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

Percentage Accurate: 83.6% → 96.3%

Time: 6.4s

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: 83.6% 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, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+130}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.4e+130) (/ (* x (- y z)) y) (- x (/ x (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.4e+130) {
		tmp = (x * (y - z)) / y;
	} else {
		tmp = x - (x / (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.4d+130)) then
        tmp = (x * (y - z)) / y
    else
        tmp = x - (x / (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.4e+130) {
		tmp = (x * (y - z)) / y;
	} else {
		tmp = x - (x / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.4e+130:
		tmp = (x * (y - z)) / y
	else:
		tmp = x - (x / (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.4e+130)
		tmp = Float64(Float64(x * Float64(y - z)) / y);
	else
		tmp = Float64(x - Float64(x / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.4e+130)
		tmp = (x * (y - z)) / y;
	else
		tmp = x - (x / (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.4e+130], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x - N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3999999999999999e130

   1. Initial program 97.0%

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

   if -1.3999999999999999e130 < z

   1. Initial program 87.2%

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

      1. --rgt-identity 87.2%

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

      2. associate-*l/ 83.3%

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

      3. sub-neg 83.3%

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

      4. distribute-rgt-in 76.3%

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

      5. *-commutative 76.3%

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

      6. distribute-lft-neg-out 76.3%

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

      7. unsub-neg 76.3%

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

      8. associate--r+ 76.3%

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

      9. associate-*l/ 83.0%

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

      10. associate-/l* 94.0%

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

      11. *-inverses 94.0%

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

      12. /-rgt-identity 94.0%

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

      13. +-rgt-identity 94.0%

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

      14. *-commutative 94.0%

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

      15. associate-/r/ 97.4%

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

   3. Simplified 97.4%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+130}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \end{array} \]

Alternative 2: 71.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -27000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -27000000000000.0) x (if (<= y 7e+23) (* x (/ (- z) y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -27000000000000.0) {
		tmp = x;
	} else if (y <= 7e+23) {
		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 <= (-27000000000000.0d0)) then
        tmp = x
    else if (y <= 7d+23) 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 <= -27000000000000.0) {
		tmp = x;
	} else if (y <= 7e+23) {
		tmp = x * (-z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -27000000000000.0:
		tmp = x
	elif y <= 7e+23:
		tmp = x * (-z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -27000000000000.0)
		tmp = x;
	elseif (y <= 7e+23)
		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 <= -27000000000000.0)
		tmp = x;
	elseif (y <= 7e+23)
		tmp = x * (-z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -27000000000000.0], x, If[LessEqual[y, 7e+23], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e13 or 7.0000000000000004e23 < y

   1. Initial program 81.1%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 85.8%

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

   if -2.7e13 < y < 7.0000000000000004e23

   1. Initial program 94.4%

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

      1. associate-*r/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in y around 0 65.9%

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

      1. neg-mul-1 65.9%

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

      2. distribute-neg-frac 65.9%

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

   6. Simplified 65.9%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -27000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 73.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -13600000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+24}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -13600000000.0) x (if (<= y 1.7e+24) (* z (/ (- x) y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -13600000000.0) {
		tmp = x;
	} else if (y <= 1.7e+24) {
		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 <= (-13600000000.0d0)) then
        tmp = x
    else if (y <= 1.7d+24) 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 <= -13600000000.0) {
		tmp = x;
	} else if (y <= 1.7e+24) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -13600000000.0:
		tmp = x
	elif y <= 1.7e+24:
		tmp = z * (-x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -13600000000.0)
		tmp = x;
	elseif (y <= 1.7e+24)
		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 <= -13600000000.0)
		tmp = x;
	elseif (y <= 1.7e+24)
		tmp = z * (-x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -13600000000.0], x, If[LessEqual[y, 1.7e+24], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.36e10 or 1.7e24 < y

   1. Initial program 81.1%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 85.8%

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

   if -1.36e10 < y < 1.7e24

   1. Initial program 94.4%

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

      1. associate-*r/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in y around 0 71.7%

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

      1. mul-1-neg 71.7%

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

      2. associate-*l/ 72.4%

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

      3. distribute-lft-neg-in 72.4%

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

      4. *-commutative 72.4%

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

      5. distribute-neg-frac 72.4%

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

   6. Simplified 72.4%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -13600000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+24}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 96.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+180}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.05e+180) (* (- y z) (/ x y)) (* x (/ (- y z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05e+180) {
		tmp = (y - z) * (x / y);
	} else {
		tmp = x * ((y - 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 <= (-1.05d+180)) then
        tmp = (y - z) * (x / y)
    else
        tmp = x * ((y - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05e+180) {
		tmp = (y - z) * (x / y);
	} else {
		tmp = x * ((y - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.05e+180:
		tmp = (y - z) * (x / y)
	else:
		tmp = x * ((y - z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.05e+180)
		tmp = Float64(Float64(y - z) * Float64(x / y));
	else
		tmp = Float64(x * Float64(Float64(y - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.05e+180)
		tmp = (y - z) * (x / y);
	else
		tmp = x * ((y - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.05e+180], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e180

   1. Initial program 96.0%

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

      1. *-commutative 96.0%

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

      2. associate-*r/ 95.5%

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

   3. Simplified 95.5%

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

   if -1.05e180 < z

   1. Initial program 87.7%

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

      1. associate-*r/ 97.1%

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

   3. Simplified 97.1%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+180}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array} \]

Alternative 5: 96.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+181}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.5e+181) (* (- y z) (/ x y)) (- x (/ x (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.5e+181) {
		tmp = (y - z) * (x / y);
	} else {
		tmp = x - (x / (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.5d+181)) then
        tmp = (y - z) * (x / y)
    else
        tmp = x - (x / (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.5e+181) {
		tmp = (y - z) * (x / y);
	} else {
		tmp = x - (x / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.5e+181:
		tmp = (y - z) * (x / y)
	else:
		tmp = x - (x / (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.5e+181)
		tmp = Float64(Float64(y - z) * Float64(x / y));
	else
		tmp = Float64(x - Float64(x / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.5e+181)
		tmp = (y - z) * (x / y);
	else
		tmp = x - (x / (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.5e+181], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000006e181

   1. Initial program 96.0%

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

      1. *-commutative 96.0%

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

      2. associate-*r/ 95.5%

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

   3. Simplified 95.5%

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

   if -1.50000000000000006e181 < z

   1. Initial program 87.7%

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

      1. --rgt-identity 87.7%

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

      2. associate-*l/ 82.7%

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

      3. sub-neg 82.7%

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

      4. distribute-rgt-in 76.0%

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

      5. *-commutative 76.0%

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

      6. distribute-lft-neg-out 76.0%

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

      7. unsub-neg 76.0%

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

      8. associate--r+ 76.0%

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

      9. associate-*l/ 83.3%

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

      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/ 97.1%

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

   3. Simplified 97.1%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+181}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \end{array} \]

Alternative 6: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.4%

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

   1. associate-*r/ 95.2%

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

3. Simplified 95.2%

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

4. Final simplification 95.2%

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

Alternative 7: 50.7% 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 88.4%

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

   1. associate-*r/ 95.2%

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

3. Simplified 95.2%

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

4. Taylor expanded in y around inf 53.8%

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

5. Final simplification 53.8%

   \[\leadsto x \]

Developer target: 96.6% 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 2023275 
(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))