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

Percentage Accurate: 84.0% → 95.8%

Time: 7.0s

Alternatives: 11

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: 84.0% 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: 95.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+92}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5e+92) (/ (* x (- y z)) y) (* x (/ (- y z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e+92) {
		tmp = (x * (y - z)) / 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 <= (-5d+92)) then
        tmp = (x * (y - z)) / 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 <= -5e+92) {
		tmp = (x * (y - z)) / y;
	} else {
		tmp = x * ((y - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5e+92:
		tmp = (x * (y - z)) / y
	else:
		tmp = x * ((y - z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5e+92)
		tmp = Float64(Float64(x * Float64(y - z)) / 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 <= -5e+92)
		tmp = (x * (y - z)) / y;
	else
		tmp = x * ((y - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5e+92], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000022e92

   1. Initial program 94.0%

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

   if -5.00000000000000022e92 < z

   1. Initial program 82.5%

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

      1. *-commutative 82.5%

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

      2. associate-*l/ 98.5%

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

      3. *-commutative 98.5%

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

   3. Simplified 98.5%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+92}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array} \]

Alternative 2: 69.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+92}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-139} \lor \neg \left(z \leq 4.05 \cdot 10^{-115}\right) \land z \leq 3.45 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.5e+92)
   (* z (/ (- x) y))
   (if (or (<= z 2.8e-139) (and (not (<= z 4.05e-115)) (<= z 3.45e-74)))
     x
     (* x (/ (- z) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.5e+92) {
		tmp = z * (-x / y);
	} else if ((z <= 2.8e-139) || (!(z <= 4.05e-115) && (z <= 3.45e-74))) {
		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 <= (-4.5d+92)) then
        tmp = z * (-x / y)
    else if ((z <= 2.8d-139) .or. (.not. (z <= 4.05d-115)) .and. (z <= 3.45d-74)) 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 <= -4.5e+92) {
		tmp = z * (-x / y);
	} else if ((z <= 2.8e-139) || (!(z <= 4.05e-115) && (z <= 3.45e-74))) {
		tmp = x;
	} else {
		tmp = x * (-z / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.5e+92:
		tmp = z * (-x / y)
	elif (z <= 2.8e-139) or (not (z <= 4.05e-115) and (z <= 3.45e-74)):
		tmp = x
	else:
		tmp = x * (-z / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.5e+92)
		tmp = Float64(z * Float64(Float64(-x) / y));
	elseif ((z <= 2.8e-139) || (!(z <= 4.05e-115) && (z <= 3.45e-74)))
		tmp = x;
	else
		tmp = Float64(x * Float64(Float64(-z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.5e+92)
		tmp = z * (-x / y);
	elseif ((z <= 2.8e-139) || (~((z <= 4.05e-115)) && (z <= 3.45e-74)))
		tmp = x;
	else
		tmp = x * (-z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.5e+92], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2.8e-139], And[N[Not[LessEqual[z, 4.05e-115]], $MachinePrecision], LessEqual[z, 3.45e-74]]], x, N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.4999999999999999e92

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-*l/ 82.4%

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

      3. *-commutative 82.4%

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

      4. div-sub 82.4%

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

      5. *-inverses 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in z around inf 84.2%

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

      1. *-commutative 84.2%

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

      2. associate-*r/ 78.3%

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

      3. associate-*l* 78.3%

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

      4. neg-mul-1 78.3%

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

   6. Simplified 78.3%

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

   if -4.4999999999999999e92 < z < 2.7999999999999999e-139 or 4.0499999999999999e-115 < z < 3.4499999999999999e-74

   1. Initial program 80.7%

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

      1. *-commutative 80.7%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 75.5%

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

   if 2.7999999999999999e-139 < z < 4.0499999999999999e-115 or 3.4499999999999999e-74 < z

   1. Initial program 84.7%

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

      1. *-commutative 84.7%

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

      2. associate-*l/ 96.7%

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

      3. *-commutative 96.7%

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

      4. div-sub 96.7%

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

      5. *-inverses 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in z around inf 71.6%

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

      1. mul-1-neg 71.6%

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

      2. *-commutative 71.6%

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

      3. associate-/l* 71.3%

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

      4. associate-/r/ 74.3%

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

      5. distribute-rgt-neg-in 74.3%

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

   6. Simplified 74.3%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+92}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-139} \lor \neg \left(z \leq 4.05 \cdot 10^{-115}\right) \land z \leq 3.45 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \end{array} \]

