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

Percentage Accurate: 66.2% → 99.7%

Time: 11.4s

Alternatives: 10

Speedup: 1.0×

• 48.8% 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: 66.2% 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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(N[Power[N[(t / z), $MachinePrecision], -1.0], $MachinePrecision] * N[(z / t), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] * N[(x / y), $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. +-commutative 68.6%

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

   2. times-frac 82.3%

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

   3. fma-define 82.3%

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

   4. times-frac 99.6%

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

3. Simplified 99.6%

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

   1. clear-num 99.7%

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

   2. inv-pow 99.7%

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

6. Applied egg-rr 99.7%

   \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\frac{t}{z}\right)}^{-1}}, \frac{z}{t}, \frac{x}{y} \cdot \frac{x}{y}\right) \]
7. Add Preprocessing

Alternative 2: 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 68.6%

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

   1. +-commutative 68.6%

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

   2. times-frac 82.3%

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

   3. fma-define 82.3%

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

   4. times-frac 99.6%

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

3. Simplified 99.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, \frac{x}{y} \cdot \frac{x}{y}\right)} \]
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 3: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 5 \cdot 10^{+116}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + \frac{z}{t \cdot \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \frac{y}{x}} + \frac{\frac{z}{t}}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 5e+116)
   (+ (* (/ x y) (/ x y)) (/ z (* t (/ t z))))
   (+ (/ x (* y (/ y x))) (/ (/ z t) (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 5e+116) {
		tmp = ((x / y) * (x / y)) + (z / (t * (t / z)));
	} else {
		tmp = (x / (y * (y / x))) + ((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 * z) / (t * t)) <= 5d+116) then
        tmp = ((x / y) * (x / y)) + (z / (t * (t / z)))
    else
        tmp = (x / (y * (y / x))) + ((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 * z) / (t * t)) <= 5e+116) {
		tmp = ((x / y) * (x / y)) + (z / (t * (t / z)));
	} else {
		tmp = (x / (y * (y / x))) + ((z / t) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * z) / (t * t)) <= 5e+116:
		tmp = ((x / y) * (x / y)) + (z / (t * (t / z)))
	else:
		tmp = (x / (y * (y / x))) + ((z / t) / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(z * z) / Float64(t * t)) <= 5e+116)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + Float64(z / Float64(t * Float64(t / z))));
	else
		tmp = Float64(Float64(x / Float64(y * Float64(y / x))) + 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 * z) / (t * t)) <= 5e+116)
		tmp = ((x / y) * (x / y)) + (z / (t * (t / z)));
	else
		tmp = (x / (y * (y / x))) + ((z / t) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision], 5e+116], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y * N[(y / x), $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)) < 5.00000000000000025e116

   1. Initial program 75.2%

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

      1. associate-/l* 79.6%

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

   3. Simplified 79.6%

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

      1. times-frac 82.7%

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

   6. Applied egg-rr 82.7%

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

      1. clear-num 82.8%

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

      2. frac-times 82.8%

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

      3. *-un-lft-identity 82.8%

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

   8. Applied egg-rr 82.8%

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

      1. associate-*r/ 78.4%

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

      2. frac-times 99.7%

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

      3. clear-num 99.6%

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

      4. un-div-inv 99.7%

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

   10. Applied egg-rr 99.7%

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

       1. div-inv 99.7%

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

       2. clear-num 99.7%

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

   12. Applied egg-rr 99.7%

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

   if 5.00000000000000025e116 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 63.0%

