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

Percentage Accurate: 66.4% → 98.2%

Time: 12.2s

Alternatives: 17

Speedup: 0.8×

• 48.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 2 \cdot 10^{+230}:\\ \;\;\;\;\frac{\frac{x \cdot x}{y}}{y} + \frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{y}{x}} + \frac{z}{t \cdot \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* x x) (* y y)) 2e+230)
   (+ (/ (/ (* x x) y) 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 (((x * x) / (y * y)) <= 2e+230) {
		tmp = (((x * x) / y) / 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 (((x * x) / (y * y)) <= 2d+230) then
        tmp = (((x * x) / y) / 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 (((x * x) / (y * y)) <= 2e+230) {
		tmp = (((x * x) / y) / 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 ((x * x) / (y * y)) <= 2e+230:
		tmp = (((x * x) / y) / 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(x * x) / Float64(y * y)) <= 2e+230)
		tmp = Float64(Float64(Float64(Float64(x * x) / y) / y) + Float64(Float64(z / t) / Float64(t / z)));
	else
		tmp = Float64(Float64(Float64(x / y) / Float64(y / x)) + Float64(z / Float64(t * Float64(t / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * x) / (y * y)) <= 2e+230)
		tmp = (((x * x) / y) / 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[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision], 2e+230], N[(N[(N[(N[(x * x), $MachinePrecision] / y), $MachinePrecision] / y), $MachinePrecision] + N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 2.0000000000000002e230

   1. Initial program 69.9%

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

      1. times-frac N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. /-lowering-/.f64 95.2

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

   4. Applied egg-rr 95.2%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. *-lowering-*.f64 97.5

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

   6. Applied egg-rr 97.5%

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

   if 2.0000000000000002e230 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 58.6%

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

      1. times-frac N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. /-lowering-/.f64 82.3

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

   4. Applied egg-rr 82.3%

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

      1. times-frac N/A

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

      2. clear-num N/A

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

      3. div-inv N/A

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

      4. frac-2neg N/A

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

      5. associate-/l/ N/A

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

      6. /-lowering-/.f64 N/A

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

      7. neg-sub0 N/A

         \[\leadsto \frac{\frac{x}{y}}{\frac{y}{x}} + \frac{\color{blue}{0 - z}}{\frac{t}{z} \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      8. --lowering--.f64 N/A

         \[\leadsto \frac{\frac{x}{y}}{\frac{y}{x}} + \frac{\color{blue}{0 - z}}{\frac{t}{z} \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \frac{\frac{x}{y}}{\frac{y}{x}} + \frac{0 - z}{\color{blue}{\frac{t}{z} \cdot \left(\mathsf{neg}\left(t\right)\right)}} \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \frac{\frac{x}{y}}{\frac{y}{x}} + \frac{0 - z}{\color{blue}{\frac{t}{z}} \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      11. neg-sub0 N/A

          \[\leadsto \frac{\frac{x}{y}}{\frac{y}{x}} + \frac{0 - z}{\frac{t}{z} \cdot \color{blue}{\left(0 - t\right)}} \]

      12. --lowering--.f64 98.1

          \[\leadsto \frac{\frac{x}{y}}{\frac{y}{x}} + \frac{0 - z}{\frac{t}{z} \cdot \color{blue}{\left(0 - t\right)}} \]

   6. Applied egg-rr 98.1%

      \[\leadsto \frac{\frac{x}{y}}{\frac{y}{x}} + \color{blue}{\frac{0 - z}{\frac{t}{z} \cdot \left(0 - t\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 2 \cdot 10^{+230}:\\ \;\;\;\;\frac{\frac{x \cdot x}{y}}{y} + \frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{y}{x}} + \frac{z}{t \cdot \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 10^{+306}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, t\_1\right)\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \frac{1}{t \cdot t}, z, \frac{\frac{x \cdot x}{y}}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \frac{z \cdot z}{t \cdot t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))))
   (if (<= t_1 1e+306)
     (fma (/ z t) (/ z t) t_1)
     (if (<= t_1 INFINITY)
       (fma (* z (/ 1.0 (* t t))) z (/ (/ (* x x) y) y))
       (fma (/ x y) (/ x y) (/ (* z z) (* t t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if (t_1 <= 1e+306) {
		tmp = fma((z / t), (z / t), t_1);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = fma((z * (1.0 / (t * t))), z, (((x * x) / y) / y));
	} else {
		tmp = fma((x / y), (x / y), ((z * z) / (t * t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) / Float64(y * y))
	tmp = 0.0
	if (t_1 <= 1e+306)
		tmp = fma(Float64(z / t), Float64(z / t), t_1);
	elseif (t_1 <= Inf)
		tmp = fma(Float64(z * Float64(1.0 / Float64(t * t))), z, Float64(Float64(Float64(x * x) / y) / y));
	else
		tmp = fma(Float64(x / y), Float64(x / y), Float64(Float64(z * z) / Float64(t * t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+306], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(z * N[(1.0 / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z + N[(N[(N[(x * x), $MachinePrecision] / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision] + N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 1.00000000000000002e306