Alternative 3: 69.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{-\frac{y}{z}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.4e+91)
   (* z (/ (- x) y))
   (if (<= z 1.38e-139)
     x
     (if (<= z 5.3e-115)
       (/ x (- (/ y z)))
       (if (<= z 1.7e-74) x (* x (/ (- z) y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.4e+91) {
		tmp = z * (-x / y);
	} else if (z <= 1.38e-139) {
		tmp = x;
	} else if (z <= 5.3e-115) {
		tmp = x / -(y / z);
	} else if (z <= 1.7e-74) {
		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 <= (-4.4d+91)) then
        tmp = z * (-x / y)
    else if (z <= 1.38d-139) then
        tmp = x
    else if (z <= 5.3d-115) then
        tmp = x / -(y / z)
    else if (z <= 1.7d-74) 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 <= -4.4e+91) {
		tmp = z * (-x / y);
	} else if (z <= 1.38e-139) {
		tmp = x;
	} else if (z <= 5.3e-115) {
		tmp = x / -(y / z);
	} else if (z <= 1.7e-74) {
		tmp = x;
	} else {
		tmp = x * (-z / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.4e+91:
		tmp = z * (-x / y)
	elif z <= 1.38e-139:
		tmp = x
	elif z <= 5.3e-115:
		tmp = x / -(y / z)
	elif z <= 1.7e-74:
		tmp = x
	else:
		tmp = x * (-z / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.4e+91)
		tmp = Float64(z * Float64(Float64(-x) / y));
	elseif (z <= 1.38e-139)
		tmp = x;
	elseif (z <= 5.3e-115)
		tmp = Float64(x / Float64(-Float64(y / z)));
	elseif (z <= 1.7e-74)
		tmp = x;
	else
		tmp = Float64(x * Float64(Float64(-z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.4e+91)
		tmp = z * (-x / y);
	elseif (z <= 1.38e-139)
		tmp = x;
	elseif (z <= 5.3e-115)
		tmp = x / -(y / z);
	elseif (z <= 1.7e-74)
		tmp = x;
	else
		tmp = x * (-z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.4e+91], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.38e-139], x, If[LessEqual[z, 5.3e-115], N[(x / (-N[(y / z), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 1.7e-74], x, N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.39999999999999999e91

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-*l/ 82.4%

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

      3. *-commutative 82.4%

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

      4. div-sub 82.4%

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

      5. *-inverses 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in z around inf 84.2%

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

      1. *-commutative 84.2%

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

      2. associate-*r/ 78.3%

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

      3. associate-*l* 78.3%

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

      4. neg-mul-1 78.3%

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

   6. Simplified 78.3%

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

   if -4.39999999999999999e91 < z < 1.3800000000000001e-139 or 5.3e-115 < z < 1.7e-74

   1. Initial program 80.7%

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

      1. *-commutative 80.7%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 75.5%

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

   if 1.3800000000000001e-139 < z < 5.3e-115

   1. Initial program 86.3%

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

      1. *-commutative 86.3%

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

      2. associate-*l/ 99.3%

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

      3. *-commutative 99.3%

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

      4. div-sub 99.3%

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

      5. *-inverses 99.3%

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

   3. Simplified 99.3%

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

      1. *-inverses 99.3%

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

      2. div-sub 99.3%

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

      3. associate-*r/ 86.3%

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

      4. clear-num 86.1%

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

   5. Applied egg-rr 86.1%

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

   6. Taylor expanded in y around 0 72.9%

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

      1. neg-mul-1 72.9%

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

      2. distribute-neg-frac 72.9%

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

   8. Simplified 72.9%

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

      1. clear-num 72.9%

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

      2. neg-mul-1 72.9%

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

      3. times-frac 85.9%

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

   10. Applied egg-rr 85.9%

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

       1. associate-*l/ 85.9%

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

       2. associate-*r/ 72.9%

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

       3. associate-/l* 86.1%

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

       4. associate-/l/ 86.1%

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

       5. neg-mul-1 86.1%

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

   12. Simplified 86.1%

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

   if 1.7e-74 < z

   1. Initial program 84.6%

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

      1. *-commutative 84.6%

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

      2. associate-*l/ 96.5%

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

      3. *-commutative 96.5%

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

      4. div-sub 96.5%

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

      5. *-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. Taylor expanded in z around inf 71.5%

