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

Percentage Accurate: 84.5% → 96.3%

Time: 5.8s

Alternatives: 10

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: 84.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.3% accurate, 1.0× speedup

Math

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

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 86.2%

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

   1. associate-*l/ 85.5%

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

3. Simplified 85.5%

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

   1. associate-/r/ 97.3%

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

5. Applied egg-rr 97.3%

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

6. Final simplification 97.3%

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

Alternative 2: 67.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \lor \neg \left(z \leq 6 \cdot 10^{-149}\right) \land \left(z \leq 1.6 \cdot 10^{+43} \lor \neg \left(z \leq 9 \cdot 10^{+83}\right)\right):\\ \;\;\;\;x \cdot \left(-\frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.7)
         (and (not (<= z 6e-149)) (or (<= z 1.6e+43) (not (<= z 9e+83)))))
   (* x (- (/ z y)))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.7) || (!(z <= 6e-149) && ((z <= 1.6e+43) || !(z <= 9e+83)))) {
		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 <= (-1.7d0)) .or. (.not. (z <= 6d-149)) .and. (z <= 1.6d+43) .or. (.not. (z <= 9d+83))) 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 <= -1.7) || (!(z <= 6e-149) && ((z <= 1.6e+43) || !(z <= 9e+83)))) {
		tmp = x * -(z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.7) or (not (z <= 6e-149) and ((z <= 1.6e+43) or not (z <= 9e+83))):
		tmp = x * -(z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.7) || (!(z <= 6e-149) && ((z <= 1.6e+43) || !(z <= 9e+83))))
		tmp = Float64(x * Float64(-Float64(z / y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.7) || (~((z <= 6e-149)) && ((z <= 1.6e+43) || ~((z <= 9e+83)))))
		tmp = x * -(z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.7], And[N[Not[LessEqual[z, 6e-149]], $MachinePrecision], Or[LessEqual[z, 1.6e+43], N[Not[LessEqual[z, 9e+83]], $MachinePrecision]]]], N[(x * (-N[(z / y), $MachinePrecision])), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.69999999999999996 or 6.0000000000000003e-149 < z < 1.60000000000000007e43 or 8.9999999999999999e83 < z

   1. Initial program 92.1%

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

      1. associate-*l/ 85.2%

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

   3. Simplified 85.2%

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

      1. associate-/r/ 95.7%

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

   5. Applied egg-rr 95.7%

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

   6. Taylor expanded in y around 0 75.4%

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

      1. associate-*l/ 74.6%

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

      2. associate-*r* 74.6%

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

      3. *-commutative 74.6%

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

      4. mul-1-neg 74.6%

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

   8. Simplified 74.6%

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

   if -1.69999999999999996 < z < 6.0000000000000003e-149 or 1.60000000000000007e43 < z < 8.9999999999999999e83

   1. Initial program 76.6%

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

      1. associate-*l/ 86.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in y around inf 82.7%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \lor \neg \left(z \leq 6 \cdot 10^{-149}\right) \land \left(z \leq 1.6 \cdot 10^{+43} \lor \neg \left(z \leq 9 \cdot 10^{+83}\right)\right):\\ \;\;\;\;x \cdot \left(-\frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 67.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-\frac{z}{y}\right)\\ \mathbf{if}\;z \leq -0.72:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+42}:\\ \;\;\;\;z \cdot \left(-\frac{x}{y}\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- (/ z y)))))
   (if (<= z -0.72)
     t_0
     (if (<= z 6e-149)
       x
       (if (<= z 7.5e+42) (* z (- (/ x y))) (if (<= z 1.9e+83) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -(z / y);
	double tmp;
	if (z <= -0.72) {
		tmp = t_0;
	} else if (z <= 6e-149) {
		tmp = x;
	} else if (z <= 7.5e+42) {
		tmp = z * -(x / y);
	} else if (z <= 1.9e+83) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x * -(z / y)
    if (z <= (-0.72d0)) then
        tmp = t_0
    else if (z <= 6d-149) then
        tmp = x
    else if (z <= 7.5d+42) then
        tmp = z * -(x / y)
    else if (z <= 1.9d+83) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -(z / y);
	double tmp;
	if (z <= -0.72) {
		tmp = t_0;
	} else if (z <= 6e-149) {
		tmp = x;
	} else if (z <= 7.5e+42) {
		tmp = z * -(x / y);
	} else if (z <= 1.9e+83) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -(z / y)
	tmp = 0
	if z <= -0.72:
		tmp = t_0
	elif z <= 6e-149:
		tmp = x
	elif z <= 7.5e+42:
		tmp = z * -(x / y)
	elif z <= 1.9e+83:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-Float64(z / y)))
	tmp = 0.0
	if (z <= -0.72)
		tmp = t_0;
	elseif (z <= 6e-149)
		tmp = x;
	elseif (z <= 7.5e+42)
		tmp = Float64(z * Float64(-Float64(x / y)));
	elseif (z <= 1.9e+83)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -(z / y);
	tmp = 0.0;
	if (z <= -0.72)
		tmp = t_0;
	elseif (z <= 6e-149)
		tmp = x;
	elseif (z <= 7.5e+42)
		tmp = z * -(x / y);
	elseif (z <= 1.9e+83)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-N[(z / y), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[z, -0.72], t$95$0, If[LessEqual[z, 6e-149], x, If[LessEqual[z, 7.5e+42], N[(z * (-N[(x / y), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 1.9e+83], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.71999999999999997 or 1.9000000000000001e83 < z

