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

Percentage Accurate: 66.1% → 99.6%

Time: 11.7s

Alternatives: 14

Speedup: 0.8×

• 47.5% 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: 66.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 69.4%

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

   1. times-frac N/A

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

   2. lift-*.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. lift-/.f64 N/A

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

   5. lower-fma.f64 N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 82.5

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

4. Applied egg-rr 82.5%

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

   1. times-frac N/A

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 N/A

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

   4. lower-/.f64 99.7

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

6. Applied egg-rr 99.7%

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

Alternative 2: 90.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+295}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t \cdot t}, z, t\_1\right)\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{x}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \frac{z \cdot z}{t \cdot t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))))
   (if (<= t_1 0.0)
     (/ (/ z t) (/ t z))
     (if (<= t_1 4e+295)
       (fma (/ z (* t t)) z t_1)
       (if (<= t_1 INFINITY)
         (/ (/ x (/ y x)) 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 <= 0.0) {
		tmp = (z / t) / (t / z);
	} else if (t_1 <= 4e+295) {
		tmp = fma((z / (t * t)), z, t_1);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (x / (y / x)) / 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 <= 0.0)
		tmp = Float64(Float64(z / t) / Float64(t / z));
	elseif (t_1 <= 4e+295)
		tmp = fma(Float64(z / Float64(t * t)), z, t_1);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(x / Float64(y / x)) / 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, 0.0], N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+295], N[(N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision] * z + t$95$1), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(x / N[(y / x), $MachinePrecision]), $MachinePrecision] / y), $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 4 regimes

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

   1. Initial program 80.9%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 82.9

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

   5. Simplified 82.9%

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

      1. lift-*.f64 N/A

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

      2. associate-*r/ N/A

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

      3. lift-*.f64 N/A

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

      4. frac-times N/A

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

      5. clear-num N/A

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

      6. lift-/.f64 N/A

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

      7. un-div-inv N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 99.1

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

   7. Applied egg-rr 99.1%

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

   if 0.0 < (/.f64 (*.f64 x x) (*.f64 y y)) < 3.9999999999999999e295

   1. Initial program 83.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-/.f64 94.2

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

   4. Applied egg-rr 94.2%

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

   if 3.9999999999999999e295 < (/.f64 (*.f64 x x) (*.f64 y y)) < +inf.0

   1. Initial program 77.6%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 93.4

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

   5. Simplified 93.4%

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

      1. lift-*.f64 N/A

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

      2. associate-*r/ N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. lift-/.f64 N/A

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

      7. lower-/.f64 90.7

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. lift-/.f64 N/A

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

      12. lower-*.f64 96.2

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

   7. Applied egg-rr 96.2%

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

      1. clear-num N/A

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

      2. lift-/.f64 N/A

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

      3. un-div-inv N/A

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

      4. lower-/.f64 96.2

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

   9. Applied egg-rr 96.2%

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

   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. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 76.5

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

   4. Applied egg-rr 76.5%

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

Alternative 3: 92.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{+295}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, t\_1\right)\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{x}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, x \cdot \frac{1}{y}, \frac{z \cdot z}{t \cdot t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))))
   (if (<= t_1 4e+295)
     (fma (/ z t) (/ z t) t_1)
     (if (<= t_1 INFINITY)
       (/ (/ x (/ y x)) y)
       (fma (/ x y) (* x (/ 1.0 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 <= 4e+295) {
		tmp = fma((z / t), (z / t), t_1);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (x / (y / x)) / y;
	} else {
		tmp = fma((x / y), (x * (1.0 / 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 <= 4e+295)
		tmp = fma(Float64(z / t), Float64(z / t), t_1);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(x / Float64(y / x)) / y);
	else
		tmp = fma(Float64(x / y), Float64(x * Float64(1.0 / 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, 4e+295], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(x / N[(y / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(x * N[(1.0 / y), $MachinePrecision]), $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)) < 3.9999999999999999e295