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

      1. mul-1-neg 71.5%

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

      2. *-commutative 71.5%

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

      3. associate-/l* 72.2%

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

      4. associate-/r/ 73.4%

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

      5. distribute-rgt-neg-in 73.4%

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

   6. Simplified 73.4%

      \[\leadsto \color{blue}{\frac{z}{y} \cdot \left(-x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{-\frac{y}{z}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \end{array} \]

Alternative 4: 69.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+91}:\\ \;\;\;\;\frac{z}{-\frac{y}{x}}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.05 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{-\frac{y}{z}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.4e+91)
   (/ z (- (/ y x)))
   (if (<= z 2.8e-139)
     x
     (if (<= z 4.05e-115)
       (/ x (- (/ y z)))
       (if (<= z 3.1e-74) x (* x (/ (- z) y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.4e+91) {
		tmp = z / -(y / x);
	} else if (z <= 2.8e-139) {
		tmp = x;
	} else if (z <= 4.05e-115) {
		tmp = x / -(y / z);
	} else if (z <= 3.1e-74) {
		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 <= (-4.4d+91)) then
        tmp = z / -(y / x)
    else if (z <= 2.8d-139) then
        tmp = x
    else if (z <= 4.05d-115) then
        tmp = x / -(y / z)
    else if (z <= 3.1d-74) 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 <= -4.4e+91) {
		tmp = z / -(y / x);
	} else if (z <= 2.8e-139) {
		tmp = x;
	} else if (z <= 4.05e-115) {
		tmp = x / -(y / z);
	} else if (z <= 3.1e-74) {
		tmp = x;
	} else {
		tmp = x * (-z / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.4e+91:
		tmp = z / -(y / x)
	elif z <= 2.8e-139:
		tmp = x
	elif z <= 4.05e-115:
		tmp = x / -(y / z)
	elif z <= 3.1e-74:
		tmp = x
	else:
		tmp = x * (-z / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.4e+91)
		tmp = Float64(z / Float64(-Float64(y / x)));
	elseif (z <= 2.8e-139)
		tmp = x;
	elseif (z <= 4.05e-115)
		tmp = Float64(x / Float64(-Float64(y / z)));
	elseif (z <= 3.1e-74)
		tmp = x;
	else
		tmp = Float64(x * Float64(Float64(-z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.4e+91)
		tmp = z / -(y / x);
	elseif (z <= 2.8e-139)
		tmp = x;
	elseif (z <= 4.05e-115)
		tmp = x / -(y / z);
	elseif (z <= 3.1e-74)
		tmp = x;
	else
		tmp = x * (-z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.4e+91], N[(z / (-N[(y / x), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 2.8e-139], x, If[LessEqual[z, 4.05e-115], N[(x / (-N[(y / z), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 3.1e-74], x, N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.39999999999999999e91

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-*l/ 82.4%

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

      3. *-commutative 82.4%

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

      4. div-sub 82.4%

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

      5. *-inverses 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in z around inf 84.2%

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

      1. *-commutative 84.2%

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

      2. associate-*r/ 78.3%

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

      3. associate-*l* 78.3%

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

      4. neg-mul-1 78.3%

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

   6. Simplified 78.3%

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

      1. associate-*r/ 84.2%

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

      2. distribute-lft-neg-in 84.2%

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

      3. distribute-rgt-neg-out 84.2%

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

      4. associate-/l* 78.3%

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

      5. frac-2neg 78.3%

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

      6. add-sqr-sqrt 78.1%

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

      7. sqrt-unprod 56.2%

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

      8. sqr-neg 56.2%

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

      9. sqrt-unprod 0.0%

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

      10. add-sqr-sqrt 1.6%

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

      11. add-sqr-sqrt 0.4%

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

      12. sqrt-unprod 37.1%

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

      13. sqr-neg 37.1%

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

      14. sqrt-unprod 44.6%

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

      15. add-sqr-sqrt 78.3%

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

   8. Applied egg-rr 78.3%

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

   if -4.39999999999999999e91 < z < 2.7999999999999999e-139 or 4.0499999999999999e-115 < z < 3.1000000000000002e-74

