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

Percentage Accurate: 66.4% → 99.7%

Time: 6.9s

Alternatives: 5

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: 66.4% 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, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 74.1%

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

   1. times-frac 86.5%

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

   2. times-frac 99.7%

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

3. Simplified 99.7%

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

   1. clear-num 99.7%

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

   2. div-inv 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 2: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 74.1%

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

   1. times-frac 86.5%

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

   2. times-frac 99.7%

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

3. Simplified 99.7%

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

4. Final simplification 99.7%

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

Alternative 3: 59.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+200}:\\ \;\;\;\;\frac{x \cdot x}{y} \cdot \frac{t}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.5e+200) (* (/ (* x x) y) (/ t (* y t))) (* (/ x y) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.5e+200) {
		tmp = ((x * x) / y) * (t / (y * t));
	} else {
		tmp = (x / y) * (x / y);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (z <= (-6.5d+200)) then
        tmp = ((x * x) / y) * (t / (y * t))
    else
        tmp = (x / y) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.5e+200) {
		tmp = ((x * x) / y) * (t / (y * t));
	} else {
		tmp = (x / y) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.5e+200:
		tmp = ((x * x) / y) * (t / (y * t))
	else:
		tmp = (x / y) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.5e+200)
		tmp = Float64(Float64(Float64(x * x) / y) * Float64(t / Float64(y * t)));
	else
		tmp = Float64(Float64(x / y) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.5e+200)
		tmp = ((x * x) / y) * (t / (y * t));
	else
		tmp = (x / y) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.5e+200], N[(N[(N[(x * x), $MachinePrecision] / y), $MachinePrecision] * N[(t / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.49999999999999963e200

   1. Initial program 70.0%

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

      1. associate-*r/ 77.6%

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

      2. fma-def 77.6%

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

      3. associate-/l* 85.5%

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

      4. associate-*r/ 92.9%

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

   3. Simplified 92.9%

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

      1. fma-udef 92.9%

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

      2. associate-*r/ 85.5%

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

      3. associate-/l* 77.6%

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

      4. frac-times 96.5%

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

      5. associate-*r/ 88.8%

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

      6. associate-*l/ 85.3%

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

      7. frac-add 58.0%

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

   5. Applied egg-rr 58.0%

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

      1. fma-def 58.0%

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

      2. associate-*l* 66.2%

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

      3. associate-*r* 66.2%

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

      4. associate-*l* 73.9%

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

   7. Simplified 73.9%

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

   8. Taylor expanded in x around inf 40.0%

      \[\leadsto \frac{\color{blue}{t \cdot {x}^{2}}}{y \cdot \left(y \cdot t\right)} \]
   9. Step-by-step derivation

      1. unpow2 40.0%

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

   10. Simplified 40.0%

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

       1. *-commutative 40.0%

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

       2. times-frac 40.1%

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

       3. *-commutative 40.1%

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

   12. Applied egg-rr 40.1%

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

   if -6.49999999999999963e200 < z

   1. Initial program 74.5%

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

      1. associate-*r/ 78.4%

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

      2. fma-def 78.4%

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

      3. associate-/l* 83.7%

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

      4. associate-*r/ 87.0%

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

   3. Simplified 87.0%

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

      1. fma-udef 87.0%

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

      2. associate-*r/ 83.7%

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

      3. associate-/l* 78.4%

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

      4. frac-times 89.4%

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

      5. associate-*r/ 85.5%

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

      6. associate-*l/ 84.8%

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

      7. frac-add 56.1%

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

   5. Applied egg-rr 56.1%

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

      1. fma-def 56.1%

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

      2. associate-*l* 68.3%

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

      3. associate-*r* 68.3%

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

      4. associate-*l* 73.5%

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

   7. Simplified 73.5%

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

   8. Taylor expanded in x around inf 50.8%

      \[\leadsto \frac{\color{blue}{t \cdot {x}^{2}}}{y \cdot \left(y \cdot t\right)} \]
   9. Step-by-step derivation

      1. unpow2 50.8%

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

   10. Simplified 50.8%

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

   11. Taylor expanded in t around 0 56.1%

       \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   12. Step-by-step derivation

       1. unpow2 56.1%

          \[\leadsto \frac{\color{blue}{x \cdot x}}{{y}^{2}} \]

       2. unpow2 56.1%

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

       3. times-frac 66.2%

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

   13. Simplified 66.2%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+200}:\\ \;\;\;\;\frac{x \cdot x}{y} \cdot \frac{t}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 4: 59.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+212}:\\ \;\;\;\;\frac{t \cdot \left(x \cdot x\right)}{y \cdot \left(y \cdot t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.3e+212) (/ (* t (* x x)) (* y (* y t))) (* (/ x y) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.3e+212) {
		tmp = (t * (x * x)) / (y * (y * t));
	} else {
		tmp = (x / y) * (x / y);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (z <= (-3.3d+212)) then
        tmp = (t * (x * x)) / (y * (y * t))
    else
        tmp = (x / y) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.3e+212) {
		tmp = (t * (x * x)) / (y * (y * t));
	} else {
		tmp = (x / y) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.3e+212:
		tmp = (t * (x * x)) / (y * (y * t))
	else:
		tmp = (x / y) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.3e+212)
		tmp = Float64(Float64(t * Float64(x * x)) / Float64(y * Float64(y * t)));
	else
		tmp = Float64(Float64(x / y) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.3e+212)
		tmp = (t * (x * x)) / (y * (y * t));
	else
		tmp = (x / y) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.3e+212], N[(N[(t * N[(x * x), $MachinePrecision]), $MachinePrecision] / N[(y * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3e212

