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

Percentage Accurate: 84.7% → 96.0%

Time: 9.8s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.7% 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: 96.0% accurate, 0.8× 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 85.1%

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

   1. associate-/l* N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

   4. /-lowering-/.f64 N/A

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

   5. /-lowering-/.f64 N/A

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

   6. --lowering--.f64 96.9

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

4. Applied egg-rr 96.9%

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

Alternative 2: 53.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-262}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;t\_0 \leq 10^{+308}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x (- y z)) y)))
   (if (<= t_0 -1e-262)
     (/ (* x (- z)) y)
     (if (<= t_0 1e+308) x (* y (/ x y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * (y - z)) / y;
	double tmp;
	if (t_0 <= -1e-262) {
		tmp = (x * -z) / y;
	} else if (t_0 <= 1e+308) {
		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) :: t_0
    real(8) :: tmp
    t_0 = (x * (y - z)) / y
    if (t_0 <= (-1d-262)) then
        tmp = (x * -z) / y
    else if (t_0 <= 1d+308) 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 t_0 = (x * (y - z)) / y;
	double tmp;
	if (t_0 <= -1e-262) {
		tmp = (x * -z) / y;
	} else if (t_0 <= 1e+308) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * (y - z)) / y
	tmp = 0
	if t_0 <= -1e-262:
		tmp = (x * -z) / y
	elif t_0 <= 1e+308:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(y - z)) / y)
	tmp = 0.0
	if (t_0 <= -1e-262)
		tmp = Float64(Float64(x * Float64(-z)) / y);
	elseif (t_0 <= 1e+308)
		tmp = x;
	else
		tmp = Float64(y * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * (y - z)) / y;
	tmp = 0.0;
	if (t_0 <= -1e-262)
		tmp = (x * -z) / y;
	elseif (t_0 <= 1e+308)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-262], N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$0, 1e+308], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -1.00000000000000001e-262

   1. Initial program 88.7%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. neg-lowering-neg.f64 42.9

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

   5. Simplified 42.9%

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

   if -1.00000000000000001e-262 < (/.f64 (*.f64 x (-.f64 y z)) y) < 1e308

   1. Initial program 91.6%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Simplified 59.0%

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

   if 1e308 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 61.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 53.1%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -1 \cdot 10^{-262}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 10^{+308}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-262}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;t\_0 \leq 10^{+308}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x (- y z)) y)))
   (if (<= t_0 -1e-262)
     (* x (/ (- z) y))
     (if (<= t_0 1e+308) x (* y (/ x y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * (y - z)) / y;
	double tmp;
	if (t_0 <= -1e-262) {
		tmp = x * (-z / y);
	} else if (t_0 <= 1e+308) {
		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) :: t_0
    real(8) :: tmp
    t_0 = (x * (y - z)) / y
    if (t_0 <= (-1d-262)) then
        tmp = x * (-z / y)
    else if (t_0 <= 1d+308) 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 t_0 = (x * (y - z)) / y;
	double tmp;
	if (t_0 <= -1e-262) {
		tmp = x * (-z / y);
	} else if (t_0 <= 1e+308) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * (y - z)) / y
	tmp = 0
	if t_0 <= -1e-262:
		tmp = x * (-z / y)
	elif t_0 <= 1e+308:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(y - z)) / y)
	tmp = 0.0
	if (t_0 <= -1e-262)
		tmp = Float64(x * Float64(Float64(-z) / y));
	elseif (t_0 <= 1e+308)
		tmp = x;
	else
		tmp = Float64(y * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * (y - z)) / y;
	tmp = 0.0;
	if (t_0 <= -1e-262)
		tmp = x * (-z / y);
	elseif (t_0 <= 1e+308)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-262], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e+308], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -1.00000000000000001e-262

   1. Initial program 88.7%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. neg-lowering-neg.f64 42.9

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

   5. Simplified 42.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. distribute-lft-neg-in N/A

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

      6. distribute-frac-neg2 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. neg-lowering-neg.f64 39.8

