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

Percentage Accurate: 66.2% → 99.7%

Time: 10.4s

Alternatives: 5

Speedup: 1.0×

• 48.3% 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, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.0%

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

   1. times-frac 82.4%

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

3. Simplified 82.4%

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

   1. frac-times 99.7%

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

5. Applied egg-rr 99.7%

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

6. Final simplification 99.7%

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

Alternative 2: 57.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 6.4 \cdot 10^{+192}:\\ \;\;\;\;\frac{x}{y \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \frac{1}{\frac{t \cdot \left(y \cdot y\right)}{x}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 6.4e+192)
   (/ x (* y (/ y x)))
   (* t (* x (/ 1.0 (/ (* t (* y y)) x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 6.4e+192) {
		tmp = x / (y * (y / x));
	} else {
		tmp = t * (x * (1.0 / ((t * (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 <= 6.4d+192) then
        tmp = x / (y * (y / x))
    else
        tmp = t * (x * (1.0d0 / ((t * (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 <= 6.4e+192) {
		tmp = x / (y * (y / x));
	} else {
		tmp = t * (x * (1.0 / ((t * (y * y)) / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 6.4e+192:
		tmp = x / (y * (y / x))
	else:
		tmp = t * (x * (1.0 / ((t * (y * y)) / x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 6.4e+192)
		tmp = Float64(x / Float64(y * Float64(y / x)));
	else
		tmp = Float64(t * Float64(x * Float64(1.0 / Float64(Float64(t * Float64(y * y)) / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 6.4e+192)
		tmp = x / (y * (y / x));
	else
		tmp = t * (x * (1.0 / ((t * (y * y)) / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 6.4e+192], N[(x / N[(y * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x * N[(1.0 / N[(N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 6.40000000000000046e192

