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

Percentage Accurate: 66.4% → 99.7%

Time: 12.6s

Alternatives: 7

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

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

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 64.7%

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

   1. associate-/l* 71.7%

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

3. Simplified 71.7%

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

   1. times-frac 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/ 82.1%

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

   2. frac-times 99.6%

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

   3. clear-num 99.6%

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

   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. Final simplification 99.7%

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

Alternative 2: 95.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+289}:\\ \;\;\;\;t\_1 + \frac{x}{y} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{x}{y \cdot y} + \frac{\frac{z}{t}}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 2e+289)
     (+ t_1 (* (/ x y) (/ x y)))
     (+ (* x (/ x (* y y))) (/ (/ z t) (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 2e+289) {
		tmp = t_1 + ((x / y) * (x / y));
	} else {
		tmp = (x * (x / (y * y))) + ((z / t) / (t / z));
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (z * z) / (t * t)
    if (t_1 <= 2d+289) then
        tmp = t_1 + ((x / y) * (x / y))
    else
        tmp = (x * (x / (y * y))) + ((z / t) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 2e+289) {
		tmp = t_1 + ((x / y) * (x / y));
	} else {
		tmp = (x * (x / (y * y))) + ((z / t) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * z) / (t * t)
	tmp = 0
	if t_1 <= 2e+289:
		tmp = t_1 + ((x / y) * (x / y))
	else:
		tmp = (x * (x / (y * y))) + ((z / t) / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * z) / Float64(t * t))
	tmp = 0.0
	if (t_1 <= 2e+289)
		tmp = Float64(t_1 + Float64(Float64(x / y) * Float64(x / y)));
	else
		tmp = Float64(Float64(x * Float64(x / Float64(y * y))) + Float64(Float64(z / t) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * z) / (t * t);
	tmp = 0.0;
	if (t_1 <= 2e+289)
		tmp = t_1 + ((x / y) * (x / y));
	else
		tmp = (x * (x / (y * y))) + ((z / t) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+289], N[(t$95$1 + N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 2.0000000000000001e289

   1. Initial program 68.5%

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

      1. frac-times 94.1%

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

   4. Applied egg-rr 94.1%

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

   if 2.0000000000000001e289 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 61.5%

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

      1. associate-/l* 67.5%

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

   3. Simplified 67.5%

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

      1. times-frac 95.8%

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

   6. Applied egg-rr 95.8%

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

      1. clear-num 95.9%

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

      2. un-div-inv 95.9%

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

   8. Applied egg-rr 95.9%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 2 \cdot 10^{+289}:\\ \;\;\;\;\frac{z \cdot z}{t \cdot t} + \frac{x}{y} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{x}{y \cdot y} + \frac{\frac{z}{t}}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 10^{+278}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + \frac{z \cdot \frac{z}{t}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t} + \frac{x \cdot \frac{x}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 1e+278)
   (+ (* (/ x y) (/ x y)) (/ (* z (/ z t)) t))
   (+ (* (/ z t) (/ z t)) (/ (* x (/ x y)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 1e+278) {
		tmp = ((x / y) * (x / y)) + ((z * (z / t)) / t);
	} else {
		tmp = ((z / t) * (z / t)) + ((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 * z) / (t * t)) <= 1d+278) then
        tmp = ((x / y) * (x / y)) + ((z * (z / t)) / t)
    else
        tmp = ((z / t) * (z / t)) + ((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 * z) / (t * t)) <= 1e+278) {
		tmp = ((x / y) * (x / y)) + ((z * (z / t)) / t);
	} else {
		tmp = ((z / t) * (z / t)) + ((x * (x / y)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * z) / (t * t)) <= 1e+278:
		tmp = ((x / y) * (x / y)) + ((z * (z / t)) / t)
	else:
		tmp = ((z / t) * (z / t)) + ((x * (x / y)) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(z * z) / Float64(t * t)) <= 1e+278)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + Float64(Float64(z * Float64(z / t)) / t));
	else
		tmp = Float64(Float64(Float64(z / t) * Float64(z / t)) + Float64(Float64(x * Float64(x / y)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * z) / (t * t)) <= 1e+278)
		tmp = ((x / y) * (x / y)) + ((z * (z / t)) / t);
	else
		tmp = ((z / t) * (z / t)) + ((x * (x / y)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision], 1e+278], 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[(z / t), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 9.99999999999999964e277

