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

Percentage Accurate: 67.1% → 99.7%

Time: 7.5s

Alternatives: 7

Speedup: 1.0×

• 48.1% 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: 67.1% 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 68.6%

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

   1. associate-/l* 73.6%

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

3. Simplified 73.6%

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

   1. frac-times 88.2%

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

6. Applied egg-rr 88.2%

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

   1. associate-*r/ 81.7%

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

   2. times-frac 99.6%

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

   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 2: 95.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+293}:\\ \;\;\;\;t\_1 + \frac{x}{y} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}} + x \cdot \frac{x}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 2e+293)
     (+ t_1 (* (/ x y) (/ x y)))
     (+ (/ (/ z t) (/ t z)) (* x (/ x (* y y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 2e+293) {
		tmp = t_1 + ((x / y) * (x / y));
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (z * z) / (t * t)
    if (t_1 <= 2d+293) then
        tmp = t_1 + ((x / y) * (x / y))
    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 t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 2e+293) {
		tmp = t_1 + ((x / y) * (x / y));
	} else {
		tmp = ((z / t) / (t / z)) + (x * (x / (y * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * z) / (t * t)
	tmp = 0
	if t_1 <= 2e+293:
		tmp = t_1 + ((x / y) * (x / y))
	else:
		tmp = ((z / t) / (t / z)) + (x * (x / (y * y)))
	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+293)
		tmp = Float64(t_1 + Float64(Float64(x / y) * Float64(x / y)));
	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)
	t_1 = (z * z) / (t * t);
	tmp = 0.0;
	if (t_1 <= 2e+293)
		tmp = t_1 + ((x / y) * (x / y));
	else
		tmp = ((z / t) / (t / z)) + (x * (x / (y * y)));
	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+293], N[(t$95$1 + N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $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 (/.f64 (*.f64 z z) (*.f64 t t)) < 1.9999999999999998e293

   1. Initial program 74.7%

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

      1. times-frac 96.4%

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

   4. Applied egg-rr 96.4%

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

   if 1.9999999999999998e293 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 61.0%

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

      1. associate-/l* 64.7%

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

   3. Simplified 64.7%

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

      1. frac-times 94.1%

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

   6. Applied egg-rr 94.1%

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

      1. clear-num 94.1%

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

      2. un-div-inv 94.1%

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

   8. Applied egg-rr 94.1%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 2 \cdot 10^{+293}:\\ \;\;\;\;\frac{z \cdot z}{t \cdot t} + \frac{x}{y} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}} + x \cdot \frac{x}{y \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7 \cdot 10^{+175}:\\ \;\;\;\;\frac{x \cdot \frac{x}{y}}{y} + \frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t} + \frac{x}{y \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 7e+175)
   (+ (/ (* x (/ x y)) y) (/ (/ z t) (/ t z)))
   (+ (* (/ z t) (/ z t)) (/ x (* y (/ y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 7e+175) {
		tmp = ((x * (x / y)) / y) + ((z / t) / (t / z));
	} 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 (x <= 7d+175) then
        tmp = ((x * (x / y)) / y) + ((z / t) / (t / z))
    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 (x <= 7e+175) {
		tmp = ((x * (x / y)) / y) + ((z / t) / (t / z));
	} else {
		tmp = ((z / t) * (z / t)) + (x / (y * (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 7e+175:
		tmp = ((x * (x / y)) / y) + ((z / t) / (t / z))
	else:
		tmp = ((z / t) * (z / t)) + (x / (y * (y / x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 7e+175)
		tmp = Float64(Float64(Float64(x * Float64(x / y)) / y) + Float64(Float64(z / t) / Float64(t / z)));
	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 (x <= 7e+175)
		tmp = ((x * (x / y)) / y) + ((z / t) / (t / z));
	else
		tmp = ((z / t) * (z / t)) + (x / (y * (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 7e+175], N[(N[(N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $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 x < 7.0000000000000006e175

