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

Percentage Accurate: 65.9% → 99.8%

Time: 8.9s

Alternatives: 6

Speedup: 1.0×

• 48.4% 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: 65.9% 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: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.5%

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

   1. associate-/l* 72.5%

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

3. Simplified 72.5%

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

   1. frac-times 89.5%

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

6. Applied egg-rr 89.5%

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

   1. associate-*r/ 80.4%

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

   2. times-frac 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 99.8%

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

8. Applied egg-rr 99.8%

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

   1. clear-num 99.8%

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

   2. un-div-inv 99.8%

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

10. Applied egg-rr 99.8%

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

11. Final simplification 99.8%

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

Alternative 2: 97.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5.5 \cdot 10^{+247}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + \frac{z \cdot \frac{z}{t}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}} + x \cdot \frac{x}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 5.5e+247)
   (+ (* (/ x y) (/ x y)) (/ (* z (/ z t)) t))
   (+ (/ (/ z t) (/ t z)) (* x (/ x (* y y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 5.5e+247) {
		tmp = ((x / y) * (x / y)) + ((z * (z / t)) / t);
	} else {
		tmp = ((z / t) / (t / z)) + (x * (x / (y * 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 <= 5.5d+247) then
        tmp = ((x / y) * (x / y)) + ((z * (z / t)) / t)
    else
        tmp = ((z / t) / (t / z)) + (x * (x / (y * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 5.5e+247) {
		tmp = ((x / y) * (x / y)) + ((z * (z / t)) / t);
	} else {
		tmp = ((z / t) / (t / z)) + (x * (x / (y * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 5.5e+247:
		tmp = ((x / y) * (x / y)) + ((z * (z / t)) / t)
	else:
		tmp = ((z / t) / (t / z)) + (x * (x / (y * y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 5.5e+247)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + Float64(Float64(z * Float64(z / t)) / t));
	else
		tmp = Float64(Float64(Float64(z / t) / Float64(t / z)) + Float64(x * Float64(x / Float64(y * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 5.5e+247)
		tmp = ((x / y) * (x / y)) + ((z * (z / t)) / t);
	else
		tmp = ((z / t) / (t / z)) + (x * (x / (y * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 5.5e+247], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(z / t), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.4999999999999998e247

   1. Initial program 65.4%

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

      1. associate-/l* 72.7%

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

      2. *-commutative 72.7%

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

      3. div-inv 72.6%

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

      4. pow2 72.6%

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \left(z \cdot \frac{1}{\color{blue}{{t}^{2}}}\right) \cdot z \]

      5. pow-flip 72.7%

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

      6. metadata-eval 72.7%

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

   4. Applied egg-rr 72.7%

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

      1. sqr-pow 72.6%

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

      2. associate-*r* 76.9%

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

      3. metadata-eval 76.9%

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \left(\left(z \cdot {t}^{\color{blue}{-1}}\right) \cdot {t}^{\left(\frac{-2}{2}\right)}\right) \cdot z \]

      4. inv-pow 76.9%

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \left(\left(z \cdot \color{blue}{\frac{1}{t}}\right) \cdot {t}^{\left(\frac{-2}{2}\right)}\right) \cdot z \]

      5. div-inv 76.9%

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

      6. metadata-eval 76.9%

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

      7. inv-pow 76.9%

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

      8. div-inv 76.9%

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

      9. associate-*l/ 77.7%

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

      10. associate-*r/ 80.6%

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

      11. associate-*l/ 77.7%

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

   6. Applied egg-rr 77.7%

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

      1. times-frac 95.6%

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

   8. Applied egg-rr 95.6%

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

   if 5.4999999999999998e247 < z

   1. Initial program 66.7%

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

      1. associate-/l* 83.7%

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

   3. Simplified 83.7%

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

      1. frac-times 100.0%

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

   6. Applied egg-rr 100.0%

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

      1. clear-num 100.0%

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

      2. un-div-inv 100.0%

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

   8. Applied egg-rr 100.0%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5.5 \cdot 10^{+247}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + \frac{z \cdot \frac{z}{t}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}} + x \cdot \frac{x}{y \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.7% 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 65.5%

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

   1. associate-/l* 72.5%

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

3. Simplified 72.5%

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

   1. frac-times 89.5%

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

6. Applied egg-rr 89.5%

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

7. Final simplification 89.5%

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

Alternative 4: 89.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.5%

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

   1. associate-/l* 72.5%

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

3. Simplified 72.5%

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

   1. frac-times 89.5%

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

6. Applied egg-rr 89.5%

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

   1. clear-num 99.8%

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

   2. un-div-inv 99.8%

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

8. Applied egg-rr 89.5%

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

9. Final simplification 89.5%

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

Alternative 5: 96.6% accurate, 1.0× speedup

Math

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

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(Float64(x * 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[(N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 65.5%

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

   1. associate-/l* 72.5%

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

3. Simplified 72.5%

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

   1. frac-times 89.5%

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

6. Applied egg-rr 89.5%

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

   1. associate-*r/ 80.4%

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

   2. times-frac 99.7%

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

   3. associate-*r/ 97.2%

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

8. Applied egg-rr 97.2%

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

9. Final simplification 97.2%

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

Alternative 6: 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 65.5%

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

   1. associate-/l* 72.5%

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

3. Simplified 72.5%

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

   1. frac-times 89.5%

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

6. Applied egg-rr 89.5%

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

   1. associate-*r/ 80.4%

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

   2. times-frac 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 99.8%

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

8. Applied egg-rr 99.8%

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

9. Final simplification 99.8%

   \[\leadsto \frac{\frac{x}{y}}{\frac{y}{x}} + \frac{z}{t} \cdot \frac{z}{t} \]
10. 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 2024059 
(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))))