Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1

Percentage Accurate: 67.2% → 99.7%

Time: 7.5s

Alternatives: 4

Speedup: 1.0×

• 48.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ \frac{\frac{x}{y}}{\frac{y}{x}} + \frac{\frac{z}{t\_m}}{\sqrt{t\_m}} \cdot \frac{z}{\sqrt{t\_m}} \end{array} \]

FPCore

t_m = (fabs.f64 t)
(FPCore (x y z t_m)
 :precision binary64
 (+ (/ (/ x y) (/ y x)) (* (/ (/ z t_m) (sqrt t_m)) (/ z (sqrt t_m)))))

C

t_m = fabs(t);
double code(double x, double y, double z, double t_m) {
	return ((x / y) / (y / x)) + (((z / t_m) / sqrt(t_m)) * (z / sqrt(t_m)));
}

Fortran

t_m = abs(t)
real(8) function code(x, y, z, t_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    code = ((x / y) / (y / x)) + (((z / t_m) / sqrt(t_m)) * (z / sqrt(t_m)))
end function

Java

t_m = Math.abs(t);
public static double code(double x, double y, double z, double t_m) {
	return ((x / y) / (y / x)) + (((z / t_m) / Math.sqrt(t_m)) * (z / Math.sqrt(t_m)));
}

Python

t_m = math.fabs(t)
def code(x, y, z, t_m):
	return ((x / y) / (y / x)) + (((z / t_m) / math.sqrt(t_m)) * (z / math.sqrt(t_m)))

Julia

t_m = abs(t)
function code(x, y, z, t_m)
	return Float64(Float64(Float64(x / y) / Float64(y / x)) + Float64(Float64(Float64(z / t_m) / sqrt(t_m)) * Float64(z / sqrt(t_m))))
end

MATLAB

t_m = abs(t);
function tmp = code(x, y, z, t_m)
	tmp = ((x / y) / (y / x)) + (((z / t_m) / sqrt(t_m)) * (z / sqrt(t_m)));
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
code[x_, y_, z_, t$95$m_] := N[(N[(N[(x / y), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z / t$95$m), $MachinePrecision] / N[Sqrt[t$95$m], $MachinePrecision]), $MachinePrecision] * N[(z / N[Sqrt[t$95$m], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 67.6%

   \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
2. Step-by-step derivation

   1. associate-/l* 75.9%

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

3. Simplified 75.9%

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

   1. associate-*r/ 67.6%

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

   2. times-frac 85.8%

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

   3. clear-num 85.8%

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

   4. un-div-inv 85.9%

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

6. Applied egg-rr 85.9%

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

   1. frac-times 99.7%

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

   2. associate-*r/ 98.6%

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

   3. add-sqr-sqrt 51.4%

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

   4. times-frac 52.1%

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

8. Applied egg-rr 52.1%

   \[\leadsto \frac{\frac{x}{y}}{\frac{y}{x}} + \color{blue}{\frac{\frac{z}{t}}{\sqrt{t}} \cdot \frac{z}{\sqrt{t}}} \]
9. Add Preprocessing

Alternative 2: 99.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ \mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \frac{z}{t\_m} \cdot \frac{z}{t\_m}\right) \end{array} \]

FPCore

t_m = (fabs.f64 t)
(FPCore (x y z t_m)
 :precision binary64
 (fma (/ x y) (/ x y) (* (/ z t_m) (/ z t_m))))

C

t_m = fabs(t);
double code(double x, double y, double z, double t_m) {
	return fma((x / y), (x / y), ((z / t_m) * (z / t_m)));
}

Julia

t_m = abs(t)
function code(x, y, z, t_m)
	return fma(Float64(x / y), Float64(x / y), Float64(Float64(z / t_m) * Float64(z / t_m)))
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
code[x_, y_, z_, t$95$m_] := N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision] + N[(N[(z / t$95$m), $MachinePrecision] * N[(z / t$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 67.6%

   \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
2. Step-by-step derivation

   1. times-frac 85.8%

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

   2. fma-define 85.8%

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

   3. times-frac 99.7%

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

3. Simplified 99.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \frac{z}{t} \cdot \frac{z}{t}\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 3: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ \frac{z}{t\_m} \cdot \frac{z}{t\_m} + \frac{x}{y} \cdot \frac{x}{y} \end{array} \]

FPCore

t_m = (fabs.f64 t)
(FPCore (x y z t_m)
 :precision binary64
 (+ (* (/ z t_m) (/ z t_m)) (* (/ x y) (/ x y))))