   1. Initial program 81.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. times-frac N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower-/.f64 98.7

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

   4. Applied egg-rr 98.7%

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

   if 3.9999999999999999e295 < (/.f64 (*.f64 x x) (*.f64 y y)) < +inf.0

   1. Initial program 77.6%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 93.4

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

   5. Simplified 93.4%

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

      1. lift-*.f64 N/A

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

      2. associate-*r/ N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. lift-/.f64 N/A

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

      7. lower-/.f64 90.7

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. lift-/.f64 N/A

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

      12. lower-*.f64 96.2

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

   7. Applied egg-rr 96.2%

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

      1. clear-num N/A

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

      2. lift-/.f64 N/A

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

      3. un-div-inv N/A

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

      4. lower-/.f64 96.2

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

   9. Applied egg-rr 96.2%

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

   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. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 76.5

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

   4. Applied egg-rr 76.5%

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. lift-/.f64 N/A

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

      4. lower-*.f64 76.6

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

   6. Applied egg-rr 76.6%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 4 \cdot 10^{+295}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, \frac{x \cdot x}{y \cdot y}\right)\\ \mathbf{elif}\;\frac{x \cdot x}{y \cdot y} \leq \infty:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{x}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, x \cdot \frac{1}{y}, \frac{z \cdot z}{t \cdot t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{+295}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, t\_1\right)\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{x}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \frac{z \cdot z}{t \cdot t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))))
   (if (<= t_1 4e+295)
     (fma (/ z t) (/ z t) t_1)
     (if (<= t_1 INFINITY)
       (/ (/ x (/ y x)) 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 <= 4e+295) {
		tmp = fma((z / t), (z / t), t_1);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (x / (y / x)) / 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 <= 4e+295)
		tmp = fma(Float64(z / t), Float64(z / t), t_1);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(x / Float64(y / x)) / 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, 4e+295], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(x / N[(y / x), $MachinePrecision]), $MachinePrecision] / y), $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)) < 3.9999999999999999e295

   1. Initial program 81.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. times-frac N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower-/.f64 98.7

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

   4. Applied egg-rr 98.7%

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

   if 3.9999999999999999e295 < (/.f64 (*.f64 x x) (*.f64 y y)) < +inf.0

   1. Initial program 77.6%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 93.4

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

   5. Simplified 93.4%

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

      1. lift-*.f64 N/A

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

      2. associate-*r/ N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. lift-/.f64 N/A

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

      7. lower-/.f64 90.7

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. lift-/.f64 N/A

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

      12. lower-*.f64 96.2

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

   7. Applied egg-rr 96.2%

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

      1. clear-num N/A

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

      2. lift-/.f64 N/A

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

      3. un-div-inv N/A

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

      4. lower-/.f64 96.2

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

   9. Applied egg-rr 96.2%

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

   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. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 76.5

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

   4. Applied egg-rr 76.5%

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

Alternative 5: 85.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+295}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t \cdot t}, z, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{y \cdot \frac{y}{x}} \cdot \left(-x\right)\\ \end{array} \end{array} \]

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 4e+295)
       (fma (/ z (* t t)) z t_1)
       (* (/ -1.0 (* y (/ y x))) (- x))))))

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 <= 4e+295) {
		tmp = fma((z / (t * t)), z, t_1);
	} else {
		tmp = (-1.0 / (y * (y / x))) * -x;
	}
	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 <= 4e+295)
		tmp = fma(Float64(z / Float64(t * t)), z, t_1);
	else
		tmp = Float64(Float64(-1.0 / Float64(y * Float64(y / x))) * Float64(-x));
	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, 4e+295], N[(N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision] * z + t$95$1), $MachinePrecision], N[(N[(-1.0 / N[(y * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-x)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 80.9%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 82.9