   1. Initial program 69.1%

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

      1. frac-times 94.0%

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

   4. Applied egg-rr 94.0%

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

      1. times-frac 99.4%

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

      2. div-inv 99.4%

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

      3. associate-*r* 98.9%

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

   6. Applied egg-rr 98.9%

      \[\leadsto \frac{x}{y} \cdot \frac{x}{y} + \color{blue}{\left(\frac{z}{t} \cdot z\right) \cdot \frac{1}{t}} \]
   7. Step-by-step derivation

      1. associate-*l* 99.4%

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

      2. div-inv 99.4%

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

      3. clear-num 99.4%

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

      4. frac-times 99.5%

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

      5. *-un-lft-identity 99.5%

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

      6. associate-/r* 98.8%

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

   8. Applied egg-rr 98.8%

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

      1. associate-/r/ 98.9%

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

   10. Applied egg-rr 98.9%

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

   if 9.99999999999999964e277 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 61.1%

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

      1. associate-/l* 67.1%

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

   3. Simplified 67.1%

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

      1. times-frac 95.2%

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

   6. Applied egg-rr 95.2%

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

      1. associate-*r/ 88.5%

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

      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. Step-by-step derivation

      1. div-inv 99.7%

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

      2. div-inv 99.7%

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

      3. times-frac 99.8%

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

   10. Applied egg-rr 99.8%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{\frac{1}{y}}{\frac{1}{x}}} + \frac{z}{t} \cdot \frac{z}{t} \]
   11. Step-by-step derivation

       1. div-inv 99.8%

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

       2. frac-times 99.7%

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

       3. metadata-eval 99.7%

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

       4. div-inv 99.7%

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

       5. clear-num 99.7%

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

       6. associate-*r/ 99.1%

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

   12. Applied egg-rr 99.1%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 10^{+278}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + \frac{z \cdot \frac{z}{t}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t} + \frac{x \cdot \frac{x}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot y \leq 4 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + \frac{\frac{z}{\frac{t}{z}}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t} + \frac{x}{y \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* y y) 4e-291)
   (+ (* (/ x y) (/ x y)) (/ (/ z (/ t z)) t))
   (+ (* (/ z t) (/ z t)) (/ x (* y (/ y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y * y) <= 4e-291) {
		tmp = ((x / y) * (x / y)) + ((z / (t / z)) / t);
	} else {
		tmp = ((z / t) * (z / t)) + (x / (y * (y / x)));
	}
	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 ((y * y) <= 4d-291) then
        tmp = ((x / y) * (x / y)) + ((z / (t / z)) / t)
    else
        tmp = ((z / t) * (z / t)) + (x / (y * (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y * y) <= 4e-291) {
		tmp = ((x / y) * (x / y)) + ((z / (t / z)) / t);
	} else {
		tmp = ((z / t) * (z / t)) + (x / (y * (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y * y) <= 4e-291:
		tmp = ((x / y) * (x / y)) + ((z / (t / z)) / t)
	else:
		tmp = ((z / t) * (z / t)) + (x / (y * (y / x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(y * y) <= 4e-291)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + Float64(Float64(z / Float64(t / z)) / t));
	else
		tmp = Float64(Float64(Float64(z / t) * Float64(z / t)) + Float64(x / Float64(y * Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y * y) <= 4e-291)
		tmp = ((x / y) * (x / y)) + ((z / (t / z)) / t);
	else
		tmp = ((z / t) * (z / t)) + (x / (y * (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(y * y), $MachinePrecision], 4e-291], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(N[(z / N[(t / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision] + N[(x / N[(y * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y y) < 3.99999999999999985e-291

   1. Initial program 58.1%

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

      1. frac-times 82.7%

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

   4. Applied egg-rr 82.7%

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

      1. times-frac 99.8%

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

      2. div-inv 99.8%

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

      3. associate-*r* 98.5%

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

   6. Applied egg-rr 98.5%

      \[\leadsto \frac{x}{y} \cdot \frac{x}{y} + \color{blue}{\left(\frac{z}{t} \cdot z\right) \cdot \frac{1}{t}} \]
   7. Step-by-step derivation