C

t_m = fabs(t);
double code(double x, double y, double z, double t_m) {
	return ((z / t_m) * (z / t_m)) + ((x / y) * (x / y));
}

Fortran

t_m = abs(t)
real(8) function code(x, y, z, t_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    code = ((z / t_m) * (z / t_m)) + ((x / y) * (x / y))
end function

Java

t_m = Math.abs(t);
public static double code(double x, double y, double z, double t_m) {
	return ((z / t_m) * (z / t_m)) + ((x / y) * (x / y));
}

Python

t_m = math.fabs(t)
def code(x, y, z, t_m):
	return ((z / t_m) * (z / t_m)) + ((x / y) * (x / y))

Julia

t_m = abs(t)
function code(x, y, z, t_m)
	return Float64(Float64(Float64(z / t_m) * Float64(z / t_m)) + Float64(Float64(x / y) * Float64(x / y)))
end

MATLAB

t_m = abs(t);
function tmp = code(x, y, z, t_m)
	tmp = ((z / t_m) * (z / t_m)) + ((x / y) * (x / y));
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
code[x_, y_, z_, t$95$m_] := N[(N[(N[(z / t$95$m), $MachinePrecision] * N[(z / t$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 67.6%

   \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. frac-times 78.7%

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

4. Applied egg-rr 78.7%

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

   1. times-frac 99.7%

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

6. Applied egg-rr 99.7%

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

7. Final simplification 99.7%

   \[\leadsto \frac{z}{t} \cdot \frac{z}{t} + \frac{x}{y} \cdot \frac{x}{y} \]
8. Add Preprocessing

Alternative 4: 89.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ \frac{z}{t\_m} \cdot \frac{z}{t\_m} + x \cdot \frac{x}{y \cdot y} \end{array} \]

FPCore

t_m = (fabs.f64 t)
(FPCore (x y z t_m)
 :precision binary64
 (+ (* (/ z t_m) (/ z t_m)) (* x (/ x (* y y)))))

C

t_m = fabs(t);
double code(double x, double y, double z, double t_m) {
	return ((z / t_m) * (z / t_m)) + (x * (x / (y * y)));
}

Fortran

t_m = abs(t)
real(8) function code(x, y, z, t_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    code = ((z / t_m) * (z / t_m)) + (x * (x / (y * y)))
end function

Java

t_m = Math.abs(t);
public static double code(double x, double y, double z, double t_m) {
	return ((z / t_m) * (z / t_m)) + (x * (x / (y * y)));
}

Python

t_m = math.fabs(t)
def code(x, y, z, t_m):
	return ((z / t_m) * (z / t_m)) + (x * (x / (y * y)))

Julia

t_m = abs(t)
function code(x, y, z, t_m)
	return Float64(Float64(Float64(z / t_m) * Float64(z / t_m)) + Float64(x * Float64(x / Float64(y * y))))
end

MATLAB

t_m = abs(t);
function tmp = code(x, y, z, t_m)
	tmp = ((z / t_m) * (z / t_m)) + (x * (x / (y * y)));
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
code[x_, y_, z_, t$95$m_] := N[(N[(N[(z / t$95$m), $MachinePrecision] * N[(z / t$95$m), $MachinePrecision]), $MachinePrecision] + N[(x * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 67.6%

   \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
2. Step-by-step derivation

   1. associate-/l* 75.9%

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

3. Simplified 75.9%

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

   1. frac-times 78.7%

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

6. Applied egg-rr 87.9%

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

7. Final simplification 87.9%

   \[\leadsto \frac{z}{t} \cdot \frac{z}{t} + x \cdot \frac{x}{y \cdot y} \]
8. Add Preprocessing

Developer target: 99.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ {\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ (pow (/ x y) 2.0) (pow (/ z t) 2.0)))

C

double code(double x, double y, double z, double t) {
	return pow((x / y), 2.0) + pow((z / t), 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x / y) ** 2.0d0) + ((z / t) ** 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return Math.pow((x / y), 2.0) + Math.pow((z / t), 2.0);
}

Python

def code(x, y, z, t):
	return math.pow((x / y), 2.0) + math.pow((z / t), 2.0)

Julia

function code(x, y, z, t)
	return Float64((Float64(x / y) ^ 2.0) + (Float64(z / t) ^ 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x / y) ^ 2.0) + ((z / t) ^ 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[Power[N[(x / y), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(z / t), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024101 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"
  :precision binary64

  :alt
  (+ (pow (/ x y) 2.0) (pow (/ z t) 2.0))

  (+ (/ (* x x) (* y y)) (/ (* z z) (* t t))))