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

      1. associate-/l* 69.1%

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

   3. Simplified 69.1%

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

      1. times-frac 94.3%

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

   6. Applied egg-rr 94.3%

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

      1. clear-num 94.4%

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

      2. un-div-inv 94.4%

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

   8. Applied egg-rr 94.4%

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

      1. associate-*r/ 85.7%

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

      2. frac-times 99.8%

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

      3. clear-num 99.8%

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

      4. frac-times 98.5%

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

      5. *-un-lft-identity 98.5%

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

   10. Applied egg-rr 98.5%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 5 \cdot 10^{+116}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + \frac{z}{t \cdot \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \frac{y}{x}} + \frac{\frac{z}{t}}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 2 \cdot 10^{+286}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + \frac{z}{t \cdot \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t} + \frac{x}{y \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 2e+286)
   (+ (* (/ x y) (/ x 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 (((z * z) / (t * t)) <= 2e+286) {
		tmp = ((x / y) * (x / 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 (((z * z) / (t * t)) <= 2d+286) then
        tmp = ((x / y) * (x / 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 (((z * z) / (t * t)) <= 2e+286) {
		tmp = ((x / y) * (x / 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 ((z * z) / (t * t)) <= 2e+286:
		tmp = ((x / y) * (x / 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 (Float64(Float64(z * z) / Float64(t * t)) <= 2e+286)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + Float64(z / Float64(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 (((z * z) / (t * t)) <= 2e+286)
		tmp = ((x / y) * (x / 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[N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision], 2e+286], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t * N[(t / z), $MachinePrecision]), $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 (/.f64 (*.f64 z z) (*.f64 t t)) < 2.00000000000000007e286

   1. Initial program 76.1%

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

      1. associate-/l* 80.0%

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

   3. Simplified 80.0%

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

      1. times-frac 83.4%

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

   6. Applied egg-rr 83.4%

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

      1. clear-num 83.5%

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

      2. frac-times 83.5%

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

      3. *-un-lft-identity 83.5%

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

   8. Applied egg-rr 83.5%

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

      1. associate-*r/ 79.6%

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

      2. frac-times 99.6%

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

      3. clear-num 99.6%

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

      4. un-div-inv 99.6%

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

   10. Applied egg-rr 99.7%

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

       1. div-inv 99.7%

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

       2. clear-num 99.7%

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

   12. Applied egg-rr 99.7%

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

   if 2.00000000000000007e286 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 60.3%

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

      1. associate-/l* 67.2%

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

   3. Simplified 67.2%

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

      1. times-frac 95.1%

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

   6. Applied egg-rr 95.1%

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

      1. associate-*r/ 85.4%

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

      2. frac-times 99.8%

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

      3. clear-num 99.8%

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

      4. frac-times 98.3%

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

      5. *-un-lft-identity 98.3%

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

   8. Applied egg-rr 98.2%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 2 \cdot 10^{+286}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + \frac{z}{t \cdot \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t} + \frac{x}{y \cdot \frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + \frac{z}{t \cdot \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t} + \frac{x \cdot \frac{x}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 2e-197)
   (+ (* (/ x y) (/ x y)) (/ z (* t (/ t z))))
   (+ (* (/ z t) (/ z t)) (/ (* x (/ x y)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 2e-197) {
		tmp = ((x / y) * (x / y)) + (z / (t * (t / z)));
	} 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 <= 2d-197) then
        tmp = ((x / y) * (x / y)) + (z / (t * (t / z)))
    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 <= 2e-197) {
		tmp = ((x / y) * (x / y)) + (z / (t * (t / z)));
	} else {
		tmp = ((z / t) * (z / t)) + ((x * (x / y)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 2e-197:
		tmp = ((x / y) * (x / y)) + (z / (t * (t / z)))
	else:
		tmp = ((z / t) * (z / t)) + ((x * (x / y)) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 2e-197)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + Float64(z / Float64(t * Float64(t / z))));
	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 <= 2e-197)
		tmp = ((x / y) * (x / y)) + (z / (t * (t / z)));
	else
		tmp = ((z / t) * (z / t)) + ((x * (x / y)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 2e-197], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t * N[(t / z), $MachinePrecision]), $MachinePrecision]), $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 z < 2e-197

