1%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+95}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \end{array} \]

Alternative 5: 52.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e-47) x (if (<= y 1.36e-171) (* y (/ x y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e-47) {
		tmp = x;
	} else if (y <= 1.36e-171) {
		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 (y <= (-2d-47)) then
        tmp = x
    else if (y <= 1.36d-171) 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 (y <= -2e-47) {
		tmp = x;
	} else if (y <= 1.36e-171) {
		tmp = y * (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e-47:
		tmp = x
	elif y <= 1.36e-171:
		tmp = y * (x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e-47)
		tmp = x;
	elseif (y <= 1.36e-171)
		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 (y <= -2e-47)
		tmp = x;
	elseif (y <= 1.36e-171)
		tmp = y * (x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e-47], x, If[LessEqual[y, 1.36e-171], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9999999999999999e-47 or 1.3599999999999999e-171 < y

   1. Initial program 76.2%

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

      1. associate-*r/ 99.4%

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

      2. div-sub 99.4%

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

      3. *-inverses 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 70.4%

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

   if -1.9999999999999999e-47 < y < 1.3599999999999999e-171

   1. Initial program 83.4%

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

   2. Taylor expanded in y around inf 13.4%

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

      1. associate-/l* 18.7%

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

      2. associate-/r/ 31.0%

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

   4. Applied egg-rr 31.0%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 96.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \frac{z}{y}\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return x * (1.0 - (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 * (1.0d0 - (z / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.4%

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

   1. associate-*r/ 96.9%

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

   2. div-sub 96.9%

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

   3. *-inverses 96.9%

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

3. Simplified 96.9%

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

4. Final simplification 96.9%

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

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 78.4%

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

   1. associate-*r/ 96.9%

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

   2. div-sub 96.9%

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

   3. *-inverses 96.9%

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

3. Simplified 96.9%

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

4. Taylor expanded in z around 0 55.0%

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

5. Final simplification 55.0%

   \[\leadsto x \]

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 2023336 
(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))