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

Percentage Accurate: 84.9% → 96.3%

Time: 6.6s

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: 84.9% 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: 96.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.0%

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

   1. --rgt-identity 83.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{y} - 0} \]

   2. associate-*l/ 82.1%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(y - z\right)} - 0 \]

   3. sub-neg 82.1%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(y + \left(-z\right)\right)} - 0 \]

   4. distribute-rgt-in 79.1%

      \[\leadsto \color{blue}{\left(y \cdot \frac{x}{y} + \left(-z\right) \cdot \frac{x}{y}\right)} - 0 \]

   5. *-commutative 79.1%

      \[\leadsto \left(\color{blue}{\frac{x}{y} \cdot y} + \left(-z\right) \cdot \frac{x}{y}\right) - 0 \]

   6. distribute-lft-neg-out 79.1%

      \[\leadsto \left(\frac{x}{y} \cdot y + \color{blue}{\left(-z \cdot \frac{x}{y}\right)}\right) - 0 \]

   7. unsub-neg 79.1%

      \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot y - z \cdot \frac{x}{y}\right)} - 0 \]

   8. associate--r+ 79.1%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot y - \left(z \cdot \frac{x}{y} + 0\right)} \]

   9. associate-*l/ 79.7%

      \[\leadsto \color{blue}{\frac{x \cdot y}{y}} - \left(z \cdot \frac{x}{y} + 0\right) \]

   10. associate-/l* 93.8%

       \[\leadsto \color{blue}{\frac{x}{\frac{y}{y}}} - \left(z \cdot \frac{x}{y} + 0\right) \]

   11. *-inverses 93.8%

       \[\leadsto \frac{x}{\color{blue}{1}} - \left(z \cdot \frac{x}{y} + 0\right) \]

   12. /-rgt-identity 93.8%

       \[\leadsto \color{blue}{x} - \left(z \cdot \frac{x}{y} + 0\right) \]

   13. +-rgt-identity 93.8%

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

   14. *-commutative 93.8%

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

   15. associate-/r/ 97.8%

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

3. Simplified 97.8%

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

4. Final simplification 97.8%

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

Alternative 2: 71.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+16}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.5e-18) x (if (<= y 1e+16) (* x (/ (- z) y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.5e-18) {
		tmp = x;
	} else if (y <= 1e+16) {
		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 <= (-3.5d-18)) then
        tmp = x
    else if (y <= 1d+16) 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 <= -3.5e-18) {
		tmp = x;
	} else if (y <= 1e+16) {
		tmp = x * (-z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.5e-18:
		tmp = x
	elif y <= 1e+16:
		tmp = x * (-z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.5e-18)
		tmp = x;
	elseif (y <= 1e+16)
		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 <= -3.5e-18)
		tmp = x;
	elseif (y <= 1e+16)
		tmp = x * (-z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.5e-18], x, If[LessEqual[y, 1e+16], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4999999999999999e-18 or 1e16 < y

   1. Initial program 74.6%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 81.9%

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

   if -3.4999999999999999e-18 < y < 1e16

   1. Initial program 93.8%

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

      1. associate-*r/ 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in y around 0 75.1%

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

      1. neg-mul-1 75.1%

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

      2. distribute-neg-frac 75.1%

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

   6. Simplified 75.1%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+16}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 72.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.45e-16) x (if (<= y 3.4e-12) (* z (/ (- x) y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.45e-16) {
		tmp = x;
	} else if (y <= 3.4e-12) {
		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 <= (-1.45d-16)) then
        tmp = x
    else if (y <= 3.4d-12) 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 <= -1.45e-16) {
		tmp = x;
	} else if (y <= 3.4e-12) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.45e-16:
		tmp = x
	elif y <= 3.4e-12:
		tmp = z * (-x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.45e-16)
		tmp = x;
	elseif (y <= 3.4e-12)
		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 <= -1.45e-16)
		tmp = x;
	elseif (y <= 3.4e-12)
		tmp = z * (-x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.45e-16], x, If[LessEqual[y, 3.4e-12], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4499999999999999e-16 or 3.4000000000000001e-12 < y

   1. Initial program 75.6%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 80.7%

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

   if -1.4499999999999999e-16 < y < 3.4000000000000001e-12

   1. Initial program 93.5%

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

      1. associate-*r/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around 0 77.2%