   1. Initial program 66.2%

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

      1. +-commutative 66.2%

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

      2. times-frac 82.6%

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

      3. fma-def 82.6%

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

      4. associate-*l/ 88.6%

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

      5. *-commutative 88.6%

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

   3. Simplified 88.6%

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

      1. fma-udef 88.6%

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

      2. frac-times 70.9%

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

      3. associate-/r* 79.3%

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

      4. associate-*r/ 73.7%

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

      5. associate-/l* 79.3%

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

      6. frac-add 46.6%

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

      7. fma-def 46.6%

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

      8. associate-*r/ 50.4%

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

      9. associate-/l* 51.7%

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

      10. associate-/l* 57.3%

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

   5. Applied egg-rr 57.3%

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

      1. associate-*r/ 53.5%

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

      2. associate-/l* 49.3%

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

      3. associate-*r/ 53.5%

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

      4. *-commutative 53.5%

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

      5. associate-/l* 47.9%

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

      6. associate-*r/ 53.5%

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

   7. Simplified 53.5%

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

   8. Taylor expanded in z around 0 58.4%

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

      1. *-commutative 58.4%

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

   10. Simplified 58.4%

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

       1. associate-*r/ 54.5%

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

   12. Applied egg-rr 54.5%

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

       1. *-commutative 54.5%

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

       2. times-frac 56.8%

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

       3. associate-/l* 65.1%

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

       4. div-inv 65.1%

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

       5. clear-num 65.1%

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

       6. *-inverses 65.1%

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

   14. Applied egg-rr 65.1%

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

   if 6.40000000000000046e192 < z

   1. Initial program 51.0%

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

      1. +-commutative 51.0%

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

      2. times-frac 79.7%

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

      3. fma-def 79.7%

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

      4. associate-*l/ 99.7%

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

      5. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. fma-udef 99.7%

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

      2. frac-times 71.0%

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

      3. associate-/r* 71.6%

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

      4. associate-*r/ 51.6%

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

      5. associate-/l* 71.6%

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

      6. frac-add 26.0%

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

      7. fma-def 26.0%

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

      8. associate-*r/ 26.0%

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

      9. associate-/l* 41.0%

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

      10. associate-/l* 46.0%

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

   5. Applied egg-rr 46.0%

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

      1. associate-*r/ 46.0%

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

      2. associate-/l* 31.0%

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

      3. associate-*r/ 46.0%

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

      4. *-commutative 46.0%

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

      5. associate-/l* 41.0%

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

      6. associate-*r/ 46.0%

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

   7. Simplified 46.0%

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

   8. Taylor expanded in z around 0 26.5%

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

      1. *-commutative 26.5%

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

   10. Simplified 26.5%

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

       1. div-inv 26.5%

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

       2. *-commutative 26.5%

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

       3. associate-*l* 41.5%

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

       4. associate-*r/ 41.4%

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

       5. associate-*r/ 51.2%

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

   12. Applied egg-rr 51.2%

       \[\leadsto \color{blue}{t \cdot \left(x \cdot \frac{1}{\frac{t \cdot \left(y \cdot y\right)}{x}}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 6.4 \cdot 10^{+192}:\\ \;\;\;\;\frac{x}{y \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \frac{1}{\frac{t \cdot \left(y \cdot y\right)}{x}}\right)\\ \end{array} \]

Alternative 3: 56.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 10^{-9}:\\ \;\;\;\;\frac{x}{y \cdot t} \cdot \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1e-9) (* (/ x (* y t)) (/ t (/ y x))) (/ x (* y (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1e-9) {
		tmp = (x / (y * t)) * (t / (y / x));
	} else {
		tmp = 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 (t <= 1d-9) then
        tmp = (x / (y * t)) * (t / (y / x))
    else
        tmp = 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 (t <= 1e-9) {
		tmp = (x / (y * t)) * (t / (y / x));
	} else {
		tmp = x / (y * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1e-9:
		tmp = (x / (y * t)) * (t / (y / x))
	else:
		tmp = x / (y * (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1e-9)
		tmp = Float64(Float64(x / Float64(y * t)) * Float64(t / Float64(y / x)));
	else
		tmp = Float64(x / Float64(y * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1e-9)
		tmp = (x / (y * t)) * (t / (y / x));
	else
		tmp = x / (y * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1e-9], N[(N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision] * N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.00000000000000006e-9

   1. Initial program 65.7%

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

      1. +-commutative 65.7%

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

      2. times-frac 82.6%

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

      3. fma-def 82.6%

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

      4. associate-*l/ 90.6%

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

      5. *-commutative 90.6%

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

   3. Simplified 90.6%

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

      1. fma-udef 90.6%

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

      2. frac-times 72.1%

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

      3. associate-/r* 80.9%

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

      4. associate-*r/ 73.5%

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

      5. associate-/l* 80.9%

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

      6. frac-add 48.0%

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

      7. fma-def 48.0%

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

      8. associate-*r/ 52.3%

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

      9. associate-/l* 55.5%

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

      10. associate-/l* 61.3%

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

   5. Applied egg-rr 61.3%

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

      1. associate-*r/ 57.0%

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

      2. associate-/l* 51.2%

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

      3. associate-*r/ 57.0%

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

      4. *-commutative 57.0%

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

      5. associate-/l* 51.2%

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

      6. associate-*r/ 57.0%

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

   7. Simplified 57.0%

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

   8. Taylor expanded in z around 0 55.5%

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

      1. *-commutative 55.5%

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

   10. Simplified 55.5%

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

       1. associate-*r* 55.4%

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

       2. times-frac 60.3%

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

   12. Applied egg-rr 60.3%

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

   if 1.00000000000000006e-9 < 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. +-commutative 63.0%

