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

Percentage Accurate: 84.1% → 96.2%

Time: 8.2s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.1% 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: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.7%

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

   1. remove-double-neg 80.7%

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

   2. distribute-frac-neg2 80.7%

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

   3. distribute-frac-neg 80.7%

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

   4. distribute-rgt-neg-in 80.7%

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

   5. associate-/l* 97.7%

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

   6. distribute-frac-neg 97.7%

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

   7. distribute-frac-neg2 97.7%

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

   8. remove-double-neg 97.7%

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

   9. div-sub 97.7%

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

   10. *-inverses 97.7%

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

3. Simplified 97.7%

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

   1. *-inverses 97.7%

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

   2. div-sub 97.7%

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

   3. clear-num 97.6%

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

   4. un-div-inv 97.8%

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

6. Applied egg-rr 97.8%

   \[\leadsto \color{blue}{\frac{x}{\frac{y}{y - z}}} \]
7. Add Preprocessing

Alternative 2: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -32000000000 \lor \neg \left(z \leq 6.6 \cdot 10^{-25}\right):\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -32000000000.0) (not (<= z 6.6e-25))) (* z (/ x (- y))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -32000000000.0) || !(z <= 6.6e-25)) {
		tmp = z * (x / -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-32000000000.0d0)) .or. (.not. (z <= 6.6d-25))) then
        tmp = z * (x / -y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -32000000000.0) || !(z <= 6.6e-25)) {
		tmp = z * (x / -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -32000000000.0) or not (z <= 6.6e-25):
		tmp = z * (x / -y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -32000000000.0) || !(z <= 6.6e-25))
		tmp = Float64(z * Float64(x / Float64(-y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -32000000000.0) || ~((z <= 6.6e-25)))
		tmp = z * (x / -y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -32000000000.0], N[Not[LessEqual[z, 6.6e-25]], $MachinePrecision]], N[(z * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.2e10 or 6.5999999999999997e-25 < z

   1. Initial program 87.1%

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

      1. remove-double-neg 87.1%

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

      2. distribute-frac-neg2 87.1%

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

      3. distribute-frac-neg 87.1%

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

      4. distribute-rgt-neg-in 87.1%

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

      5. associate-/l* 95.1%

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

      6. distribute-frac-neg 95.1%

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

      7. distribute-frac-neg2 95.1%

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

      8. remove-double-neg 95.1%

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

      9. div-sub 95.1%

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

      10. *-inverses 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in z around inf 74.4%

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

      1. mul-1-neg 74.4%

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

      2. distribute-frac-neg2 74.4%

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

      3. *-commutative 74.4%

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

      4. associate-/l* 73.1%

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

   7. Simplified 73.1%

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

   if -3.2e10 < z < 6.5999999999999997e-25

   1. Initial program 75.2%

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

      1. remove-double-neg 75.2%

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

      2. distribute-frac-neg2 75.2%

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

      3. distribute-frac-neg 75.2%

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

      4. distribute-rgt-neg-in 75.2%

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

      5. associate-/l* 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. remove-double-neg 99.9%

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

      9. div-sub 99.9%

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

      10. *-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. Add Preprocessing

   5. Taylor expanded in z around 0 78.3%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -32000000000 \lor \neg \left(z \leq 6.6 \cdot 10^{-25}\right):\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -650000000000 \lor \neg \left(z \leq 2.5 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -650000000000.0) (not (<= z 2.5e-25))) (* x (/ z (- y))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -650000000000.0) || !(z <= 2.5e-25)) {
		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 <= (-650000000000.0d0)) .or. (.not. (z <= 2.5d-25))) 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 <= -650000000000.0) || !(z <= 2.5e-25)) {
		tmp = x * (z / -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -650000000000.0) or not (z <= 2.5e-25):
		tmp = x * (z / -y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -650000000000.0) || !(z <= 2.5e-25))
		tmp = Float64(x * Float64(z / Float64(-y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -650000000000.0) || ~((z <= 2.5e-25)))
		tmp = x * (z / -y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -650000000000.0], N[Not[LessEqual[z, 2.5e-25]], $MachinePrecision]], N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e11 or 2.49999999999999981e-25 < z

