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

Percentage Accurate: 84.1% → 96.8%

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: 84.1% 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: 96.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+174}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5e+174)
   (- x (/ (* z x) y))
   (if (<= z 1.45e-61) (* x (- 1.0 (/ z y))) (- x (* z (/ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e+174) {
		tmp = x - ((z * x) / y);
	} else if (z <= 1.45e-61) {
		tmp = x * (1.0 - (z / y));
	} else {
		tmp = x - (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 <= (-5d+174)) then
        tmp = x - ((z * x) / y)
    else if (z <= 1.45d-61) then
        tmp = x * (1.0d0 - (z / y))
    else
        tmp = x - (z * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e+174) {
		tmp = x - ((z * x) / y);
	} else if (z <= 1.45e-61) {
		tmp = x * (1.0 - (z / y));
	} else {
		tmp = x - (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5e+174:
		tmp = x - ((z * x) / y)
	elif z <= 1.45e-61:
		tmp = x * (1.0 - (z / y))
	else:
		tmp = x - (z * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5e+174)
		tmp = Float64(x - Float64(Float64(z * x) / y));
	elseif (z <= 1.45e-61)
		tmp = Float64(x * Float64(1.0 - Float64(z / y)));
	else
		tmp = Float64(x - Float64(z * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5e+174)
		tmp = x - ((z * x) / y);
	elseif (z <= 1.45e-61)
		tmp = x * (1.0 - (z / y));
	else
		tmp = x - (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5e+174], N[(x - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-61], N[(x * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.9999999999999997e174

   1. Initial program 95.8%

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

      1. associate-*l/ 83.9%

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

      2. distribute-rgt-out-- 79.8%

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

      3. associate-*r/ 86.5%

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

      4. associate-*l/ 90.4%

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

      5. *-inverses 90.4%

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

      6. *-lft-identity 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in z around 0 95.8%

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

   if -4.9999999999999997e174 < z < 1.45e-61

   1. Initial program 83.4%

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

      1. *-un-lft-identity 83.4%

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

      2. times-frac 99.3%

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

   3. Applied egg-rr 99.3%

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

      1. clear-num 99.1%

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

      2. frac-2neg 99.1%

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

      3. frac-times 80.4%

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

      4. *-un-lft-identity 80.4%

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

      5. sub-neg 80.4%

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

      6. distribute-neg-in 80.4%

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

      7. remove-double-neg 80.4%

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

   5. Applied egg-rr 80.4%

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

      1. *-lft-identity 80.4%

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

      2. times-frac 99.1%

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

      3. remove-double-div 99.3%

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

      4. +-commutative 99.3%

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

      5. unsub-neg 99.3%

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

   7. Simplified 99.3%

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

   8. Taylor expanded in z around 0 99.3%

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

      1. mul-1-neg 99.3%

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

      2. unsub-neg 99.3%

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

   10. Simplified 99.3%

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

   if 1.45e-61 < z

   1. Initial program 87.2%

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

      1. associate-*l/ 94.1%

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

      2. distribute-rgt-out-- 85.6%

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

      3. associate-*r/ 90.4%

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

      4. associate-*l/ 99.9%

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

      5. *-inverses 99.9%

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

      6. *-lft-identity 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+174}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \end{array} \]

Alternative 2: 97.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{+96} \lor \neg \left(x \leq 7.2 \cdot 10^{-218}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.8e+96) (not (<= x 7.2e-218)))
   (* x (- 1.0 (/ z y)))
   (- x (* z (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.8e+96) || !(x <= 7.2e-218)) {
		tmp = x * (1.0 - (z / y));
	} else {
		tmp = x - (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 ((x <= (-9.8d+96)) .or. (.not. (x <= 7.2d-218))) then
        tmp = x * (1.0d0 - (z / y))
    else
        tmp = x - (z * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.8e+96) || !(x <= 7.2e-218)) {
		tmp = x * (1.0 - (z / y));
	} else {
		tmp = x - (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9.8e+96) or not (x <= 7.2e-218):
		tmp = x * (1.0 - (z / y))
	else:
		tmp = x - (z * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.8e+96) || !(x <= 7.2e-218))
		tmp = Float64(x * Float64(1.0 - Float64(z / y)));
	else
		tmp = Float64(x - Float64(z * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -9.8e+96) || ~((x <= 7.2e-218)))
		tmp = x * (1.0 - (z / y));
	else
		tmp = x - (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.8e+96], N[Not[LessEqual[x, 7.2e-218]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.7999999999999993e96 or 7.20000000000000023e-218 < x