   1. Initial program 92.8%

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

      1. associate-*l/ 82.7%

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

   3. Simplified 82.7%

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

      1. associate-/r/ 94.4%

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

   5. Applied egg-rr 94.4%

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

   6. Taylor expanded in y around 0 79.4%

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

      1. associate-*l/ 77.5%

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

      2. associate-*r* 77.5%

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

      3. *-commutative 77.5%

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

      4. mul-1-neg 77.5%

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

   8. Simplified 77.5%

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

   if -0.71999999999999997 < z < 6.0000000000000003e-149 or 7.50000000000000041e42 < z < 1.9000000000000001e83

   1. Initial program 76.6%

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

      1. associate-*l/ 86.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in y around inf 82.7%

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

   if 6.0000000000000003e-149 < z < 7.50000000000000041e42

   1. Initial program 90.1%

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

      1. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in y around 0 63.1%

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

      1. *-commutative 63.1%

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

      2. associate-*r/ 63.1%

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

      3. neg-mul-1 63.1%

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

      4. distribute-rgt-neg-in 63.1%

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

      5. associate-*l/ 65.7%

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

   6. Simplified 65.7%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.72:\\ \;\;\;\;x \cdot \left(-\frac{z}{y}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+42}:\\ \;\;\;\;z \cdot \left(-\frac{x}{y}\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-\frac{z}{y}\right)\\ \end{array} \]

Alternative 4: 67.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\frac{-y}{z}}\\ \mathbf{if}\;z \leq -2.6:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+42}:\\ \;\;\;\;z \cdot \left(-\frac{x}{y}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (/ (- y) z))))
   (if (<= z -2.6)
     t_0
     (if (<= z 6e-149)
       x
       (if (<= z 6.5e+42) (* z (- (/ x y))) (if (<= z 9.5e+82) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (-y / z);
	double tmp;
	if (z <= -2.6) {
		tmp = t_0;
	} else if (z <= 6e-149) {
		tmp = x;
	} else if (z <= 6.5e+42) {
		tmp = z * -(x / y);
	} else if (z <= 9.5e+82) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x / (-y / z)
    if (z <= (-2.6d0)) then
        tmp = t_0
    else if (z <= 6d-149) then
        tmp = x
    else if (z <= 6.5d+42) then
        tmp = z * -(x / y)
    else if (z <= 9.5d+82) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x / (-y / z);
	double tmp;
	if (z <= -2.6) {
		tmp = t_0;
	} else if (z <= 6e-149) {
		tmp = x;
	} else if (z <= 6.5e+42) {
		tmp = z * -(x / y);
	} else if (z <= 9.5e+82) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (-y / z)
	tmp = 0
	if z <= -2.6:
		tmp = t_0
	elif z <= 6e-149:
		tmp = x
	elif z <= 6.5e+42:
		tmp = z * -(x / y)
	elif z <= 9.5e+82:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(Float64(-y) / z))
	tmp = 0.0
	if (z <= -2.6)
		tmp = t_0;
	elseif (z <= 6e-149)
		tmp = x;
	elseif (z <= 6.5e+42)
		tmp = Float64(z * Float64(-Float64(x / y)));
	elseif (z <= 9.5e+82)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (-y / z);
	tmp = 0.0;
	if (z <= -2.6)
		tmp = t_0;
	elseif (z <= 6e-149)
		tmp = x;
	elseif (z <= 6.5e+42)
		tmp = z * -(x / y);
	elseif (z <= 9.5e+82)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[((-y) / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6], t$95$0, If[LessEqual[z, 6e-149], x, If[LessEqual[z, 6.5e+42], N[(z * (-N[(x / y), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 9.5e+82], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.60000000000000009 or 9.50000000000000049e82 < z