   1. Initial program 87.1%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.6%

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

      1. neg-mul-1 71.6%

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

   7. Simplified 71.6%

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

   if -6.5e11 < z < 2.49999999999999981e-25

   1. Initial program 75.2%

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

      1. remove-double-neg 75.2%

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

      2. distribute-frac-neg2 75.2%

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

      3. distribute-frac-neg 75.2%

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

      4. distribute-rgt-neg-in 75.2%

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

      5. associate-/l* 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. remove-double-neg 99.9%

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

      9. div-sub 99.9%

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

      10. *-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. Add Preprocessing

   5. Taylor expanded in z around 0 78.3%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -650000000000 \lor \neg \left(z \leq 2.5 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -800000000:\\ \;\;\;\;\frac{x}{\frac{y}{-z}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -800000000.0)
   (/ x (/ y (- z)))
   (if (<= z 3e-25) x (/ (* x (- z)) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -800000000.0) {
		tmp = x / (y / -z);
	} else if (z <= 3e-25) {
		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 <= (-800000000.0d0)) then
        tmp = x / (y / -z)
    else if (z <= 3d-25) 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 <= -800000000.0) {
		tmp = x / (y / -z);
	} else if (z <= 3e-25) {
		tmp = x;
	} else {
		tmp = (x * -z) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -800000000.0:
		tmp = x / (y / -z)
	elif z <= 3e-25:
		tmp = x
	else:
		tmp = (x * -z) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -800000000.0)
		tmp = Float64(x / Float64(y / Float64(-z)));
	elseif (z <= 3e-25)
		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 <= -800000000.0)
		tmp = x / (y / -z);
	elseif (z <= 3e-25)
		tmp = x;
	else
		tmp = (x * -z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -800000000.0], N[(x / N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-25], x, N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8e8

   1. Initial program 89.6%

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

      1. remove-double-neg 89.6%

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

      2. distribute-frac-neg2 89.6%

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

      3. distribute-frac-neg 89.6%

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

      4. distribute-rgt-neg-in 89.6%

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

      5. associate-/l* 96.5%

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

      6. distribute-frac-neg 96.5%

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

      7. distribute-frac-neg2 96.5%

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

      8. remove-double-neg 96.5%

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

      9. div-sub 96.5%

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

      10. *-inverses 96.5%

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

   3. Simplified 96.5%

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

      1. *-inverses 96.5%

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

      2. div-sub 96.5%

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

      3. clear-num 96.4%

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

      4. un-div-inv 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in y around 0 74.1%

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

      1. associate-*r/ 74.1%

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

      2. neg-mul-1 74.1%

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

   9. Simplified 74.1%

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

   if -8e8 < z < 2.9999999999999998e-25

   1. Initial program 75.2%

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

      1. remove-double-neg 75.2%

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

      2. distribute-frac-neg2 75.2%

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

      3. distribute-frac-neg 75.2%

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

      4. distribute-rgt-neg-in 75.2%

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

      5. associate-/l* 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. remove-double-neg 99.9%

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

      9. div-sub 99.9%

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

      10. *-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. Add Preprocessing

   5. Taylor expanded in z around 0 78.3%

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

   if 2.9999999999999998e-25 < z

   1. Initial program 84.8%

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

      1. remove-double-neg 84.8%

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

      2. distribute-frac-neg2 84.8%

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

      3. distribute-frac-neg 84.8%

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

      4. distribute-rgt-neg-in 84.8%

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

      5. associate-/l* 93.8%

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

      6. distribute-frac-neg 93.8%

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

      7. distribute-frac-neg2 93.8%

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

      8. remove-double-neg 93.8%

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

      9. div-sub 93.8%

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

      10. *-inverses 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in z around inf 74.7%