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

   7. Applied egg-rr 39.8%

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

   if -1.00000000000000001e-262 < (/.f64 (*.f64 x (-.f64 y z)) y) < 1e308

   1. Initial program 91.6%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Simplified 59.0%

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

   if 1e308 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 61.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 53.1%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -1 \cdot 10^{-262}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 10^{+308}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-262}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-z\right)\\ \mathbf{elif}\;t\_0 \leq 10^{+308}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x (- y z)) y)))
   (if (<= t_0 -1e-262)
     (* (/ x y) (- z))
     (if (<= t_0 1e+308) x (* y (/ x y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * (y - z)) / y;
	double tmp;
	if (t_0 <= -1e-262) {
		tmp = (x / y) * -z;
	} else if (t_0 <= 1e+308) {
		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) :: t_0
    real(8) :: tmp
    t_0 = (x * (y - z)) / y
    if (t_0 <= (-1d-262)) then
        tmp = (x / y) * -z
    else if (t_0 <= 1d+308) 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 t_0 = (x * (y - z)) / y;
	double tmp;
	if (t_0 <= -1e-262) {
		tmp = (x / y) * -z;
	} else if (t_0 <= 1e+308) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * (y - z)) / y
	tmp = 0
	if t_0 <= -1e-262:
		tmp = (x / y) * -z
	elif t_0 <= 1e+308:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(y - z)) / y)
	tmp = 0.0
	if (t_0 <= -1e-262)
		tmp = Float64(Float64(x / y) * Float64(-z));
	elseif (t_0 <= 1e+308)
		tmp = x;
	else
		tmp = Float64(y * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * (y - z)) / y;
	tmp = 0.0;
	if (t_0 <= -1e-262)
		tmp = (x / y) * -z;
	elseif (t_0 <= 1e+308)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-262], N[(N[(x / y), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[t$95$0, 1e+308], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -1.00000000000000001e-262

   1. Initial program 88.7%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. neg-lowering-neg.f64 42.9

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

   5. Simplified 42.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. frac-2neg N/A

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

      5. remove-double-neg N/A

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

      6. /-lowering-/.f64 N/A

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

      7. neg-lowering-neg.f64 41.8

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

   7. Applied egg-rr 41.8%

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

   if -1.00000000000000001e-262 < (/.f64 (*.f64 x (-.f64 y z)) y) < 1e308

   1. Initial program 91.6%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Simplified 59.0%

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

   if 1e308 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 61.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 53.1%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -1 \cdot 10^{-262}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-z\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 10^{+308}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq 10^{+308}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (/ (* x (- y z)) y) 1e+308) x (* y (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x * (y - z)) / y) <= 1e+308) {
		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 * (y - z)) / y) <= 1d+308) 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 * (y - z)) / y) <= 1e+308) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x * (y - z)) / y) <= 1e+308:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(x * Float64(y - z)) / y) <= 1e+308)
		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 * (y - z)) / y) <= 1e+308)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], 1e+308], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < 1e308

   1. Initial program 90.0%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Simplified 57.9%

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

   if 1e308 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 61.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 53.1%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq 10^{+308}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.6% 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 85.1%

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

   1. associate-/l* N/A

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

   2. *-commutative N/A

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

   3. *-lowering-*.f64 N/A

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

   4. div-sub N/A

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

   5. *-inverses N/A

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

   6. --lowering--.f64 N/A

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

   7. /-lowering-/.f64 96.9

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

4. Applied egg-rr 96.9%

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

5. Final simplification 96.9%

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

Alternative 7: 51.1% accurate, 20.0× 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 85.1%

   \[\frac{x \cdot \left(y - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

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

5. Simplified 54.2%

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

Developer Target 1: 96.0% accurate, 0.5× 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 2024198 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

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

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