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

   5. Simplified 82.9%

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

      1. lift-*.f64 N/A

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

      2. associate-*r/ N/A

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

      3. lift-*.f64 N/A

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

      4. frac-times N/A

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

      5. clear-num N/A

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

      6. lift-/.f64 N/A

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

      7. un-div-inv N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 99.1

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

   7. Applied egg-rr 99.1%

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

   if 0.0 < (/.f64 (*.f64 x x) (*.f64 y y)) < 3.9999999999999999e295

   1. Initial program 83.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-/.f64 94.2

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

   4. Applied egg-rr 94.2%

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

   if 3.9999999999999999e295 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 57.9%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 75.6

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

   5. Simplified 75.6%

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

      1. *-lft-identity N/A

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

      2. *-commutative N/A

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

      3. frac-times N/A

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

      4. clear-num N/A

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. metadata-eval N/A

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

      8. frac-times N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 84.1

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

   7. Applied egg-rr 84.1%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 0:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{x \cdot x}{y \cdot y} \leq 4 \cdot 10^{+295}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t \cdot t}, z, \frac{x \cdot x}{y \cdot y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{y \cdot \frac{y}{x}} \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+120}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y \cdot y}, x, \frac{z \cdot z}{t \cdot t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{y \cdot \frac{y}{x}} \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))))
   (if (<= t_1 2e-119)
     (/ (/ z t) (/ t z))
     (if (<= t_1 2e+120)
       (fma (/ x (* y y)) x (/ (* z z) (* t t)))
       (* (/ -1.0 (* y (/ y x))) (- x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if (t_1 <= 2e-119) {
		tmp = (z / t) / (t / z);
	} else if (t_1 <= 2e+120) {
		tmp = fma((x / (y * y)), x, ((z * z) / (t * t)));
	} else {
		tmp = (-1.0 / (y * (y / x))) * -x;
	}
	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-119)
		tmp = Float64(Float64(z / t) / Float64(t / z));
	elseif (t_1 <= 2e+120)
		tmp = fma(Float64(x / Float64(y * y)), x, Float64(Float64(z * z) / Float64(t * t)));
	else
		tmp = Float64(Float64(-1.0 / Float64(y * Float64(y / x))) * Float64(-x));
	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-119], N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+120], N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] * x + N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 / N[(y * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-x)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 2.00000000000000003e-119

   1. Initial program 79.7%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 80.1

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

   5. Simplified 80.1%

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

      1. lift-*.f64 N/A

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

      2. associate-*r/ N/A

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

      3. lift-*.f64 N/A

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

      4. frac-times N/A

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

      5. clear-num N/A

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

      6. lift-/.f64 N/A

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

      7. un-div-inv N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 96.0

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

   7. Applied egg-rr 96.0%

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

   if 2.00000000000000003e-119 < (/.f64 (*.f64 x x) (*.f64 y y)) < 2e120

   1. Initial program 91.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. lift-/.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 91.8

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

   4. Applied egg-rr 91.8%

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

   if 2e120 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 58.9%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 75.7

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

   5. Simplified 75.7%

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

      1. *-lft-identity N/A

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

      2. *-commutative N/A

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

      3. frac-times N/A

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

      4. clear-num N/A

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. metadata-eval N/A

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

      8. frac-times N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 83.7

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

   7. Applied egg-rr 83.7%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 2 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{x \cdot x}{y \cdot y} \leq 2 \cdot 10^{+120}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y \cdot y}, x, \frac{z \cdot z}{t \cdot t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{y \cdot \frac{y}{x}} \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ t_2 := x \cdot \frac{\frac{x}{y}}{y}\\ \mathbf{if}\;t\_1 \leq 10^{-109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\left(z \cdot z\right) \cdot \frac{1}{t \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))) (t_2 (* x (/ (/ x y) y))))
   (if (<= t_1 1e-109)
     t_2
     (if (<= t_1 INFINITY) (* (* z z) (/ 1.0 (* 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 <= 1e-109) {
		tmp = t_2;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (z * z) * (1.0 / (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 <= 1e-109) {
		tmp = t_2;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (z * z) * (1.0 / (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 <= 1e-109:
		tmp = t_2
	elif t_1 <= math.inf:
		tmp = (z * z) * (1.0 / (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 <= 1e-109)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(z * z) * Float64(1.0 / 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 <= 1e-109)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = (z * z) * (1.0 / (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, 1e-109], t$95$2, If[LessEqual[t$95$1, Infinity], N[(N[(z * z), $MachinePrecision] * N[(1.0 / 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)) < 9.9999999999999999e-110 or +inf.0 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 63.7%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 76.1