   1. Initial program 83.0%

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

      1. *-un-lft-identity 83.0%

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

      2. times-frac 99.3%

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

   3. Applied egg-rr 99.3%

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

      1. clear-num 99.1%

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

      2. frac-2neg 99.1%

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

      3. frac-times 86.1%

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

      4. *-un-lft-identity 86.1%

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

      5. sub-neg 86.1%

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

      6. distribute-neg-in 86.1%

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

      7. remove-double-neg 86.1%

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

   5. Applied egg-rr 86.1%

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

      1. *-lft-identity 86.1%

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

      2. times-frac 99.1%

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

      3. remove-double-div 99.3%

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

      4. +-commutative 99.3%

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

      5. unsub-neg 99.3%

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

   7. Simplified 99.3%

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

   8. Taylor expanded in z around 0 99.3%

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

      1. mul-1-neg 99.3%

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

      2. unsub-neg 99.3%

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

   10. Simplified 99.3%

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

   if -9.7999999999999993e96 < x < 7.20000000000000023e-218

   1. Initial program 89.5%

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

      1. associate-*l/ 81.6%

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

      2. distribute-rgt-out-- 81.6%

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

      3. associate-*r/ 93.5%

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

      4. associate-*l/ 98.0%

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

      5. *-inverses 98.0%

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

      6. *-lft-identity 98.0%

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

   3. Simplified 98.0%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{+96} \lor \neg \left(x \leq 7.2 \cdot 10^{-218}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \end{array} \]

Alternative 3: 70.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.9e-37) x (if (<= y 1.08e+15) (* x (/ (- z) y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e-37) {
		tmp = x;
	} else if (y <= 1.08e+15) {
		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 (y <= (-1.9d-37)) then
        tmp = x
    else if (y <= 1.08d+15) 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 (y <= -1.9e-37) {
		tmp = x;
	} else if (y <= 1.08e+15) {
		tmp = x * (-z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.9e-37:
		tmp = x
	elif y <= 1.08e+15:
		tmp = x * (-z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.9e-37)
		tmp = x;
	elseif (y <= 1.08e+15)
		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 (y <= -1.9e-37)
		tmp = x;
	elseif (y <= 1.08e+15)
		tmp = x * (-z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.9e-37], x, If[LessEqual[y, 1.08e+15], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9000000000000002e-37 or 1.08e15 < y

   1. Initial program 76.4%

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

   2. Taylor expanded in y around inf 81.9%

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

   if -1.9000000000000002e-37 < y < 1.08e15

   1. Initial program 93.5%

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

   2. Taylor expanded in y around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. associate-*l/ 65.7%

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

      3. *-commutative 65.7%

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

      4. distribute-rgt-neg-in 65.7%

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

      5. distribute-frac-neg 65.7%

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

   4. Simplified 65.7%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 72.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 45000000000:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.2e-37) x (if (<= y 45000000000.0) (* z (/ (- x) y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.2e-37) {
		tmp = x;
	} else if (y <= 45000000000.0) {
		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 (y <= (-7.2d-37)) then
        tmp = x
    else if (y <= 45000000000.0d0) 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 (y <= -7.2e-37) {
		tmp = x;
	} else if (y <= 45000000000.0) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.2e-37:
		tmp = x
	elif y <= 45000000000.0:
		tmp = z * (-x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.2e-37)
		tmp = x;
	elseif (y <= 45000000000.0)
		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 <= -7.2e-37)
		tmp = x;
	elseif (y <= 45000000000.0)
		tmp = z * (-x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.2e-37], x, If[LessEqual[y, 45000000000.0], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -7.20000000000000014e-37 or 4.5e10 < y