   1. Initial program 80.7%

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

      1. *-commutative 80.7%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 75.5%

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

   if 2.7999999999999999e-139 < z < 4.0499999999999999e-115

   1. Initial program 86.3%

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

      1. *-commutative 86.3%

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

      2. associate-*l/ 99.3%

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

      3. *-commutative 99.3%

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

      4. div-sub 99.3%

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

      5. *-inverses 99.3%

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

   3. Simplified 99.3%

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

      1. *-inverses 99.3%

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

      2. div-sub 99.3%

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

      3. associate-*r/ 86.3%

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

      4. clear-num 86.1%

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

   5. Applied egg-rr 86.1%

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

   6. Taylor expanded in y around 0 72.9%

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

      1. neg-mul-1 72.9%

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

      2. distribute-neg-frac 72.9%

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

   8. Simplified 72.9%

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

      1. clear-num 72.9%

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

      2. neg-mul-1 72.9%

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

      3. times-frac 85.9%

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

   10. Applied egg-rr 85.9%

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

       1. associate-*l/ 85.9%

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

       2. associate-*r/ 72.9%

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

       3. associate-/l* 86.1%

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

       4. associate-/l/ 86.1%

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

       5. neg-mul-1 86.1%

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

   12. Simplified 86.1%

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

   if 3.1000000000000002e-74 < z

   1. Initial program 84.6%

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

      1. *-commutative 84.6%

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

      2. associate-*l/ 96.5%

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

      3. *-commutative 96.5%

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

      4. div-sub 96.5%

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

      5. *-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. Taylor expanded in z around inf 71.5%

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

      1. mul-1-neg 71.5%

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

      2. *-commutative 71.5%

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

      3. associate-/l* 72.2%

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

      4. associate-/r/ 73.4%

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

      5. distribute-rgt-neg-in 73.4%

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

   6. Simplified 73.4%

      \[\leadsto \color{blue}{\frac{z}{y} \cdot \left(-x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+91}:\\ \;\;\;\;\frac{z}{-\frac{y}{x}}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.05 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{-\frac{y}{z}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \end{array} \]

Alternative 5: 69.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+92}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{-\frac{y}{z}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.5e+92)
   (/ (* z (- x)) y)
   (if (<= z 2.8e-139)
     x
     (if (<= z 1.02e-114)
       (/ x (- (/ y z)))
       (if (<= z 1.6e-78) x (* x (/ (- z) y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.5e+92) {
		tmp = (z * -x) / y;
	} else if (z <= 2.8e-139) {
		tmp = x;
	} else if (z <= 1.02e-114) {
		tmp = x / -(y / z);
	} else if (z <= 1.6e-78) {
		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 <= (-4.5d+92)) then
        tmp = (z * -x) / y
    else if (z <= 2.8d-139) then
        tmp = x
    else if (z <= 1.02d-114) then
        tmp = x / -(y / z)
    else if (z <= 1.6d-78) 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 <= -4.5e+92) {
		tmp = (z * -x) / y;
	} else if (z <= 2.8e-139) {
		tmp = x;
	} else if (z <= 1.02e-114) {
		tmp = x / -(y / z);
	} else if (z <= 1.6e-78) {
		tmp = x;
	} else {
		tmp = x * (-z / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.5e+92:
		tmp = (z * -x) / y
	elif z <= 2.8e-139:
		tmp = x
	elif z <= 1.02e-114:
		tmp = x / -(y / z)
	elif z <= 1.6e-78:
		tmp = x
	else:
		tmp = x * (-z / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.5e+92)
		tmp = Float64(Float64(z * Float64(-x)) / y);
	elseif (z <= 2.8e-139)
		tmp = x;
	elseif (z <= 1.02e-114)
		tmp = Float64(x / Float64(-Float64(y / z)));
	elseif (z <= 1.6e-78)
		tmp = x;
	else
		tmp = Float64(x * Float64(Float64(-z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.5e+92)
		tmp = (z * -x) / y;
	elseif (z <= 2.8e-139)
		tmp = x;
	elseif (z <= 1.02e-114)
		tmp = x / -(y / z);
	elseif (z <= 1.6e-78)
		tmp = x;
	else
		tmp = x * (-z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.5e+92], N[(N[(z * (-x)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 2.8e-139], x, If[LessEqual[z, 1.02e-114], N[(x / (-N[(y / z), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 1.6e-78], x, N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.4999999999999999e92