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

      2. times-frac 81.7%

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

      3. fma-def 81.7%

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

      4. associate-*l/ 86.4%

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

      5. *-commutative 86.4%

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

   3. Simplified 86.4%

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

      1. fma-udef 86.4%

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

      2. frac-times 67.7%

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

      3. associate-/r* 72.4%

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

      4. associate-*r/ 67.7%

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

      5. associate-/l* 72.4%

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

      6. frac-add 36.7%

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

      7. fma-def 36.7%

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

      8. associate-*r/ 38.2%

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

      9. associate-/l* 38.2%

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

      10. associate-/l* 43.2%

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

   5. Applied egg-rr 43.2%

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

      1. associate-*r/ 41.7%

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

      2. associate-/l* 38.8%

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

      3. associate-*r/ 41.7%

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

      4. *-commutative 41.7%

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

      5. associate-/l* 36.7%

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

      6. associate-*r/ 41.7%

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

   7. Simplified 41.7%

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

   8. Taylor expanded in z around 0 57.2%

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

      1. *-commutative 57.2%

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

   10. Simplified 57.2%

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

       1. associate-*r/ 56.4%

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

   12. Applied egg-rr 56.4%

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

       1. *-commutative 56.4%

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

       2. times-frac 58.2%

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

       3. associate-/l* 68.8%

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

       4. div-inv 68.7%

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

       5. clear-num 68.7%

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

       6. *-inverses 68.7%

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

   14. Applied egg-rr 68.7%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \frac{y}{x}} \cdot 1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 10^{-9}:\\ \;\;\;\;\frac{x}{y \cdot t} \cdot \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \frac{y}{x}}\\ \end{array} \]

Alternative 4: 56.8% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t)
	tmp = (1.0 / y) * (x * (x / y));
end

Wolfram

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

Derivation

1. Initial program 65.0%

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

   1. +-commutative 65.0%

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

   2. times-frac 82.4%

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

   3. fma-def 82.4%

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

   4. associate-*l/ 89.5%

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

   5. *-commutative 89.5%

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

3. Simplified 89.5%

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

   1. fma-udef 89.5%

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

   2. frac-times 70.9%

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

   3. associate-/r* 78.7%

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

   4. associate-*r/ 72.0%

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

   5. associate-/l* 78.7%

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

   6. frac-add 45.0%

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

   7. fma-def 45.0%

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

   8. associate-*r/ 48.5%

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

   9. associate-/l* 50.9%

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

   10. associate-/l* 56.5%

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

5. Applied egg-rr 56.5%

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

   1. associate-*r/ 52.9%

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

   2. associate-/l* 47.9%

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

   3. associate-*r/ 52.9%

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

   4. *-commutative 52.9%

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

   5. associate-/l* 47.4%

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

   6. associate-*r/ 52.9%

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

7. Simplified 52.9%

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

8. Taylor expanded in z around 0 55.9%

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

   1. *-commutative 55.9%

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

10. Simplified 55.9%

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

    1. *-commutative 55.9%

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

    2. associate-*r* 55.9%

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

    3. times-frac 57.1%

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

    4. un-div-inv 57.1%

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

    5. clear-num 57.1%

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

12. Applied egg-rr 57.1%

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

13. Taylor expanded in t around 0 57.5%

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

14. Final simplification 57.5%

    \[\leadsto \frac{1}{y} \cdot \left(x \cdot \frac{x}{y}\right) \]

Alternative 5: 56.7% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.0%

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

   1. +-commutative 65.0%

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

   2. times-frac 82.4%

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

   3. fma-def 82.4%

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

   4. associate-*l/ 89.5%

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

   5. *-commutative 89.5%

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

3. Simplified 89.5%

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

   1. fma-udef 89.5%

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

   2. frac-times 70.9%

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

   3. associate-/r* 78.7%

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

   4. associate-*r/ 72.0%

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

   5. associate-/l* 78.7%

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

   6. frac-add 45.0%

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

   7. fma-def 45.0%

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

   8. associate-*r/ 48.5%

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

   9. associate-/l* 50.9%

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

   10. associate-/l* 56.5%

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

5. Applied egg-rr 56.5%

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

   1. associate-*r/ 52.9%

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

   2. associate-/l* 47.9%

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

   3. associate-*r/ 52.9%

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

   4. *-commutative 52.9%

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

   5. associate-/l* 47.4%

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

   6. associate-*r/ 52.9%

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

7. Simplified 52.9%

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

8. Taylor expanded in z around 0 55.9%

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

   1. *-commutative 55.9%

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

10. Simplified 55.9%

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

    1. associate-*r/ 52.3%

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

12. Applied egg-rr 52.3%

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

    1. *-commutative 52.3%

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

    2. times-frac 55.6%

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

    3. associate-/l* 62.2%

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

    4. div-inv 62.1%

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

    5. clear-num 62.2%

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

    6. *-inverses 62.2%

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

14. Applied egg-rr 62.2%

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

15. Final simplification 62.2%

    \[\leadsto \frac{x}{y \cdot \frac{y}{x}} \]

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 2023293 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"
  :precision binary64

  :herbie-target
  (+ (pow (/ x y) 2.0) (pow (/ z t) 2.0))

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