   1. Initial program 76.4%

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

   2. Taylor expanded in y around inf 81.9%

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

   if -7.20000000000000014e-37 < y < 4.5e10

   1. Initial program 93.5%

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

   2. Taylor expanded in y around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. associate-*r/ 71.8%

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

      3. *-commutative 71.8%

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

      4. distribute-rgt-neg-in 71.8%

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

   4. Simplified 71.8%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 45000000000:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 72.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 90000000000000:\\ \;\;\;\;\frac{z}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.5e-37) x (if (<= y 90000000000000.0) (/ z (/ (- y) x)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e-37) {
		tmp = x;
	} else if (y <= 90000000000000.0) {
		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 (y <= (-6.5d-37)) then
        tmp = x
    else if (y <= 90000000000000.0d0) 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 (y <= -6.5e-37) {
		tmp = x;
	} else if (y <= 90000000000000.0) {
		tmp = z / (-y / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.5e-37:
		tmp = x
	elif y <= 90000000000000.0:
		tmp = z / (-y / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.5e-37)
		tmp = x;
	elseif (y <= 90000000000000.0)
		tmp = Float64(z / Float64(Float64(-y) / x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.5e-37)
		tmp = x;
	elseif (y <= 90000000000000.0)
		tmp = z / (-y / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.5e-37], x, If[LessEqual[y, 90000000000000.0], N[(z / N[((-y) / x), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5000000000000001e-37 or 9e13 < y

   1. Initial program 76.4%

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

   2. Taylor expanded in y around inf 81.9%

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

   if -6.5000000000000001e-37 < y < 9e13

   1. Initial program 93.5%

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

   2. Taylor expanded in y around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. associate-*l/ 65.7%

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

      3. *-commutative 65.7%

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

      4. distribute-rgt-neg-in 65.7%

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

      5. distribute-frac-neg 65.7%

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

   4. Simplified 65.7%

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

      1. associate-*r/ 70.3%

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

      2. distribute-rgt-neg-out 70.3%

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

      3. distribute-lft-neg-out 70.3%

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

      4. *-commutative 70.3%

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

      5. associate-/l* 71.9%

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

      6. frac-2neg 71.9%

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

      7. add-sqr-sqrt 36.7%

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

      8. sqrt-unprod 24.9%

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

      9. sqr-neg 24.9%

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

      10. sqrt-unprod 0.8%

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

      11. add-sqr-sqrt 1.6%

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

      12. add-sqr-sqrt 0.8%

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

      13. sqrt-unprod 23.9%

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

      14. sqr-neg 23.9%

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

      15. sqrt-unprod 29.1%

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

      16. add-sqr-sqrt 71.9%

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

   6. Applied egg-rr 71.9%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 90000000000000:\\ \;\;\;\;\frac{z}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 96.1% 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 85.6%

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

   1. *-un-lft-identity 85.6%

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

   2. times-frac 95.1%

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

3. Applied egg-rr 95.1%

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

   1. clear-num 95.0%

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

   2. frac-2neg 95.0%

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

   3. frac-times 84.2%

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

   4. *-un-lft-identity 84.2%

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

   5. sub-neg 84.2%

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

   6. distribute-neg-in 84.2%

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

   7. remove-double-neg 84.2%

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

5. Applied egg-rr 84.2%

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

   1. *-lft-identity 84.2%

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

   2. times-frac 95.0%

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

   3. remove-double-div 95.1%

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

   4. +-commutative 95.1%

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

   5. unsub-neg 95.1%

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

7. Simplified 95.1%

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

8. Taylor expanded in z around 0 95.1%

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

   1. mul-1-neg 95.1%

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

   2. unsub-neg 95.1%

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

10. Simplified 95.1%

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

11. Final simplification 95.1%

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

Alternative 7: 50.3% 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 85.6%

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

2. Taylor expanded in y around inf 52.3%

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

3. Final simplification 52.3%

   \[\leadsto x \]

Developer target: 96.0% 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 2023175 
(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))