   1. Initial program 70.7%

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

      1. +-commutative N/A

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

      2. times-frac N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. /-lowering-/.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 95.3

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

   4. Applied egg-rr 95.3%

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

   if 1.00000000000000002e306 < (/.f64 (*.f64 x x) (*.f64 y y)) < +inf.0

   1. Initial program 76.4%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. associate-*r* N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. /-lowering-/.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 83.5

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

   4. Applied egg-rr 83.5%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. *-lowering-*.f64 94.7

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

   6. Applied egg-rr 94.7%

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

   if +inf.0 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 0.0%

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

      1. times-frac N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 77.9

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

   4. Applied egg-rr 77.9%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 10^{+306}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, \frac{x \cdot x}{y \cdot y}\right)\\ \mathbf{elif}\;\frac{x \cdot x}{y \cdot y} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \frac{1}{t \cdot t}, z, \frac{\frac{x \cdot x}{y}}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \frac{z \cdot z}{t \cdot t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, t\_1\right)\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot \frac{1}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \frac{z \cdot z}{t \cdot t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))))
   (if (<= t_1 2e+300)
     (fma (/ z t) (/ z t) t_1)
     (if (<= t_1 INFINITY)
       (* (/ x y) (* x (/ 1.0 y)))
       (fma (/ x y) (/ x y) (/ (* z z) (* t t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if (t_1 <= 2e+300) {
		tmp = fma((z / t), (z / t), t_1);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (x / y) * (x * (1.0 / y));
	} else {
		tmp = fma((x / y), (x / y), ((z * z) / (t * t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) / Float64(y * y))
	tmp = 0.0
	if (t_1 <= 2e+300)
		tmp = fma(Float64(z / t), Float64(z / t), t_1);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(x / y) * Float64(x * Float64(1.0 / y)));
	else
		tmp = fma(Float64(x / y), Float64(x / y), Float64(Float64(z * z) / Float64(t * t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+300], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(x / y), $MachinePrecision] * N[(x * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision] + N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 2.0000000000000001e300

   1. Initial program 70.5%

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

      1. +-commutative N/A

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

      2. times-frac N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. /-lowering-/.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 95.2

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

   4. Applied egg-rr 95.2%

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

   if 2.0000000000000001e300 < (/.f64 (*.f64 x x) (*.f64 y y)) < +inf.0

   1. Initial program 76.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 84.8

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

   5. Simplified 84.8%

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

      1. associate-*r/ N/A

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

      2. times-frac N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 91.6

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

   7. Applied egg-rr 91.6%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 91.7

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

   9. Applied egg-rr 91.7%

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

   if +inf.0 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 0.0%

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

      1. times-frac N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 77.9

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

   4. Applied egg-rr 77.9%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 2 \cdot 10^{+300}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, \frac{x \cdot x}{y \cdot y}\right)\\ \mathbf{elif}\;\frac{x \cdot x}{y \cdot y} \leq \infty:\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot \frac{1}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \frac{z \cdot z}{t \cdot t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \frac{1}{t \cdot t}, z, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))))
   (if (<= t_1 0.0)
     (/ (/ z t) (/ t z))
     (if (<= t_1 2e+90)
       (fma (* z (/ 1.0 (* t t))) z t_1)
       (* (/ x y) (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if (t_1 <= 0.0) {
		tmp = (z / t) / (t / z);
	} else if (t_1 <= 2e+90) {
		tmp = fma((z * (1.0 / (t * t))), z, t_1);
	} else {
		tmp = (x / y) * (x / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) / Float64(y * y))
	tmp = 0.0
	if (t_1 <= 0.0)
		tmp = Float64(Float64(z / t) / Float64(t / z));
	elseif (t_1 <= 2e+90)
		tmp = fma(Float64(z * Float64(1.0 / Float64(t * t))), z, t_1);
	else
		tmp = Float64(Float64(x / y) * Float64(x / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.0], N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+90], N[(N[(z * N[(1.0 / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z + t$95$1), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 0.0

   1. Initial program 64.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{{z}^{2}}{{t}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 72.2

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

   5. Simplified 72.2%

      \[\leadsto \color{blue}{z \cdot \frac{z}{t \cdot t}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\frac{z}{t}\right)}{\mathsf{neg}\left(t\right)}} \cdot z \]

      4. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\left(\mathsf{neg}\left(\frac{z}{t}\right)\right) \cdot z}{\mathsf{neg}\left(t\right)}} \]