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

      1. associate-*r/ 74.7%

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

      2. mul-1-neg 74.7%

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

      3. distribute-rgt-neg-out 74.7%

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

   7. Simplified 74.7%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -800000000:\\ \;\;\;\;\frac{x}{\frac{y}{-z}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -85000000000:\\ \;\;\;\;\frac{x}{\frac{y}{-z}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -85000000000.0)
   (/ x (/ y (- z)))
   (if (<= z 2.3e-26) x (* z (/ x (- y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -85000000000.0) {
		tmp = x / (y / -z);
	} else if (z <= 2.3e-26) {
		tmp = x;
	} else {
		tmp = 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 <= (-85000000000.0d0)) then
        tmp = x / (y / -z)
    else if (z <= 2.3d-26) then
        tmp = x
    else
        tmp = z * (x / -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -85000000000.0) {
		tmp = x / (y / -z);
	} else if (z <= 2.3e-26) {
		tmp = x;
	} else {
		tmp = z * (x / -y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -85000000000.0:
		tmp = x / (y / -z)
	elif z <= 2.3e-26:
		tmp = x
	else:
		tmp = z * (x / -y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -85000000000.0)
		tmp = Float64(x / Float64(y / Float64(-z)));
	elseif (z <= 2.3e-26)
		tmp = x;
	else
		tmp = Float64(z * Float64(x / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -85000000000.0)
		tmp = x / (y / -z);
	elseif (z <= 2.3e-26)
		tmp = x;
	else
		tmp = z * (x / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -85000000000.0], N[(x / N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e-26], x, N[(z * N[(x / (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5e10

   1. Initial program 89.6%

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

      1. remove-double-neg 89.6%

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

      2. distribute-frac-neg2 89.6%

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

      3. distribute-frac-neg 89.6%

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

      4. distribute-rgt-neg-in 89.6%

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

      5. associate-/l* 96.5%

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

      6. distribute-frac-neg 96.5%

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

      7. distribute-frac-neg2 96.5%

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

      8. remove-double-neg 96.5%

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

      9. div-sub 96.5%

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

      10. *-inverses 96.5%

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

   3. Simplified 96.5%

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

      1. *-inverses 96.5%

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

      2. div-sub 96.5%

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

      3. clear-num 96.4%

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

      4. un-div-inv 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in y around 0 74.1%

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

      1. associate-*r/ 74.1%

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

      2. neg-mul-1 74.1%

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

   9. Simplified 74.1%

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

   if -8.5e10 < z < 2.30000000000000009e-26

   1. Initial program 75.2%

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

      1. remove-double-neg 75.2%

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

      2. distribute-frac-neg2 75.2%

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

      3. distribute-frac-neg 75.2%

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

      4. distribute-rgt-neg-in 75.2%

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

      5. associate-/l* 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. remove-double-neg 99.9%

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

      9. div-sub 99.9%

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

      10. *-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. Add Preprocessing

   5. Taylor expanded in z around 0 78.3%

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

   if 2.30000000000000009e-26 < z

   1. Initial program 84.8%

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

      1. remove-double-neg 84.8%

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

      2. distribute-frac-neg2 84.8%

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

      3. distribute-frac-neg 84.8%

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

      4. distribute-rgt-neg-in 84.8%

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

      5. associate-/l* 93.8%

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

      6. distribute-frac-neg 93.8%

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

      7. distribute-frac-neg2 93.8%

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

      8. remove-double-neg 93.8%

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

      9. div-sub 93.8%

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

      10. *-inverses 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in z around inf 74.7%