   1. Initial program 92.8%

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

      1. associate-*l/ 82.7%

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

   3. Simplified 82.7%

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

      1. associate-/r/ 94.4%

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

   5. Applied egg-rr 94.4%

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

   6. Taylor expanded in y around 0 77.6%

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

      1. associate-*r/ 77.6%

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

      2. neg-mul-1 77.6%

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

   8. Simplified 77.6%

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

   if -2.60000000000000009 < z < 6.0000000000000003e-149 or 6.50000000000000052e42 < z < 9.50000000000000049e82

   1. Initial program 76.6%

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

      1. associate-*l/ 86.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in y around inf 82.7%

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

   if 6.0000000000000003e-149 < z < 6.50000000000000052e42

   1. Initial program 90.1%

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

      1. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in y around 0 63.1%

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

      1. *-commutative 63.1%

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

      2. associate-*r/ 63.1%

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

      3. neg-mul-1 63.1%

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

      4. distribute-rgt-neg-in 63.1%

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

      5. associate-*l/ 65.7%

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

   6. Simplified 65.7%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+42}:\\ \;\;\;\;z \cdot \left(-\frac{x}{y}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \end{array} \]

Alternative 5: 68.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.125:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+43}:\\ \;\;\;\;z \cdot \left(-\frac{x}{y}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.125)
   (/ x (/ (- y) z))
   (if (<= z 6e-149)
     x
     (if (<= z 1.25e+43)
       (* z (- (/ x y)))
       (if (<= z 9.5e+82) x (/ (* z (- x)) y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.125) {
		tmp = x / (-y / z);
	} else if (z <= 6e-149) {
		tmp = x;
	} else if (z <= 1.25e+43) {
		tmp = z * -(x / y);
	} else if (z <= 9.5e+82) {
		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 <= (-0.125d0)) then
        tmp = x / (-y / z)
    else if (z <= 6d-149) then
        tmp = x
    else if (z <= 1.25d+43) then
        tmp = z * -(x / y)
    else if (z <= 9.5d+82) 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 <= -0.125) {
		tmp = x / (-y / z);
	} else if (z <= 6e-149) {
		tmp = x;
	} else if (z <= 1.25e+43) {
		tmp = z * -(x / y);
	} else if (z <= 9.5e+82) {
		tmp = x;
	} else {
		tmp = (z * -x) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.125:
		tmp = x / (-y / z)
	elif z <= 6e-149:
		tmp = x
	elif z <= 1.25e+43:
		tmp = z * -(x / y)
	elif z <= 9.5e+82:
		tmp = x
	else:
		tmp = (z * -x) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.125)
		tmp = Float64(x / Float64(Float64(-y) / z));
	elseif (z <= 6e-149)
		tmp = x;
	elseif (z <= 1.25e+43)
		tmp = Float64(z * Float64(-Float64(x / y)));
	elseif (z <= 9.5e+82)
		tmp = x;
	else
		tmp = Float64(Float64(z * Float64(-x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.125)
		tmp = x / (-y / z);
	elseif (z <= 6e-149)
		tmp = x;
	elseif (z <= 1.25e+43)
		tmp = z * -(x / y);
	elseif (z <= 9.5e+82)
		tmp = x;
	else
		tmp = (z * -x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.125], N[(x / N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-149], x, If[LessEqual[z, 1.25e+43], N[(z * (-N[(x / y), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 9.5e+82], x, N[(N[(z * (-x)), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.125

   1. Initial program 90.7%

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

      1. associate-*l/ 88.0%

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

   3. Simplified 88.0%

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

      1. associate-/r/ 96.0%

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

   5. Applied egg-rr 96.0%

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

   6. Taylor expanded in y around 0 78.2%

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

      1. associate-*r/ 78.2%

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

      2. neg-mul-1 78.2%

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

   8. Simplified 78.2%

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

   if -0.125 < z < 6.0000000000000003e-149 or 1.2500000000000001e43 < z < 9.50000000000000049e82

   1. Initial program 76.6%

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

      1. associate-*l/ 86.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in y around inf 82.7%

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

   if 6.0000000000000003e-149 < z < 1.2500000000000001e43

   1. Initial program 90.1%

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

      1. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in y around 0 63.1%

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

      1. *-commutative 63.1%

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

      2. associate-*r/ 63.1%

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

      3. neg-mul-1 63.1%

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

      4. distribute-rgt-neg-in 63.1%

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

      5. associate-*l/ 65.7%

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

   6. Simplified 65.7%

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

   if 9.50000000000000049e82 < z

   1. Initial program 95.9%

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

   2. Taylor expanded in y around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. distribute-rgt-neg-out 82.6%

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

   4. Simplified 82.6%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.125:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+43}:\\ \;\;\;\;z \cdot \left(-\frac{x}{y}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \end{array} \]