      1. associate-*l* 99.8%

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

      2. div-inv 99.8%

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

      3. clear-num 99.8%

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

      4. frac-times 95.8%

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

      5. *-un-lft-identity 95.8%

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

      6. associate-/r* 98.5%

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

   8. Applied egg-rr 98.5%

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

   if 3.99999999999999985e-291 < (*.f64 y y)

   1. Initial program 67.1%

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

      1. associate-/l* 75.0%

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

   3. Simplified 75.0%

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

      1. times-frac 95.6%

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

   6. Applied egg-rr 95.6%

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

      1. associate-*r/ 87.2%

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

      2. frac-times 99.5%

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

      3. clear-num 99.6%

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

      4. frac-times 99.1%

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

      5. *-un-lft-identity 99.1%

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

   8. Applied egg-rr 99.1%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot y \leq 4 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + \frac{\frac{z}{\frac{t}{z}}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t} + \frac{x}{y \cdot \frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{+160}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + \frac{z \cdot \frac{z}{t}}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{x}{y \cdot y} + \frac{\frac{z}{t}}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 2e+160)
   (+ (* (/ x y) (/ x y)) (/ (* z (/ z t)) t))
   (+ (* x (/ x (* y y))) (/ (/ z t) (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 2e+160) {
		tmp = ((x / y) * (x / y)) + ((z * (z / t)) / t);
	} else {
		tmp = (x * (x / (y * y))) + ((z / t) / (t / z));
	}
	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 <= 2d+160) then
        tmp = ((x / y) * (x / y)) + ((z * (z / t)) / t)
    else
        tmp = (x * (x / (y * y))) + ((z / t) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 2e+160) {
		tmp = ((x / y) * (x / y)) + ((z * (z / t)) / t);
	} else {
		tmp = (x * (x / (y * y))) + ((z / t) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 2e+160:
		tmp = ((x / y) * (x / y)) + ((z * (z / t)) / t)
	else:
		tmp = (x * (x / (y * y))) + ((z / t) / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 2e+160)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + Float64(Float64(z * Float64(z / t)) / t));
	else
		tmp = Float64(Float64(x * Float64(x / Float64(y * y))) + Float64(Float64(z / t) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 2e+160)
		tmp = ((x / y) * (x / y)) + ((z * (z / t)) / t);
	else
		tmp = (x * (x / (y * y))) + ((z / t) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 2e+160], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(z / t), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.00000000000000001e160

   1. Initial program 64.2%

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

      1. frac-times 81.1%

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

   4. Applied egg-rr 81.1%

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

      1. times-frac 99.6%

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

      2. div-inv 99.6%

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

      3. associate-*r* 96.9%

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

   6. Applied egg-rr 96.9%

      \[\leadsto \frac{x}{y} \cdot \frac{x}{y} + \color{blue}{\left(\frac{z}{t} \cdot z\right) \cdot \frac{1}{t}} \]
   7. Step-by-step derivation

      1. associate-*l* 99.6%

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

      2. div-inv 99.6%

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

      3. clear-num 99.6%

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

      4. frac-times 95.8%

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

      5. *-un-lft-identity 95.8%

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

      6. associate-/r* 96.9%

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

   8. Applied egg-rr 96.9%

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

      1. associate-/r/ 96.9%

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

   10. Applied egg-rr 96.9%

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

   if 2.00000000000000001e160 < z

   1. Initial program 67.9%

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

      1. associate-/l* 70.8%

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

   3. Simplified 70.8%

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

      1. times-frac 94.9%

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

   6. Applied egg-rr 94.9%

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

      1. clear-num 95.0%

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

      2. un-div-inv 95.0%

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

   8. Applied egg-rr 95.0%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{+160}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + \frac{z \cdot \frac{z}{t}}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{x}{y \cdot y} + \frac{\frac{z}{t}}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.9% 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 64.7%

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

   1. associate-/l* 71.7%

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

3. Simplified 71.7%

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

   1. times-frac 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 7: 89.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 64.7%

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

   1. associate-/l* 71.7%

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

3. Simplified 71.7%

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

   1. times-frac 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 89.5%

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

   2. un-div-inv 89.6%

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

8. Applied egg-rr 89.6%

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

9. Final simplification 89.6%

   \[\leadsto x \cdot \frac{x}{y \cdot y} + \frac{\frac{z}{t}}{\frac{t}{z}} \]
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 2024047 
(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))))