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

Percentage Accurate: 66.5% → 96.2%

Time: 14.2s

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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: 66.5% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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: 96.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ \begin{array}{l} \mathbf{if}\;z\_m \leq 7.6 \cdot 10^{+146}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \frac{\frac{z\_m \cdot z\_m}{t}}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \frac{z\_m}{t \cdot t} \cdot z\_m\right)\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
(FPCore (x y z_m t)
 :precision binary64
 (if (<= z_m 7.6e+146)
   (fma (/ x y) (/ x y) (/ (/ (* z_m z_m) t) t))
   (fma (/ x y) (/ x y) (* (/ z_m (* t t)) z_m))))

C

z_m = fabs(z);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if (z_m <= 7.6e+146) {
		tmp = fma((x / y), (x / y), (((z_m * z_m) / t) / t));
	} else {
		tmp = fma((x / y), (x / y), ((z_m / (t * t)) * z_m));
	}
	return tmp;
}

Julia

z_m = abs(z)
function code(x, y, z_m, t)
	tmp = 0.0
	if (z_m <= 7.6e+146)
		tmp = fma(Float64(x / y), Float64(x / y), Float64(Float64(Float64(z_m * z_m) / t) / t));
	else
		tmp = fma(Float64(x / y), Float64(x / y), Float64(Float64(z_m / Float64(t * t)) * z_m));
	end
	return tmp
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
code[x_, y_, z$95$m_, t_] := If[LessEqual[z$95$m, 7.6e+146], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision] + N[(N[(N[(z$95$m * z$95$m), $MachinePrecision] / t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision] + N[(N[(z$95$m / N[(t * t), $MachinePrecision]), $MachinePrecision] * z$95$m), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 7.59999999999999958e146

   1. Initial program 66.5%

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

   3. Applied rewrites 81.7%

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

   5. Applied rewrites 89.6%

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

   if 7.59999999999999958e146 < z

   1. Initial program 66.5%

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

   3. Applied rewrites 81.7%

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

   5. Applied rewrites 89.7%

      \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \color{blue}{\frac{z}{t \cdot t} \cdot z}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 92.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 5 \cdot 10^{+168}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y \cdot y}, x, \frac{z\_m}{t} \cdot \frac{z\_m}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \frac{z\_m}{t \cdot t} \cdot z\_m\right)\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
(FPCore (x y z_m t)
 :precision binary64
 (if (<= (/ (* x x) (* y y)) 5e+168)
   (fma (/ x (* y y)) x (* (/ z_m t) (/ z_m t)))
   (fma (/ x y) (/ x y) (* (/ z_m (* t t)) z_m))))

C

z_m = fabs(z);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if (((x * x) / (y * y)) <= 5e+168) {
		tmp = fma((x / (y * y)), x, ((z_m / t) * (z_m / t)));
	} else {
		tmp = fma((x / y), (x / y), ((z_m / (t * t)) * z_m));
	}
	return tmp;
}

Julia

z_m = abs(z)
function code(x, y, z_m, t)
	tmp = 0.0
	if (Float64(Float64(x * x) / Float64(y * y)) <= 5e+168)
		tmp = fma(Float64(x / Float64(y * y)), x, Float64(Float64(z_m / t) * Float64(z_m / t)));
	else
		tmp = fma(Float64(x / y), Float64(x / y), Float64(Float64(z_m / Float64(t * t)) * z_m));
	end
	return tmp
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
code[x_, y_, z$95$m_, t_] := If[LessEqual[N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision], 5e+168], N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] * x + N[(N[(z$95$m / t), $MachinePrecision] * N[(z$95$m / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision] + N[(N[(z$95$m / N[(t * t), $MachinePrecision]), $MachinePrecision] * z$95$m), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 4.99999999999999967e168

   1. Initial program 66.5%

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

   3. Applied rewrites 73.6%

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

   5. Applied rewrites 89.4%

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

   if 4.99999999999999967e168 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 66.5%

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

   3. Applied rewrites 81.7%

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

   5. Applied rewrites 89.7%

      \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \color{blue}{\frac{z}{t \cdot t} \cdot z}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 89.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 66.5%

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

3. Applied rewrites 81.7%

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

5. Applied rewrites 89.7%

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

Alternative 4: 80.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 66.5%

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

3. Applied rewrites 73.6%

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

5. Applied rewrites 80.7%

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

Reproduce

herbie shell --seed 2025153 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"
  :precision binary64
  (+ (/ (* x x) (* y y)) (/ (* z z) (* t t))))