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

      1. mul-1-neg 77.2%

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

      2. associate-*l/ 77.1%

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

      3. distribute-lft-neg-in 77.1%

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

      4. *-commutative 77.1%

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

      5. distribute-neg-frac 77.1%

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

   6. Simplified 77.1%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 71.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{-x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.5e-17) x (if (<= y 3.5e+15) (/ (- x) (/ y z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.5e-17) {
		tmp = x;
	} else if (y <= 3.5e+15) {
		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 (y <= (-5.5d-17)) then
        tmp = x
    else if (y <= 3.5d+15) 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 (y <= -5.5e-17) {
		tmp = x;
	} else if (y <= 3.5e+15) {
		tmp = -x / (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.5e-17:
		tmp = x
	elif y <= 3.5e+15:
		tmp = -x / (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.5e-17)
		tmp = x;
	elseif (y <= 3.5e+15)
		tmp = Float64(Float64(-x) / Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.5e-17)
		tmp = x;
	elseif (y <= 3.5e+15)
		tmp = -x / (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.5e-17], x, If[LessEqual[y, 3.5e+15], N[((-x) / N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -5.50000000000000001e-17 or 3.5e15 < y

   1. Initial program 74.6%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 81.9%

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

   if -5.50000000000000001e-17 < y < 3.5e15

   1. Initial program 93.8%

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

      1. *-commutative 93.8%

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

      2. flip-- 76.1%

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

      3. associate-*l/ 72.1%

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

   3. Applied egg-rr 72.1%

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

   4. Taylor expanded in y around 0 75.9%

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

      1. mul-1-neg 75.9%

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

      2. associate-/l* 76.2%

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

      3. distribute-neg-frac 76.2%

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

   6. Simplified 76.2%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{-x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 51.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-164}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{-12}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e-164) x (if (<= y 1e-12) (* y (/ x y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e-164) {
		tmp = x;
	} else if (y <= 1e-12) {
		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 <= (-2.7d-164)) then
        tmp = x
    else if (y <= 1d-12) 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 <= -2.7e-164) {
		tmp = x;
	} else if (y <= 1e-12) {
		tmp = y * (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.7e-164:
		tmp = x
	elif y <= 1e-12:
		tmp = y * (x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e-164)
		tmp = x;
	elseif (y <= 1e-12)
		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 <= -2.7e-164)
		tmp = x;
	elseif (y <= 1e-12)
		tmp = y * (x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.7e-164], x, If[LessEqual[y, 1e-12], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7000000000000001e-164 or 9.9999999999999998e-13 < y

   1. Initial program 79.1%

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

      1. associate-*r/ 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around inf 73.9%

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

   if -2.7000000000000001e-164 < y < 9.9999999999999998e-13

   1. Initial program 91.5%

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

   2. Taylor expanded in y around inf 12.3%

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

      1. associate-/l* 13.6%

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

      2. associate-/r/ 25.2%

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

   4. Applied egg-rr 25.2%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-164}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{-12}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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 83.0%

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

   1. --rgt-identity 83.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{y} - 0} \]

   2. associate-*l/ 82.1%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(y - z\right)} - 0 \]

   3. sub-neg 82.1%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(y + \left(-z\right)\right)} - 0 \]

   4. distribute-rgt-in 79.1%

      \[\leadsto \color{blue}{\left(y \cdot \frac{x}{y} + \left(-z\right) \cdot \frac{x}{y}\right)} - 0 \]

   5. *-commutative 79.1%

      \[\leadsto \left(\color{blue}{\frac{x}{y} \cdot y} + \left(-z\right) \cdot \frac{x}{y}\right) - 0 \]

   6. distribute-lft-neg-out 79.1%

      \[\leadsto \left(\frac{x}{y} \cdot y + \color{blue}{\left(-z \cdot \frac{x}{y}\right)}\right) - 0 \]

   7. unsub-neg 79.1%

      \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot y - z \cdot \frac{x}{y}\right)} - 0 \]

   8. associate--r+ 79.1%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot y - \left(z \cdot \frac{x}{y} + 0\right)} \]

   9. associate-*l/ 79.7%

      \[\leadsto \color{blue}{\frac{x \cdot y}{y}} - \left(z \cdot \frac{x}{y} + 0\right) \]

   10. associate-/l* 93.8%

       \[\leadsto \color{blue}{\frac{x}{\frac{y}{y}}} - \left(z \cdot \frac{x}{y} + 0\right) \]

   11. *-inverses 93.8%

       \[\leadsto \frac{x}{\color{blue}{1}} - \left(z \cdot \frac{x}{y} + 0\right) \]

   12. /-rgt-identity 93.8%

       \[\leadsto \color{blue}{x} - \left(z \cdot \frac{x}{y} + 0\right) \]

   13. +-rgt-identity 93.8%

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

   14. *-commutative 93.8%

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

   15. associate-/r/ 97.8%

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

3. Simplified 97.8%

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

   1. *-un-lft-identity 97.8%

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

   2. div-inv 97.8%

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

   3. times-frac 94.8%

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

5. Applied egg-rr 94.8%

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

6. Taylor expanded in x around 0 97.3%

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

7. Final simplification 97.3%

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

Alternative 7: 49.7% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 83.0%

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

   1. associate-*r/ 97.3%

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

3. Simplified 97.3%

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

4. Taylor expanded in y around inf 55.1%

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

5. Final simplification 55.1%

   \[\leadsto x \]

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 2023290 
(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))