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

      1. mul-1-neg 74.7%

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

      2. distribute-frac-neg2 74.7%

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

      3. *-commutative 74.7%

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

      4. associate-/l* 72.1%

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

   7. Simplified 72.1%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -85000000000:\\ \;\;\;\;\frac{x}{\frac{y}{-z}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.2 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 1.2e-66) x (* y (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.2e-66) {
		tmp = x;
	} else {
		tmp = y * (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 <= 1.2d-66) then
        tmp = x
    else
        tmp = y * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.2e-66) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.2e-66:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.2e-66)
		tmp = x;
	else
		tmp = Float64(y * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.2e-66)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.2e-66], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.20000000000000013e-66

   1. Initial program 80.6%

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

      1. remove-double-neg 80.6%

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

      2. distribute-frac-neg2 80.6%

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

      3. distribute-frac-neg 80.6%

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

      4. distribute-rgt-neg-in 80.6%

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

      5. associate-/l* 98.9%

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

      6. distribute-frac-neg 98.9%

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

      7. distribute-frac-neg2 98.9%

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

      8. remove-double-neg 98.9%

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

      9. div-sub 98.9%

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

      10. *-inverses 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in z around 0 61.1%

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

   if 1.20000000000000013e-66 < z

   1. Initial program 80.8%

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

      1. remove-double-neg 80.8%

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

      2. distribute-frac-neg2 80.8%

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

      3. distribute-frac-neg 80.8%

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

      4. distribute-rgt-neg-in 80.8%

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

      5. associate-/l* 94.4%

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

      6. distribute-frac-neg 94.4%

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

      7. distribute-frac-neg2 94.4%

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

      8. remove-double-neg 94.4%

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

      9. div-sub 94.4%

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

      10. *-inverses 94.4%

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

   3. Simplified 94.4%

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

      1. *-inverses 94.4%

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

      2. div-sub 94.4%

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

      3. clear-num 94.4%

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

      4. un-div-inv 94.4%

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

   6. Applied egg-rr 94.4%

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

      1. frac-2neg 94.4%

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

      2. div-inv 94.4%

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

      3. distribute-neg-frac2 94.4%

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

      4. sub-neg 94.4%

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

      5. distribute-neg-in 94.4%

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

      6. remove-double-neg 94.4%

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

   8. Applied egg-rr 94.4%

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

      1. associate-*r/ 94.4%

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

      2. *-rgt-identity 94.4%

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

      3. distribute-neg-frac 94.4%

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

      4. associate-/r/ 94.4%

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

      5. distribute-rgt-neg-in 94.4%

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

      6. distribute-neg-in 94.4%

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

      7. remove-double-neg 94.4%

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

      8. sub-neg 94.4%

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

   10. Simplified 94.4%

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

   11. Taylor expanded in y around inf 46.5%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.2 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 80.7%

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

   1. remove-double-neg 80.7%

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

   2. distribute-frac-neg2 80.7%

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

   3. distribute-frac-neg 80.7%

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

   4. distribute-rgt-neg-in 80.7%

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

   5. associate-/l* 97.7%

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

   6. distribute-frac-neg 97.7%

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

   7. distribute-frac-neg2 97.7%

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

   8. remove-double-neg 97.7%

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

   9. div-sub 97.7%

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

   10. *-inverses 97.7%

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

3. Simplified 97.7%

   \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{y}\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 8: 50.2% 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 80.7%

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

   1. remove-double-neg 80.7%

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

   2. distribute-frac-neg2 80.7%

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

   3. distribute-frac-neg 80.7%

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

   4. distribute-rgt-neg-in 80.7%

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

   5. associate-/l* 97.7%

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

   6. distribute-frac-neg 97.7%

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

   7. distribute-frac-neg2 97.7%

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

   8. remove-double-neg 97.7%

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

   9. div-sub 97.7%

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

   10. *-inverses 97.7%

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

3. Simplified 97.7%

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

5. Taylor expanded in z around 0 53.5%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 96.1% accurate, 0.4× 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 2024152 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -206020233192173900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- x (/ (* z x) y)) (if (< z 1693976601382852600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))

  (/ (* x (- y z)) y))