   1. Initial program 94.0%

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

   2. Taylor expanded in y around 0 84.2%

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

      1. mul-1-neg 84.2%

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

      2. *-commutative 84.2%

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

      3. distribute-rgt-neg-in 84.2%

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

   4. Simplified 84.2%

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

   if -4.4999999999999999e92 < z < 2.7999999999999999e-139 or 1.0199999999999999e-114 < z < 1.6e-78

   1. Initial program 80.7%

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

      1. *-commutative 80.7%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 75.5%

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

   if 2.7999999999999999e-139 < z < 1.0199999999999999e-114

   1. Initial program 86.3%

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

      1. *-commutative 86.3%

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

      2. associate-*l/ 99.3%

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

      3. *-commutative 99.3%

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

      4. div-sub 99.3%

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

      5. *-inverses 99.3%

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

   3. Simplified 99.3%

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

      1. *-inverses 99.3%

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

      2. div-sub 99.3%

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

      3. associate-*r/ 86.3%

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

      4. clear-num 86.1%

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

   5. Applied egg-rr 86.1%

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

   6. Taylor expanded in y around 0 72.9%

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

      1. neg-mul-1 72.9%

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

      2. distribute-neg-frac 72.9%

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

   8. Simplified 72.9%

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

      1. clear-num 72.9%

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

      2. neg-mul-1 72.9%

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

      3. times-frac 85.9%

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

   10. Applied egg-rr 85.9%

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

       1. associate-*l/ 85.9%

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

       2. associate-*r/ 72.9%

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

       3. associate-/l* 86.1%

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

       4. associate-/l/ 86.1%

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

       5. neg-mul-1 86.1%

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

   12. Simplified 86.1%

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

   if 1.6e-78 < z

   1. Initial program 84.6%

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

      1. *-commutative 84.6%

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

      2. associate-*l/ 96.5%

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

      3. *-commutative 96.5%

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

      4. div-sub 96.5%

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

      5. *-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. Taylor expanded in z around inf 71.5%

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

      1. mul-1-neg 71.5%

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

      2. *-commutative 71.5%

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

      3. associate-/l* 72.2%

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

      4. associate-/r/ 73.4%

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

      5. distribute-rgt-neg-in 73.4%

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

   6. Simplified 73.4%

      \[\leadsto \color{blue}{\frac{z}{y} \cdot \left(-x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+92}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{-\frac{y}{z}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \end{array} \]

Alternative 6: 71.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+91} \lor \neg \left(z \leq 4 \cdot 10^{-74}\right):\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.4e+91) (not (<= z 4e-74))) (* z (/ (- x) y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.4e+91) || !(z <= 4e-74)) {
		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 <= (-4.4d+91)) .or. (.not. (z <= 4d-74))) 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 <= -4.4e+91) || !(z <= 4e-74)) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.4e+91) or not (z <= 4e-74):
		tmp = z * (-x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.4e+91) || !(z <= 4e-74))
		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 ((z <= -4.4e+91) || ~((z <= 4e-74)))
		tmp = z * (-x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.4e+91], N[Not[LessEqual[z, 4e-74]], $MachinePrecision]], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.39999999999999999e91 or 3.99999999999999983e-74 < z

   1. Initial program 88.0%

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

      1. *-commutative 88.0%

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

      2. associate-*l/ 91.5%

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

      3. *-commutative 91.5%

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

      4. div-sub 91.5%

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

      5. *-inverses 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in z around inf 76.1%

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

      1. *-commutative 76.1%

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

      2. associate-*r/ 73.8%

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

      3. associate-*l* 73.8%

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

      4. neg-mul-1 73.8%

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

   6. Simplified 73.8%

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

   if -4.39999999999999999e91 < z < 3.99999999999999983e-74

   1. Initial program 81.0%

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

      1. *-commutative 81.0%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 72.2%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+91} \lor \neg \left(z \leq 4 \cdot 10^{-74}\right):\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 51.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.35 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 1.35e+108) x (* y (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.35e+108) {
		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 (x <= 1.35d+108) 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 (x <= 1.35e+108) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.35e+108:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.35e+108)
		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 (x <= 1.35e+108)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.35e+108], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.35e108