      5. distribute-neg-frac N/A

         \[\leadsto \frac{\color{blue}{\frac{\mathsf{neg}\left(z\right)}{t}} \cdot z}{\mathsf{neg}\left(t\right)} \]

      6. sub0-neg N/A

         \[\leadsto \frac{\frac{\color{blue}{0 - z}}{t} \cdot z}{\mathsf{neg}\left(t\right)} \]

      7. associate-/r/ N/A

         \[\leadsto \frac{\color{blue}{\frac{0 - z}{\frac{t}{z}}}}{\mathsf{neg}\left(t\right)} \]

      8. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{0 - z}{\left(\mathsf{neg}\left(t\right)\right) \cdot \frac{t}{z}}} \]

      9. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{0 - z}{\mathsf{neg}\left(t\right)}}{\frac{t}{z}}} \]

      10. sub0-neg N/A

          \[\leadsto \frac{\frac{\color{blue}{\mathsf{neg}\left(z\right)}}{\mathsf{neg}\left(t\right)}}{\frac{t}{z}} \]

      11. frac-2neg N/A

          \[\leadsto \frac{\color{blue}{\frac{z}{t}}}{\frac{t}{z}} \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\frac{z}{t}}{\frac{t}{z}}} \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \frac{\color{blue}{\frac{z}{t}}}{\frac{t}{z}} \]

      14. /-lowering-/.f64 94.6

          \[\leadsto \frac{\frac{z}{t}}{\color{blue}{\frac{t}{z}}} \]

   7. Applied egg-rr 94.6%

      \[\leadsto \color{blue}{\frac{\frac{z}{t}}{\frac{t}{z}}} \]

   if 0.0 < (/.f64 (*.f64 x x) (*.f64 y y)) < 1.99999999999999993e90

   1. Initial program 83.8%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. associate-*r* N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. /-lowering-/.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 88.7

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

   4. Applied egg-rr 88.7%

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

   if 1.99999999999999993e90 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 59.1%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 66.7

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

   5. Simplified 66.7%

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

      1. associate-*r/ N/A

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

      2. times-frac N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 82.7

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

   7. Applied egg-rr 82.7%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 0:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{x \cdot x}{y \cdot y} \leq 2 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \frac{1}{t \cdot t}, z, \frac{x \cdot x}{y \cdot y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t \cdot t}, z, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))))
   (if (<= t_1 0.0)
     (/ (/ z t) (/ t z))
     (if (<= t_1 2e+90) (fma (/ z (* t t)) z t_1) (* (/ x y) (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if (t_1 <= 0.0) {
		tmp = (z / t) / (t / z);
	} else if (t_1 <= 2e+90) {
		tmp = fma((z / (t * t)), z, t_1);
	} else {
		tmp = (x / y) * (x / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) / Float64(y * y))
	tmp = 0.0
	if (t_1 <= 0.0)
		tmp = Float64(Float64(z / t) / Float64(t / z));
	elseif (t_1 <= 2e+90)
		tmp = fma(Float64(z / Float64(t * t)), z, t_1);
	else
		tmp = Float64(Float64(x / y) * Float64(x / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.0], N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+90], N[(N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision] * z + t$95$1), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 0.0

   1. Initial program 64.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{{z}^{2}}{{t}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 72.2

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

   5. Simplified 72.2%

      \[\leadsto \color{blue}{z \cdot \frac{z}{t \cdot t}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\frac{z}{t}\right)}{\mathsf{neg}\left(t\right)}} \cdot z \]

      4. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\left(\mathsf{neg}\left(\frac{z}{t}\right)\right) \cdot z}{\mathsf{neg}\left(t\right)}} \]

      5. distribute-neg-frac N/A

         \[\leadsto \frac{\color{blue}{\frac{\mathsf{neg}\left(z\right)}{t}} \cdot z}{\mathsf{neg}\left(t\right)} \]

      6. sub0-neg N/A

         \[\leadsto \frac{\frac{\color{blue}{0 - z}}{t} \cdot z}{\mathsf{neg}\left(t\right)} \]

      7. associate-/r/ N/A

         \[\leadsto \frac{\color{blue}{\frac{0 - z}{\frac{t}{z}}}}{\mathsf{neg}\left(t\right)} \]

      8. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{0 - z}{\left(\mathsf{neg}\left(t\right)\right) \cdot \frac{t}{z}}} \]

      9. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{0 - z}{\mathsf{neg}\left(t\right)}}{\frac{t}{z}}} \]

      10. sub0-neg N/A

          \[\leadsto \frac{\frac{\color{blue}{\mathsf{neg}\left(z\right)}}{\mathsf{neg}\left(t\right)}}{\frac{t}{z}} \]

      11. frac-2neg N/A

          \[\leadsto \frac{\color{blue}{\frac{z}{t}}}{\frac{t}{z}} \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\frac{z}{t}}{\frac{t}{z}}} \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \frac{\color{blue}{\frac{z}{t}}}{\frac{t}{z}} \]