   1. Initial program 69.8%

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

      1. associate-/l* 72.4%

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

   3. Simplified 72.4%

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

      1. frac-times 87.7%

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

   6. Applied egg-rr 87.7%

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

      1. clear-num 87.7%

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

      2. un-div-inv 87.8%

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

   8. Applied egg-rr 87.8%

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

      1. associate-*r/ 84.3%

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

      2. times-frac 99.7%

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

      3. associate-*r/ 98.7%

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

   10. Applied egg-rr 98.7%

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

   if 7.0000000000000006e175 < x

   1. Initial program 60.2%

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

      1. associate-/l* 81.8%

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

   3. Simplified 81.8%

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

      1. frac-times 91.0%

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

   6. Applied egg-rr 91.0%

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

      1. associate-*r/ 63.3%

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

      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 99.8%

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

      4. frac-times 99.9%

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

      5. *-un-lft-identity 99.9%

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

   8. Applied egg-rr 99.9%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7 \cdot 10^{+175}:\\ \;\;\;\;\frac{x \cdot \frac{x}{y}}{y} + \frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t} + \frac{x}{y \cdot \frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot \frac{z}{t}\\ \mathbf{if}\;x \leq 6 \cdot 10^{+153}:\\ \;\;\;\;t\_1 + \frac{x \cdot \frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{x}{y \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z t) (/ z t))))
   (if (<= x 6e+153) (+ t_1 (/ (* x (/ x y)) y)) (+ t_1 (/ x (* y (/ y x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * (z / t);
	double tmp;
	if (x <= 6e+153) {
		tmp = t_1 + ((x * (x / y)) / y);
	} else {
		tmp = t_1 + (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) :: t_1
    real(8) :: tmp
    t_1 = (z / t) * (z / t)
    if (x <= 6d+153) then
        tmp = t_1 + ((x * (x / y)) / y)
    else
        tmp = t_1 + (x / (y * (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * (z / t);
	double tmp;
	if (x <= 6e+153) {
		tmp = t_1 + ((x * (x / y)) / y);
	} else {
		tmp = t_1 + (x / (y * (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / t) * (z / t)
	tmp = 0
	if x <= 6e+153:
		tmp = t_1 + ((x * (x / y)) / y)
	else:
		tmp = t_1 + (x / (y * (y / x)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / t) * Float64(z / t))
	tmp = 0.0
	if (x <= 6e+153)
		tmp = Float64(t_1 + Float64(Float64(x * Float64(x / y)) / y));
	else
		tmp = Float64(t_1 + Float64(x / Float64(y * Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / t) * (z / t);
	tmp = 0.0;
	if (x <= 6e+153)
		tmp = t_1 + ((x * (x / y)) / y);
	else
		tmp = t_1 + (x / (y * (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 6e+153], N[(t$95$1 + N[(N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x / N[(y * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 6.00000000000000037e153

   1. Initial program 69.5%

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

      1. associate-/l* 72.2%

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

   3. Simplified 72.2%

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

      1. frac-times 87.6%

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

   6. Applied egg-rr 87.6%

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

      1. associate-*r/ 84.2%

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

      2. times-frac 99.7%

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

      3. associate-*r/ 98.7%

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

   8. Applied egg-rr 98.7%

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

   if 6.00000000000000037e153 < x

   1. Initial program 62.5%

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

      1. associate-/l* 82.9%

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

   3. Simplified 82.9%

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

      1. frac-times 91.5%

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

   6. Applied egg-rr 91.5%

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

      1. associate-*r/ 65.5%

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

      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 99.8%

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

      4. frac-times 99.9%

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

      5. *-un-lft-identity 99.9%

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

   8. Applied egg-rr 99.9%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6 \cdot 10^{+153}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t} + \frac{x \cdot \frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t} + \frac{x}{y \cdot \frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / (y * (y / x)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.6%

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

   1. associate-/l* 73.6%

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

3. Simplified 73.6%

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

   1. frac-times 88.2%

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

6. Applied egg-rr 88.2%

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

   1. associate-*r/ 81.7%

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

   2. times-frac 99.6%

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

   3. clear-num 99.7%

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

   4. frac-times 97.6%

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

   5. *-un-lft-identity 97.6%

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

8. Applied egg-rr 97.6%

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

9. Final simplification 97.6%

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

Alternative 6: 89.7% 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 68.6%

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

   1. associate-/l* 73.6%

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

3. Simplified 73.6%

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

   1. frac-times 88.2%

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

6. Applied egg-rr 88.2%

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

   1. clear-num 88.2%

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

   2. un-div-inv 88.2%

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

8. Applied egg-rr 88.2%

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

9. Final simplification 88.2%

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

Alternative 7: 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 68.6%

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

   1. associate-/l* 73.6%

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

3. Simplified 73.6%

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

   1. frac-times 88.2%

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

6. Applied egg-rr 88.2%

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

7. Final simplification 88.2%

   \[\leadsto \frac{z}{t} \cdot \frac{z}{t} + x \cdot \frac{x}{y \cdot y} \]
8. 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 2024108 
(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))))