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

Percentage Accurate: 84.9% → 94.3%

Time: 5.9s

Alternatives: 3

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: 84.9% 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: 94.3% accurate, 1.0× speedup

Math

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

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(Float64(x * z) / y))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.2%

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

3. Taylor expanded in x around 0

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

   1. associate-/l* N/A

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

   2. div-sub N/A

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

   3. *-inverses N/A

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

   4. distribute-lft-out-- N/A

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

   5. *-rgt-identity N/A

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

   6. associate-/l* N/A

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

   7. lower--.f64 N/A

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

   8. lower-/.f64 N/A

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

   9. lower-*.f64 95.8

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

5. Simplified 95.8%

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

Alternative 2: 58.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ t_1 := -\frac{x \cdot z}{y}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 10^{+196}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x (- y z)) y)) (t_1 (- (/ (* x z) y))))
   (if (<= t_0 -2e-176) t_1 (if (<= t_0 1e+196) (/ (* x y) y) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (x * (y - z)) / y;
	double t_1 = -((x * z) / y);
	double tmp;
	if (t_0 <= -2e-176) {
		tmp = t_1;
	} else if (t_0 <= 1e+196) {
		tmp = (x * y) / y;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = (x * (y - z)) / y
    t_1 = -((x * z) / y)
    if (t_0 <= (-2d-176)) then
        tmp = t_1
    else if (t_0 <= 1d+196) then
        tmp = (x * y) / y
    else
        tmp = t_1
    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 t_1 = -((x * z) / y);
	double tmp;
	if (t_0 <= -2e-176) {
		tmp = t_1;
	} else if (t_0 <= 1e+196) {
		tmp = (x * y) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * (y - z)) / y
	t_1 = -((x * z) / y)
	tmp = 0
	if t_0 <= -2e-176:
		tmp = t_1
	elif t_0 <= 1e+196:
		tmp = (x * y) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(y - z)) / y)
	t_1 = Float64(-Float64(Float64(x * z) / y))
	tmp = 0.0
	if (t_0 <= -2e-176)
		tmp = t_1;
	elseif (t_0 <= 1e+196)
		tmp = Float64(Float64(x * y) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * (y - z)) / y;
	t_1 = -((x * z) / y);
	tmp = 0.0;
	if (t_0 <= -2e-176)
		tmp = t_1;
	elseif (t_0 <= 1e+196)
		tmp = (x * y) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = (-N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision])}, If[LessEqual[t$95$0, -2e-176], t$95$1, If[LessEqual[t$95$0, 1e+196], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -2e-176 or 9.9999999999999995e195 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 80.7%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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. lower-/.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. lower-*.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. lower-neg.f64 56.2

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

   5. Simplified 56.2%

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

   if -2e-176 < (/.f64 (*.f64 x (-.f64 y z)) y) < 9.9999999999999995e195

   1. Initial program 90.6%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 66.2

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

   5. Simplified 66.2%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -2 \cdot 10^{-176}:\\ \;\;\;\;-\frac{x \cdot z}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 10^{+196}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;-\frac{x \cdot z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 40.4% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.2%

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

3. Taylor expanded in y around inf

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

   1. lower-*.f64 40.7

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

5. Simplified 40.7%

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

Developer Target 1: 96.6% 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 2024215 
(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))