      14. /-lowering-/.f64 94.6

          \[\leadsto \frac{\frac{z}{t}}{\color{blue}{\frac{t}{z}}} \]

   7. Applied egg-rr 94.6%

      \[\leadsto \color{blue}{\frac{\frac{z}{t}}{\frac{t}{z}}} \]

   if 0.0 < (/.f64 (*.f64 x x) (*.f64 y y)) < 1.99999999999999993e90

   1. Initial program 83.8%

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. *-lowering-*.f64 88.7

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

   4. Applied egg-rr 88.7%

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

   if 1.99999999999999993e90 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 59.1%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 66.7

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

   5. Simplified 66.7%

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

      1. associate-*r/ N/A

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

      2. times-frac N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 82.7

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

   7. Applied egg-rr 82.7%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 85.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+102}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y \cdot y}, x, \frac{z \cdot z}{t \cdot t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))))
   (if (<= t_1 0.0)
     (/ (/ z t) (/ t z))
     (if (<= t_1 2e+102)
       (fma (/ x (* y y)) x (/ (* z z) (* t t)))
       (* (/ x y) (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if (t_1 <= 0.0) {
		tmp = (z / t) / (t / z);
	} else if (t_1 <= 2e+102) {
		tmp = fma((x / (y * y)), x, ((z * z) / (t * t)));
	} else {
		tmp = (x / y) * (x / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) / Float64(y * y))
	tmp = 0.0
	if (t_1 <= 0.0)
		tmp = Float64(Float64(z / t) / Float64(t / z));
	elseif (t_1 <= 2e+102)
		tmp = fma(Float64(x / Float64(y * y)), x, Float64(Float64(z * z) / Float64(t * t)));
	else
		tmp = Float64(Float64(x / y) * Float64(x / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.0], N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+102], N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] * x + N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 0.0

   1. Initial program 64.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{{z}^{2}}{{t}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 72.2

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

   5. Simplified 72.2%

      \[\leadsto \color{blue}{z \cdot \frac{z}{t \cdot t}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\frac{z}{t}\right)}{\mathsf{neg}\left(t\right)}} \cdot z \]

      4. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\left(\mathsf{neg}\left(\frac{z}{t}\right)\right) \cdot z}{\mathsf{neg}\left(t\right)}} \]

      5. distribute-neg-frac N/A

         \[\leadsto \frac{\color{blue}{\frac{\mathsf{neg}\left(z\right)}{t}} \cdot z}{\mathsf{neg}\left(t\right)} \]

      6. sub0-neg N/A

         \[\leadsto \frac{\frac{\color{blue}{0 - z}}{t} \cdot z}{\mathsf{neg}\left(t\right)} \]

      7. associate-/r/ N/A

         \[\leadsto \frac{\color{blue}{\frac{0 - z}{\frac{t}{z}}}}{\mathsf{neg}\left(t\right)} \]

      8. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{0 - z}{\left(\mathsf{neg}\left(t\right)\right) \cdot \frac{t}{z}}} \]

      9. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{0 - z}{\mathsf{neg}\left(t\right)}}{\frac{t}{z}}} \]

      10. sub0-neg N/A

          \[\leadsto \frac{\frac{\color{blue}{\mathsf{neg}\left(z\right)}}{\mathsf{neg}\left(t\right)}}{\frac{t}{z}} \]

      11. frac-2neg N/A

          \[\leadsto \frac{\color{blue}{\frac{z}{t}}}{\frac{t}{z}} \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\frac{z}{t}}{\frac{t}{z}}} \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \frac{\color{blue}{\frac{z}{t}}}{\frac{t}{z}} \]

      14. /-lowering-/.f64 94.6

          \[\leadsto \frac{\frac{z}{t}}{\color{blue}{\frac{t}{z}}} \]

   7. Applied egg-rr 94.6%

      \[\leadsto \color{blue}{\frac{\frac{z}{t}}{\frac{t}{z}}} \]

   if 0.0 < (/.f64 (*.f64 x x) (*.f64 y y)) < 1.99999999999999995e102

   1. Initial program 84.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. /-lowering-/.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 85.6

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

   4. Applied egg-rr 85.6%

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

   if 1.99999999999999995e102 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 58.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 66.1

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

   5. Simplified 66.1%

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

      1. associate-*r/ N/A

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

      2. times-frac N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 82.4

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

   7. Applied egg-rr 82.4%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 94.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq \infty:\\ \;\;\;\;\frac{\frac{x \cdot x}{y}}{y} + \frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \frac{z \cdot z}{t \cdot t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* x x) (* y y)) INFINITY)
   (+ (/ (/ (* x x) y) y) (/ (/ z t) (/ t z)))
   (fma (/ x y) (/ x y) (/ (* z z) (* t t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * x) / (y * y)) <= ((double) INFINITY)) {
		tmp = (((x * x) / y) / y) + ((z / t) / (t / z));
	} else {
		tmp = fma((x / y), (x / y), ((z * z) / (t * t)));
	}
	return tmp;
}