   1. Initial program 69.3%

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

      1. associate-/l* 75.9%

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

   3. Simplified 75.9%

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

      1. times-frac 90.6%

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

   6. Applied egg-rr 90.6%

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

      1. clear-num 90.7%

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

      2. frac-times 88.9%

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

      3. *-un-lft-identity 88.9%

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

   8. Applied egg-rr 88.9%

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

      1. associate-*r/ 81.6%

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

      2. frac-times 99.7%

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

      3. clear-num 99.7%

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

      4. un-div-inv 99.7%

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

   10. Applied egg-rr 98.0%

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

       1. div-inv 98.0%

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

       2. clear-num 98.0%

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

   12. Applied egg-rr 98.0%

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

   if 2e-197 < z

   1. Initial program 67.5%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. associate-*r/ 67.5%

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

      2. associate-/r* 79.1%

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

      3. pow2 79.1%

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

   6. Applied egg-rr 79.1%

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

      1. unpow2 79.1%

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

      2. associate-*l/ 81.9%

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

   8. Applied egg-rr 81.9%

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

      1. times-frac 86.6%

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

   10. Applied egg-rr 99.6%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + \frac{z}{t \cdot \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t} + \frac{x \cdot \frac{x}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return ((x / y) / (y / x)) + ((z / t) * (z * (1.0 / 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 * (1.0d0 / t)))
end function

Java

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

Python

def code(x, y, z, t):
	return ((x / y) / (y / x)) + ((z / t) * (z * (1.0 / t)))

Julia

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

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x / y) / (y / x)) + ((z / t) * (z * (1.0 / 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 * N[(1.0 / t), $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* 73.9%

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

3. Simplified 73.9%

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

   1. times-frac 89.0%

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

6. Applied egg-rr 89.0%

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

   1. clear-num 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%

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

8. Applied egg-rr 89.1%

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

   1. associate-*r/ 82.3%

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

   2. frac-times 99.7%

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

   3. clear-num 99.7%

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

   4. un-div-inv 99.7%

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

10. Applied egg-rr 99.7%

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

11. Final simplification 99.7%

    \[\leadsto \frac{\frac{x}{y}}{\frac{y}{x}} + \frac{z}{t} \cdot \left(z \cdot \frac{1}{t}\right) \]
12. Add Preprocessing

Alternative 7: 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* 73.9%

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

3. Simplified 73.9%

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

   1. times-frac 89.0%

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

6. Applied egg-rr 89.0%

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

   1. associate-*r/ 82.3%

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

   2. frac-times 99.7%

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

   3. clear-num 99.7%

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

   4. un-div-inv 99.7%

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

8. Applied egg-rr 99.6%

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

Alternative 8: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x / y) * (x / y)) + (z / (t * (t / z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t * N[(t / z), $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* 73.9%

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

3. Simplified 73.9%

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

   1. times-frac 89.0%

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

6. Applied egg-rr 89.0%

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

   1. clear-num 89.1%

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

   2. frac-times 86.3%

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

   3. *-un-lft-identity 86.3%

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

8. Applied egg-rr 86.3%

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

   1. associate-*r/ 82.3%

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

   2. frac-times 99.7%

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

   3. clear-num 99.7%

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

   4. un-div-inv 99.7%

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

10. Applied egg-rr 96.5%

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

    1. div-inv 96.5%

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

    2. clear-num 96.5%

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

12. Applied egg-rr 96.5%

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

13. Final simplification 96.5%

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

Alternative 9: 89.2% 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* 73.9%

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

3. Simplified 73.9%

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

   1. times-frac 89.0%

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

6. Applied egg-rr 89.0%

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

   1. clear-num 89.1%

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

   2. un-div-inv 89.1%

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

8. Applied egg-rr 89.1%

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

9. Final simplification 89.1%

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

Alternative 10: 89.1% 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* 73.9%

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

3. Simplified 73.9%

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

   1. times-frac 89.0%

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

6. Applied egg-rr 89.0%

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

7. Final simplification 89.0%

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

Developer Target 1: 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 2024116 
(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))))