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

Percentage Accurate: 66.6% → 99.7%

Time: 12.5s

Alternatives: 6

Speedup: 1.0×

• 48.5% 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: 66.6% 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

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{z}{t}, z \cdot \frac{1}{t}, \frac{x}{y} \cdot \frac{x}{y}\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (fma (/ z t) (* z (/ 1.0 t)) (* (/ x y) (/ x y))))

C

double code(double x, double y, double z, double t) {
	return fma((z / t), (z * (1.0 / t)), ((x / y) * (x / y)));
}

Julia

function code(x, y, z, t)
	return fma(Float64(z / t), Float64(z * Float64(1.0 / t)), Float64(Float64(x / y) * Float64(x / y)))
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(z / t), $MachinePrecision] * N[(z * N[(1.0 / t), $MachinePrecision]), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.6%

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

   1. +-commutative 69.6%

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

   2. times-frac 83.7%

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

   3. fma-define 83.7%

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

   4. times-frac 99.7%

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

3. Simplified 99.7%

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

   1. clear-num 99.7%

      \[\leadsto \mathsf{fma}\left(\frac{z}{t}, \color{blue}{\frac{1}{\frac{t}{z}}}, \frac{x}{y} \cdot \frac{x}{y}\right) \]

   2. associate-/r/ 99.7%

      \[\leadsto \mathsf{fma}\left(\frac{z}{t}, \color{blue}{\frac{1}{t} \cdot z}, \frac{x}{y} \cdot \frac{x}{y}\right) \]

6. Applied egg-rr 99.7%

   \[\leadsto \mathsf{fma}\left(\frac{z}{t}, \color{blue}{\frac{1}{t} \cdot z}, \frac{x}{y} \cdot \frac{x}{y}\right) \]

7. Final simplification 99.7%

   \[\leadsto \mathsf{fma}\left(\frac{z}{t}, z \cdot \frac{1}{t}, \frac{x}{y} \cdot \frac{x}{y}\right) \]
8. Add Preprocessing

Alternative 2: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.6%

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

   1. associate-/l* 76.3%

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

3. Simplified 76.3%

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

   1. times-frac 91.2%

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

6. Applied egg-rr 91.2%

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

   1. associate-*r/ 83.7%

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

   2. frac-times 99.7%

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

   3. clear-num 99.7%

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

   4. un-div-inv 99.7%

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

8. Applied egg-rr 99.7%

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

Alternative 3: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.6%

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

   1. associate-/l* 76.3%

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

3. Simplified 76.3%

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

   1. add-cbrt-cube 70.0%

      \[\leadsto x \cdot \frac{x}{y \cdot y} + \color{blue}{\sqrt[3]{\left(\frac{z \cdot z}{t \cdot t} \cdot \frac{z \cdot z}{t \cdot t}\right) \cdot \frac{z \cdot z}{t \cdot t}}} \]

   2. pow3 70.0%

      \[\leadsto x \cdot \frac{x}{y \cdot y} + \sqrt[3]{\color{blue}{{\left(\frac{z \cdot z}{t \cdot t}\right)}^{3}}} \]

   3. times-frac 80.6%

      \[\leadsto x \cdot \frac{x}{y \cdot y} + \sqrt[3]{{\color{blue}{\left(\frac{z}{t} \cdot \frac{z}{t}\right)}}^{3}} \]

   4. pow2 80.6%

      \[\leadsto x \cdot \frac{x}{y \cdot y} + \sqrt[3]{{\color{blue}{\left({\left(\frac{z}{t}\right)}^{2}\right)}}^{3}} \]

6. Applied egg-rr 80.6%

   \[\leadsto x \cdot \frac{x}{y \cdot y} + \color{blue}{\sqrt[3]{{\left({\left(\frac{z}{t}\right)}^{2}\right)}^{3}}} \]
7. Step-by-step derivation

   1. pow2 80.6%

      \[\leadsto x \cdot \frac{x}{y \cdot y} + \sqrt[3]{{\color{blue}{\left(\frac{z}{t} \cdot \frac{z}{t}\right)}}^{3}} \]

   2. rem-cbrt-cube 91.2%

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

   3. associate-*l/ 88.6%

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

   4. associate-/l* 89.9%

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

8. Applied egg-rr 89.9%

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

   1. associate-*r/ 83.7%

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

   2. frac-times 99.7%

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

   3. clear-num 99.7%

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

   4. un-div-inv 99.7%

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

10. Applied egg-rr 98.5%

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

Alternative 4: 96.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.6%

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

   1. associate-/l* 76.3%

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

3. Simplified 76.3%

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

   1. times-frac 91.2%

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

6. Applied egg-rr 91.2%

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

   1. associate-*r/ 83.7%

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

   2. associate-/r* 92.0%

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

   3. pow2 92.0%

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

8. Applied egg-rr 92.0%

   \[\leadsto \color{blue}{\frac{\frac{{x}^{2}}{y}}{y}} + \frac{z}{t} \cdot \frac{z}{t} \]
9. Step-by-step derivation

   1. associate-/l/ 83.7%

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

   2. unpow2 83.7%

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

   3. frac-times 99.7%

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

   4. clear-num 99.7%

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

   5. div-inv 99.7%

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

   6. associate-/r/ 98.4%

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

10. Applied egg-rr 98.4%

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

11. Final simplification 98.4%

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

Alternative 5: 89.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.6%

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

   1. associate-/l* 76.3%

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

3. Simplified 76.3%

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

   1. times-frac 91.2%

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

6. Applied egg-rr 91.2%

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

7. Final simplification 91.2%

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

Alternative 6: 86.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.6%

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

   1. associate-/l* 76.3%

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

3. Simplified 76.3%

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

   1. add-cbrt-cube 70.0%

      \[\leadsto x \cdot \frac{x}{y \cdot y} + \color{blue}{\sqrt[3]{\left(\frac{z \cdot z}{t \cdot t} \cdot \frac{z \cdot z}{t \cdot t}\right) \cdot \frac{z \cdot z}{t \cdot t}}} \]

   2. pow3 70.0%

      \[\leadsto x \cdot \frac{x}{y \cdot y} + \sqrt[3]{\color{blue}{{\left(\frac{z \cdot z}{t \cdot t}\right)}^{3}}} \]

   3. times-frac 80.6%

      \[\leadsto x \cdot \frac{x}{y \cdot y} + \sqrt[3]{{\color{blue}{\left(\frac{z}{t} \cdot \frac{z}{t}\right)}}^{3}} \]

   4. pow2 80.6%

      \[\leadsto x \cdot \frac{x}{y \cdot y} + \sqrt[3]{{\color{blue}{\left({\left(\frac{z}{t}\right)}^{2}\right)}}^{3}} \]

6. Applied egg-rr 80.6%

   \[\leadsto x \cdot \frac{x}{y \cdot y} + \color{blue}{\sqrt[3]{{\left({\left(\frac{z}{t}\right)}^{2}\right)}^{3}}} \]
7. Step-by-step derivation

   1. pow2 80.6%

      \[\leadsto x \cdot \frac{x}{y \cdot y} + \sqrt[3]{{\color{blue}{\left(\frac{z}{t} \cdot \frac{z}{t}\right)}}^{3}} \]

   2. rem-cbrt-cube 91.2%

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

   3. associate-*l/ 88.6%

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

   4. associate-/l* 89.9%

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

8. Applied egg-rr 89.9%

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

9. Final simplification 89.9%

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

Developer Target 1: 99.6% 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 2024137 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (pow (/ x y) 2) (pow (/ z t) 2)))

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