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < +inf.0

   1. Initial program 72.6%

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

      1. times-frac N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. /-lowering-/.f64 91.3

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

   4. Applied egg-rr 91.3%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. *-lowering-*.f64 97.0

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

   6. Applied egg-rr 97.0%

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

   if +inf.0 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 0.0%

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

      1. times-frac N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 77.9

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

   4. Applied egg-rr 77.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \frac{z \cdot z}{t \cdot t}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 95.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+251}:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{y}{x}} + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}} + x \cdot \frac{x}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 2e+251)
     (+ (/ (/ x y) (/ y x)) t_1)
     (+ (/ (/ 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+251) {
		tmp = ((x / y) / (y / x)) + t_1;
	} 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+251) then
        tmp = ((x / y) / (y / x)) + t_1
    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+251) {
		tmp = ((x / y) / (y / x)) + t_1;
	} 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+251:
		tmp = ((x / y) / (y / x)) + t_1
	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+251)
		tmp = Float64(Float64(Float64(x / y) / Float64(y / x)) + t_1);
	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+251)
		tmp = ((x / y) / (y / x)) + t_1;
	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+251], N[(N[(N[(x / y), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision] + t$95$1), $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)) < 2.0000000000000001e251

   1. Initial program 73.3%

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

      1. times-frac N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. /-lowering-/.f64 94.1

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

   4. Applied egg-rr 94.1%

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

   if 2.0000000000000001e251 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 56.4%

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

      1. times-frac N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. /-lowering-/.f64 84.6

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

   4. Applied egg-rr 84.6%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. *-lowering-*.f64 93.3

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

   6. Applied egg-rr 93.3%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 2 \cdot 10^{+251}:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{y}{x}} + \frac{z \cdot z}{t \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}} + x \cdot \frac{x}{y \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 95.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+251}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}} + x \cdot \frac{x}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 2e+251)
     (fma (/ x y) (/ x y) t_1)
     (+ (/ (/ 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+251) {
		tmp = fma((x / y), (x / y), t_1);
	} 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+251)
		tmp = fma(Float64(x / y), Float64(x / y), t_1);
	else
		tmp = Float64(Float64(Float64(z / t) / Float64(t / z)) + Float64(x * Float64(x / Float64(y * y))));
	end
	return 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+251], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision] + t$95$1), $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)) < 2.0000000000000001e251

   1. Initial program 73.3%

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

      1. times-frac N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 94.1

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

   4. Applied egg-rr 94.1%

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

   if 2.0000000000000001e251 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 56.4%

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

      1. times-frac N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. /-lowering-/.f64 84.6

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

   4. Applied egg-rr 84.6%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. *-lowering-*.f64 93.3

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

   6. Applied egg-rr 93.3%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 2 \cdot 10^{+251}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \frac{z \cdot z}{t \cdot t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}} + x \cdot \frac{x}{y \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ t_2 := x \cdot \frac{\frac{x}{y}}{y}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-140}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;z \cdot \frac{z}{t \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))) (t_2 (* x (/ (/ x y) y))))
   (if (<= t_1 2e-140) t_2 (if (<= t_1 INFINITY) (* z (/ z (* t t))) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double t_2 = x * ((x / y) / y);
	double tmp;
	if (t_1 <= 2e-140) {
		tmp = t_2;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = z * (z / (t * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double t_2 = x * ((x / y) / y);
	double tmp;
	if (t_1 <= 2e-140) {
		tmp = t_2;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = z * (z / (t * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * z) / (t * t)
	t_2 = x * ((x / y) / y)
	tmp = 0
	if t_1 <= 2e-140:
		tmp = t_2
	elif t_1 <= math.inf:
		tmp = z * (z / (t * t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * z) / Float64(t * t))
	t_2 = Float64(x * Float64(Float64(x / y) / y))
	tmp = 0.0
	if (t_1 <= 2e-140)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = Float64(z * Float64(z / Float64(t * t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * z) / (t * t);
	t_2 = x * ((x / y) / y);
	tmp = 0.0;
	if (t_1 <= 2e-140)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = z * (z / (t * t));
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x * N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e-140], t$95$2, If[LessEqual[t$95$1, Infinity], N[(z * N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 2e-140 or +inf.0 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 53.3%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 62.8

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

   5. Simplified 62.8%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

      3. /-lowering-/.f64 75.6

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

   7. Applied egg-rr 75.6%

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

   if 2e-140 < (/.f64 (*.f64 z z) (*.f64 t t)) < +inf.0

   1. Initial program 76.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{{z}^{2}}{{t}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 76.5