   1. Initial program 70.4%

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

      1. associate-*r/ 79.1%

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

      2. fma-def 79.1%

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

      3. associate-/l* 87.8%

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

      4. associate-*r/ 96.2%

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

   3. Simplified 96.2%

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

      1. fma-udef 96.2%

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

      2. associate-*r/ 87.8%

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

      3. associate-/l* 79.1%

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

      4. frac-times 96.1%

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

      5. associate-*r/ 87.4%

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

      6. associate-*l/ 83.4%

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

      7. frac-add 56.9%

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

   5. Applied egg-rr 56.9%

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

      1. fma-def 56.9%

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

      2. associate-*l* 66.2%

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

      3. associate-*r* 66.2%

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

      4. associate-*l* 74.9%

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

   7. Simplified 74.9%

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

   8. Taylor expanded in x around inf 45.0%

      \[\leadsto \frac{\color{blue}{t \cdot {x}^{2}}}{y \cdot \left(y \cdot t\right)} \]
   9. Step-by-step derivation

      1. unpow2 45.0%

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

   10. Simplified 45.0%

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

   if -3.3e212 < z

   1. Initial program 74.4%

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

      1. associate-*r/ 78.2%

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

      2. fma-def 78.2%

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

      3. associate-/l* 83.5%

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

      4. associate-*r/ 86.8%

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

   3. Simplified 86.8%

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

      1. fma-udef 86.8%

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

      2. associate-*r/ 83.5%

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

      3. associate-/l* 78.2%

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

      4. frac-times 89.5%

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

      5. associate-*r/ 85.6%

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

      6. associate-*l/ 85.0%

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

      7. frac-add 56.2%

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

   5. Applied egg-rr 56.2%

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

      1. fma-def 56.2%

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

      2. associate-*l* 68.3%

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

      3. associate-*r* 68.3%

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

      4. associate-*l* 73.4%

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

   7. Simplified 73.4%

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

   8. Taylor expanded in x around inf 50.1%

      \[\leadsto \frac{\color{blue}{t \cdot {x}^{2}}}{y \cdot \left(y \cdot t\right)} \]
   9. Step-by-step derivation

      1. unpow2 50.1%

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

   10. Simplified 50.1%

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

   11. Taylor expanded in t around 0 55.4%

       \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   12. Step-by-step derivation

       1. unpow2 55.4%

          \[\leadsto \frac{\color{blue}{x \cdot x}}{{y}^{2}} \]

       2. unpow2 55.4%

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

       3. times-frac 65.4%

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

   13. Simplified 65.4%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+212}:\\ \;\;\;\;\frac{t \cdot \left(x \cdot x\right)}{y \cdot \left(y \cdot t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5: 58.7% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

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) * (x / y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 74.1%

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

   1. associate-*r/ 78.3%

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

   2. fma-def 78.3%

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

   3. associate-/l* 83.8%

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

   4. associate-*r/ 87.6%

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

3. Simplified 87.6%

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

   1. fma-udef 87.6%

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

   2. associate-*r/ 83.8%

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

   3. associate-/l* 78.3%

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

   4. frac-times 90.1%

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

   5. associate-*r/ 85.8%

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

   6. associate-*l/ 84.8%

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

   7. frac-add 56.3%

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

5. Applied egg-rr 56.3%

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

   1. fma-def 56.3%

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

   2. associate-*l* 68.1%

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

   3. associate-*r* 68.1%

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

   4. associate-*l* 73.6%

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

7. Simplified 73.6%

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

8. Taylor expanded in x around inf 49.7%

   \[\leadsto \frac{\color{blue}{t \cdot {x}^{2}}}{y \cdot \left(y \cdot t\right)} \]
9. Step-by-step derivation

   1. unpow2 49.7%

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

10. Simplified 49.7%

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

11. Taylor expanded in t around 0 53.3%

    \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
12. Step-by-step derivation

    1. unpow2 53.3%

       \[\leadsto \frac{\color{blue}{x \cdot x}}{{y}^{2}} \]

    2. unpow2 53.3%

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

    3. times-frac 61.7%

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

13. Simplified 61.7%

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

14. Final simplification 61.7%

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

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 2023195 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"
  :precision binary64

  :herbie-target
  (+ (pow (/ x y) 2.0) (pow (/ z t) 2.0))

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