   1. Initial program 85.4%

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

      1. *-commutative 85.4%

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

      2. associate-*l/ 94.9%

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

      3. *-commutative 94.9%

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

      4. div-sub 94.9%

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

      5. *-inverses 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in z around 0 49.4%

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

   if 1.35e108 < x

   1. Initial program 79.7%

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

   2. Taylor expanded in y around inf 8.5%

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

      1. associate-/l* 20.2%

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

      2. associate-/r/ 29.4%

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

   4. Applied egg-rr 29.4%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.35 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]

Alternative 8: 51.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.8 \cdot 10^{+134}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 4.8e+134) x (/ y (/ y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 4.8e+134) {
		tmp = x;
	} else {
		tmp = y / (y / 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 (x <= 4.8d+134) then
        tmp = x
    else
        tmp = y / (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 4.8e+134) {
		tmp = x;
	} else {
		tmp = y / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 4.8e+134:
		tmp = x
	else:
		tmp = y / (y / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 4.8e+134)
		tmp = x;
	else
		tmp = Float64(y / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 4.8e+134)
		tmp = x;
	else
		tmp = y / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 4.8e+134], x, N[(y / N[(y / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.80000000000000011e134

   1. Initial program 85.6%

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

      1. *-commutative 85.6%

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

      2. associate-*l/ 94.9%

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

      3. *-commutative 94.9%

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

      4. div-sub 94.9%

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

      5. *-inverses 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in z around 0 48.7%

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

   if 4.80000000000000011e134 < x

   1. Initial program 77.6%

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

   2. Taylor expanded in y around inf 9.3%

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

      1. associate-/l* 22.2%

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

      2. associate-/r/ 32.4%

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

   4. Applied egg-rr 32.4%

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

      1. *-commutative 32.4%

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

      2. clear-num 32.4%

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

      3. div-inv 32.4%

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

   6. Applied egg-rr 32.4%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.8 \cdot 10^{+134}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \end{array} \]

Alternative 9: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - (z / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.7%

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

   1. *-commutative 84.7%

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

   2. associate-*l/ 95.5%

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

   3. *-commutative 95.5%

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

   4. div-sub 95.5%

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

   5. *-inverses 95.5%

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

3. Simplified 95.5%

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

4. Final simplification 95.5%

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

Alternative 10: 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 84.7%

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

   1. *-commutative 84.7%

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

   2. associate-*l/ 95.5%

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

   3. *-commutative 95.5%

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

3. Simplified 95.5%

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

4. Final simplification 95.5%

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

Alternative 11: 50.8% 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 84.7%

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

   1. *-commutative 84.7%

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

   2. associate-*l/ 95.5%

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

   3. *-commutative 95.5%

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

   4. div-sub 95.5%

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

   5. *-inverses 95.5%

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

3. Simplified 95.5%

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

4. Taylor expanded in z around 0 45.7%

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

5. Final simplification 45.7%

   \[\leadsto x \]

Developer target: 96.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< z -2.060202331921739e+104)
   (- x (/ (* z x) y))
   (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z < (-2.060202331921739d+104)) then
        tmp = x - ((z * x) / y)
    else if (z < 1.6939766013828526d+213) then
        tmp = x / (y / (y - z))
    else
        tmp = (y - z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z < -2.060202331921739e+104:
		tmp = x - ((z * x) / y)
	elif z < 1.6939766013828526e+213:
		tmp = x / (y / (y - z))
	else:
		tmp = (y - z) * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z < -2.060202331921739e+104)
		tmp = Float64(x - Float64(Float64(z * x) / y));
	elseif (z < 1.6939766013828526e+213)
		tmp = Float64(x / Float64(y / Float64(y - z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z < -2.060202331921739e+104)
		tmp = x - ((z * x) / y);
	elseif (z < 1.6939766013828526e+213)
		tmp = x / (y / (y - z));
	else
		tmp = (y - z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[z, -2.060202331921739e+104], N[(x - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Less[z, 1.6939766013828526e+213], N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023325 
(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))