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

   5. Simplified 76.5%

      \[\leadsto \color{blue}{z \cdot \frac{z}{t \cdot t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ t_2 := z \cdot \frac{z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-165}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;x \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))) (t_2 (* z (/ z (* t t)))))
   (if (<= t_1 5e-165) t_2 (if (<= t_1 INFINITY) (* x (/ x (* y y))) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double t_2 = z * (z / (t * t));
	double tmp;
	if (t_1 <= 5e-165) {
		tmp = t_2;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = x * (x / (y * y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double t_2 = z * (z / (t * t));
	double tmp;
	if (t_1 <= 5e-165) {
		tmp = t_2;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = x * (x / (y * y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * x) / (y * y)
	t_2 = z * (z / (t * t))
	tmp = 0
	if t_1 <= 5e-165:
		tmp = t_2
	elif t_1 <= math.inf:
		tmp = x * (x / (y * y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) / Float64(y * y))
	t_2 = Float64(z * Float64(z / Float64(t * t)))
	tmp = 0.0
	if (t_1 <= 5e-165)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = Float64(x * Float64(x / Float64(y * y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * x) / (y * y);
	t_2 = z * (z / (t * t));
	tmp = 0.0;
	if (t_1 <= 5e-165)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = x * (x / (y * y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-165], t$95$2, If[LessEqual[t$95$1, Infinity], N[(x * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 4.99999999999999981e-165 or +inf.0 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 53.8%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{{z}^{2}}{{t}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 64.9

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

   5. Simplified 64.9%

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

   if 4.99999999999999981e-165 < (/.f64 (*.f64 x x) (*.f64 y y)) < +inf.0

   1. Initial program 76.3%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 75.7

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

   5. Simplified 75.7%

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

Alternative 12: 72.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 8.8 \cdot 10^{-125}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+163}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \frac{z \cdot z}{t \cdot t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 8.8e-125)
   (/ (/ z t) (/ t z))
   (if (<= t 1.02e+163)
     (fma (/ x y) (/ x y) (/ (* z z) (* t t)))
     (/ (/ x y) (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 8.8e-125) {
		tmp = (z / t) / (t / z);
	} else if (t <= 1.02e+163) {
		tmp = fma((x / y), (x / y), ((z * z) / (t * t)));
	} else {
		tmp = (x / y) / (y / x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 8.8e-125)
		tmp = Float64(Float64(z / t) / Float64(t / z));
	elseif (t <= 1.02e+163)
		tmp = fma(Float64(x / y), Float64(x / y), Float64(Float64(z * z) / Float64(t * t)));
	else
		tmp = Float64(Float64(x / y) / Float64(y / x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 8.8e-125], N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e+163], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision] + N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 8.79999999999999979e-125

   1. Initial program 62.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{{z}^{2}}{{t}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 52.6

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

   5. Simplified 52.6%

      \[\leadsto \color{blue}{z \cdot \frac{z}{t \cdot t}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\frac{z}{t}\right)}{\mathsf{neg}\left(t\right)}} \cdot z \]

      4. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\left(\mathsf{neg}\left(\frac{z}{t}\right)\right) \cdot z}{\mathsf{neg}\left(t\right)}} \]

      5. distribute-neg-frac N/A

         \[\leadsto \frac{\color{blue}{\frac{\mathsf{neg}\left(z\right)}{t}} \cdot z}{\mathsf{neg}\left(t\right)} \]

      6. sub0-neg N/A

         \[\leadsto \frac{\frac{\color{blue}{0 - z}}{t} \cdot z}{\mathsf{neg}\left(t\right)} \]

      7. associate-/r/ N/A

         \[\leadsto \frac{\color{blue}{\frac{0 - z}{\frac{t}{z}}}}{\mathsf{neg}\left(t\right)} \]

      8. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{0 - z}{\left(\mathsf{neg}\left(t\right)\right) \cdot \frac{t}{z}}} \]

      9. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{0 - z}{\mathsf{neg}\left(t\right)}}{\frac{t}{z}}} \]

      10. sub0-neg N/A

          \[\leadsto \frac{\frac{\color{blue}{\mathsf{neg}\left(z\right)}}{\mathsf{neg}\left(t\right)}}{\frac{t}{z}} \]

      11. frac-2neg N/A

          \[\leadsto \frac{\color{blue}{\frac{z}{t}}}{\frac{t}{z}} \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\frac{z}{t}}{\frac{t}{z}}} \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \frac{\color{blue}{\frac{z}{t}}}{\frac{t}{z}} \]

      14. /-lowering-/.f64 63.9

          \[\leadsto \frac{\frac{z}{t}}{\color{blue}{\frac{t}{z}}} \]