Alternative 6: 90.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+186}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+175}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.5e+186) x (if (<= y 9.5e+175) (* (- y z) (/ x y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.5e+186) {
		tmp = x;
	} else if (y <= 9.5e+175) {
		tmp = (y - z) * (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-8.5d+186)) then
        tmp = x
    else if (y <= 9.5d+175) then
        tmp = (y - z) * (x / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.5e+186) {
		tmp = x;
	} else if (y <= 9.5e+175) {
		tmp = (y - z) * (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.5e+186:
		tmp = x
	elif y <= 9.5e+175:
		tmp = (y - z) * (x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.5e+186)
		tmp = x;
	elseif (y <= 9.5e+175)
		tmp = Float64(Float64(y - z) * Float64(x / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.5e+186)
		tmp = x;
	elseif (y <= 9.5e+175)
		tmp = (y - z) * (x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.5e+186], x, If[LessEqual[y, 9.5e+175], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -8.4999999999999999e186 or 9.5000000000000006e175 < y

   1. Initial program 69.4%

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

      1. associate-*l/ 57.2%

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

   3. Simplified 57.2%

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

   4. Taylor expanded in y around inf 83.8%

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

   if -8.4999999999999999e186 < y < 9.5000000000000006e175

   1. Initial program 90.6%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+186}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+175}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 93.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.25 \cdot 10^{+206}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 2.25e+206) (- x (* z (/ x y))) (/ (* z (- x)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.25e+206) {
		tmp = x - (z * (x / y));
	} 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 <= 2.25d+206) then
        tmp = x - (z * (x / y))
    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 <= 2.25e+206) {
		tmp = x - (z * (x / y));
	} else {
		tmp = (z * -x) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 2.25e+206:
		tmp = x - (z * (x / y))
	else:
		tmp = (z * -x) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 2.25e+206)
		tmp = Float64(x - Float64(z * Float64(x / y)));
	else
		tmp = Float64(Float64(z * Float64(-x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 2.25e+206)
		tmp = x - (z * (x / y));
	else
		tmp = (z * -x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 2.25e+206], N[(x - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * (-x)), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.25000000000000009e206

   1. Initial program 84.8%

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

      1. associate-*l/ 86.7%

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

      2. distribute-rgt-out-- 84.4%

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

      3. associate-*r/ 82.2%

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

      4. associate-*l/ 94.9%

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

      5. *-inverses 94.9%

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

      6. *-lft-identity 94.9%

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

   3. Simplified 94.9%

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

   if 2.25000000000000009e206 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 93.5%

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

      1. mul-1-neg 93.5%

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

      2. distribute-rgt-neg-out 93.5%

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

   4. Simplified 93.5%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.25 \cdot 10^{+206}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \end{array} \]

Alternative 8: 52.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -2.4e+79) (* y (/ x y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.4e+79) {
		tmp = y * (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2.4d+79)) then
        tmp = y * (x / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.4e+79) {
		tmp = y * (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.4e+79:
		tmp = y * (x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.4e+79)
		tmp = Float64(y * Float64(x / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.4e+79)
		tmp = y * (x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.4e+79], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if x < -2.39999999999999986e79

   1. Initial program 83.6%

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

   2. Taylor expanded in y around inf 27.2%

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

      1. associate-/l* 43.6%

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

      2. div-inv 45.4%

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

      3. clear-num 45.5%

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

   4. Applied egg-rr 45.5%

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

   if -2.39999999999999986e79 < x

   1. Initial program 86.9%

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

      1. associate-*l/ 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in y around inf 47.7%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.2%

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

   1. associate-*l/ 85.5%

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

   2. distribute-rgt-out-- 82.3%

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

   3. associate-*r/ 81.4%

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

   4. associate-*l/ 93.2%

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

   5. *-inverses 93.2%

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

   6. *-lft-identity 93.2%

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

3. Simplified 93.2%

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

4. Taylor expanded in z around 0 94.5%

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

   1. associate-*l/ 97.2%

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

6. Simplified 97.2%

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

7. Final simplification 97.2%

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

Alternative 10: 51.7% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 86.2%

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

   1. associate-*l/ 85.5%

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

3. Simplified 85.5%

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

4. Taylor expanded in y around inf 45.4%

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

5. Final simplification 45.4%

   \[\leadsto x \]

Developer target: 96.4% 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 2023252 
(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))