   7. Applied egg-rr 63.9%

      \[\leadsto \color{blue}{\frac{\frac{z}{t}}{\frac{t}{z}}} \]

   if 8.79999999999999979e-125 < t < 1.02e163

   1. Initial program 79.3%

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

      1. times-frac N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 93.0

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

   4. Applied egg-rr 93.0%

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

   if 1.02e163 < t

   1. Initial program 43.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 59.5

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

   5. Simplified 59.5%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. associate-/r/ N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. /-lowering-/.f64 90.5

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

   7. Applied egg-rr 90.5%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{\frac{y}{x}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 2 \cdot 10^{+90}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* x x) (* y y)) 2e+90) (/ (/ z t) (/ t z)) (* (/ x y) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * x) / (y * y)) <= 2e+90) {
		tmp = (z / t) / (t / z);
	} else {
		tmp = (x / y) * (x / 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 (((x * x) / (y * y)) <= 2d+90) then
        tmp = (z / t) / (t / z)
    else
        tmp = (x / y) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * x) / (y * y)) <= 2e+90) {
		tmp = (z / t) / (t / z);
	} else {
		tmp = (x / y) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * x) / (y * y)) <= 2e+90:
		tmp = (z / t) / (t / z)
	else:
		tmp = (x / y) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x * x) / Float64(y * y)) <= 2e+90)
		tmp = Float64(Float64(z / t) / Float64(t / z));
	else
		tmp = Float64(Float64(x / y) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * x) / (y * y)) <= 2e+90)
		tmp = (z / t) / (t / z);
	else
		tmp = (x / y) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision], 2e+90], N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 1.99999999999999993e90

   1. Initial program 70.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{{z}^{2}}{{t}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 65.6

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

   5. Simplified 65.6%

      \[\leadsto \color{blue}{z \cdot \frac{z}{t \cdot t}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\frac{z}{t}\right)}{\mathsf{neg}\left(t\right)}} \cdot z \]

      4. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\left(\mathsf{neg}\left(\frac{z}{t}\right)\right) \cdot z}{\mathsf{neg}\left(t\right)}} \]

      5. distribute-neg-frac N/A

         \[\leadsto \frac{\color{blue}{\frac{\mathsf{neg}\left(z\right)}{t}} \cdot z}{\mathsf{neg}\left(t\right)} \]

      6. sub0-neg N/A

         \[\leadsto \frac{\frac{\color{blue}{0 - z}}{t} \cdot z}{\mathsf{neg}\left(t\right)} \]

      7. associate-/r/ N/A

         \[\leadsto \frac{\color{blue}{\frac{0 - z}{\frac{t}{z}}}}{\mathsf{neg}\left(t\right)} \]

      8. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{0 - z}{\left(\mathsf{neg}\left(t\right)\right) \cdot \frac{t}{z}}} \]

      9. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{0 - z}{\mathsf{neg}\left(t\right)}}{\frac{t}{z}}} \]

      10. sub0-neg N/A

          \[\leadsto \frac{\frac{\color{blue}{\mathsf{neg}\left(z\right)}}{\mathsf{neg}\left(t\right)}}{\frac{t}{z}} \]

      11. frac-2neg N/A

          \[\leadsto \frac{\color{blue}{\frac{z}{t}}}{\frac{t}{z}} \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\frac{z}{t}}{\frac{t}{z}}} \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \frac{\color{blue}{\frac{z}{t}}}{\frac{t}{z}} \]

      14. /-lowering-/.f64 83.2

          \[\leadsto \frac{\frac{z}{t}}{\color{blue}{\frac{t}{z}}} \]

   7. Applied egg-rr 83.2%

      \[\leadsto \color{blue}{\frac{\frac{z}{t}}{\frac{t}{z}}} \]

   if 1.99999999999999993e90 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 59.1%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 66.7

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

   5. Simplified 66.7%

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

      1. associate-*r/ N/A

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

      2. times-frac N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 82.7

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

   7. Applied egg-rr 82.7%

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

Alternative 14: 82.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 2 \cdot 10^{+90}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* x x) (* y y)) 2e+90) (* (/ z t) (/ z t)) (* (/ x y) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * x) / (y * y)) <= 2e+90) {
		tmp = (z / t) * (z / t);
	} else {
		tmp = (x / y) * (x / 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 (((x * x) / (y * y)) <= 2d+90) then
        tmp = (z / t) * (z / t)
    else
        tmp = (x / y) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * x) / (y * y)) <= 2e+90) {
		tmp = (z / t) * (z / t);
	} else {
		tmp = (x / y) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * x) / (y * y)) <= 2e+90:
		tmp = (z / t) * (z / t)
	else:
		tmp = (x / y) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x * x) / Float64(y * y)) <= 2e+90)
		tmp = Float64(Float64(z / t) * Float64(z / t));
	else
		tmp = Float64(Float64(x / y) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * x) / (y * y)) <= 2e+90)
		tmp = (z / t) * (z / t);
	else
		tmp = (x / y) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision], 2e+90], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 1.99999999999999993e90

   1. Initial program 70.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{{z}^{2}}{{t}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 65.6

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

   5. Simplified 65.6%

      \[\leadsto \color{blue}{z \cdot \frac{z}{t \cdot t}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. times-frac N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 83.1

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

   7. Applied egg-rr 83.1%

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

   if 1.99999999999999993e90 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 59.1%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 66.7

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

   5. Simplified 66.7%

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

      1. associate-*r/ N/A

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

      2. times-frac N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 82.7

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

   7. Applied egg-rr 82.7%

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

Alternative 15: 80.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 5 \cdot 10^{-165}:\\ \;\;\;\;z \cdot \frac{\frac{z}{t}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* x x) (* y y)) 5e-165) (* z (/ (/ z t) t)) (* (/ x y) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * x) / (y * y)) <= 5e-165) {
		tmp = z * ((z / t) / t);
	} else {
		tmp = (x / y) * (x / 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 (((x * x) / (y * y)) <= 5d-165) then
        tmp = z * ((z / t) / t)
    else
        tmp = (x / y) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * x) / (y * y)) <= 5e-165) {
		tmp = z * ((z / t) / t);
	} else {
		tmp = (x / y) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * x) / (y * y)) <= 5e-165:
		tmp = z * ((z / t) / t)
	else:
		tmp = (x / y) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x * x) / Float64(y * y)) <= 5e-165)
		tmp = Float64(z * Float64(Float64(z / t) / t));
	else
		tmp = Float64(Float64(x / y) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * x) / (y * y)) <= 5e-165)
		tmp = z * ((z / t) / t);
	else
		tmp = (x / y) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision], 5e-165], N[(z * N[(N[(z / t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 4.99999999999999981e-165

   1. Initial program 68.1%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{{z}^{2}}{{t}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 72.5

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

   5. Simplified 72.5%

      \[\leadsto \color{blue}{z \cdot \frac{z}{t \cdot t}} \]
   6. Step-by-step derivation

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

      3. /-lowering-/.f64 85.7

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

   7. Applied egg-rr 85.7%

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

   if 4.99999999999999981e-165 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 62.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 63.6

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

   5. Simplified 63.6%

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

      1. associate-*r/ N/A

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

      2. times-frac N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 76.5

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

   7. Applied egg-rr 76.5%

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

Alternative 16: 78.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 5 \cdot 10^{-165}:\\ \;\;\;\;z \cdot \frac{\frac{z}{t}}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{x}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* x x) (* y y)) 5e-165) (* z (/ (/ z t) t)) (* x (/ (/ x y) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * x) / (y * y)) <= 5e-165) {
		tmp = z * ((z / t) / t);
	} else {
		tmp = 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 (((x * x) / (y * y)) <= 5d-165) then
        tmp = z * ((z / t) / t)
    else
        tmp = 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 (((x * x) / (y * y)) <= 5e-165) {
		tmp = z * ((z / t) / t);
	} else {
		tmp = x * ((x / y) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * x) / (y * y)) <= 5e-165:
		tmp = z * ((z / t) / t)
	else:
		tmp = x * ((x / y) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x * x) / Float64(y * y)) <= 5e-165)
		tmp = Float64(z * Float64(Float64(z / t) / t));
	else
		tmp = Float64(x * Float64(Float64(x / y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * x) / (y * y)) <= 5e-165)
		tmp = z * ((z / t) / t);
	else
		tmp = x * ((x / y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision], 5e-165], N[(z * N[(N[(z / t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 4.99999999999999981e-165

   1. Initial program 68.1%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{{z}^{2}}{{t}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 72.5

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

   5. Simplified 72.5%

      \[\leadsto \color{blue}{z \cdot \frac{z}{t \cdot t}} \]
   6. Step-by-step derivation

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

      3. /-lowering-/.f64 85.7

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

   7. Applied egg-rr 85.7%

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

   if 4.99999999999999981e-165 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 62.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 63.6

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

   5. Simplified 63.6%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

      3. /-lowering-/.f64 72.9

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

   7. Applied egg-rr 72.9%

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

Alternative 17: 52.6% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(x / N[(y * 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. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
4. Step-by-step derivation

   1. unpow2 N/A

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

   2. associate-/l* N/A

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

   3. *-lowering-*.f64 N/A

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

   4. /-lowering-/.f64 N/A

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

   5. unpow2 N/A

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

   6. *-lowering-*.f64 47.7

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

5. Simplified 47.7%

   \[\leadsto \color{blue}{x \cdot \frac{x}{y \cdot y}} \]
6. Add Preprocessing

Developer Target 1: 99.7% accurate, 0.2× 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 2024196 
(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))))