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

   5. Simplified 76.1%

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

      1. associate-/r* N/A

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

      2. lift-/.f64 N/A

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

      3. lower-/.f64 85.2

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

   7. Applied egg-rr 85.2%

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

   if 9.9999999999999999e-110 < (/.f64 (*.f64 z z) (*.f64 t t)) < +inf.0

   1. Initial program 76.9%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 80.3

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

   5. Simplified 80.3%

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

      1. lift-*.f64 N/A

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

      2. associate-*r/ N/A

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

      3. lift-*.f64 N/A

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

      4. *-lft-identity N/A

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

      5. associate-*l/ N/A

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

      6. lift-/.f64 N/A

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

      7. lower-*.f64 82.0

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

   7. Applied egg-rr 82.0%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 10^{-109}:\\ \;\;\;\;x \cdot \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;\frac{z \cdot z}{t \cdot t} \leq \infty:\\ \;\;\;\;\left(z \cdot z\right) \cdot \frac{1}{t \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{x}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ t_2 := x \cdot \frac{x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{-170}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\left(z \cdot z\right) \cdot \frac{1}{t \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))) (t_2 (* x (/ x (* y y)))))
   (if (<= t_1 4e-170)
     t_2
     (if (<= t_1 INFINITY) (* (* z z) (/ 1.0 (* 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 <= 4e-170) {
		tmp = t_2;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (z * z) * (1.0 / (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 <= 4e-170) {
		tmp = t_2;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (z * z) * (1.0 / (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 <= 4e-170:
		tmp = t_2
	elif t_1 <= math.inf:
		tmp = (z * z) * (1.0 / (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(x / Float64(y * y)))
	tmp = 0.0
	if (t_1 <= 4e-170)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(z * z) * Float64(1.0 / 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 <= 4e-170)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = (z * z) * (1.0 / (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[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e-170], t$95$2, If[LessEqual[t$95$1, Infinity], N[(N[(z * z), $MachinePrecision] * N[(1.0 / 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)) < 3.99999999999999993e-170 or +inf.0 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 63.0%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. 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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 77.8

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

   5. Simplified 77.8%

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

   if 3.99999999999999993e-170 < (/.f64 (*.f64 z z) (*.f64 t t)) < +inf.0

   1. Initial program 77.0%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 78.9

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

   5. Simplified 78.9%

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

      1. lift-*.f64 N/A

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

      2. associate-*r/ N/A

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

      3. lift-*.f64 N/A

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

      4. *-lft-identity N/A

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

      5. associate-*l/ N/A

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

      6. lift-/.f64 N/A

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

      7. lower-*.f64 80.2

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

   7. Applied egg-rr 80.2%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 4 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \frac{x}{y \cdot y}\\ \mathbf{elif}\;\frac{z \cdot z}{t \cdot t} \leq \infty:\\ \;\;\;\;\left(z \cdot z\right) \cdot \frac{1}{t \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{x}{y \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ t_2 := x \cdot \frac{x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{-170}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))) (t_2 (* x (/ x (* y y)))))
   (if (<= t_1 4e-170) t_2 (if (<= t_1 INFINITY) t_1 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 <= 4e-170) {
		tmp = t_2;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} 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 <= 4e-170) {
		tmp = t_2;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} 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 <= 4e-170:
		tmp = t_2
	elif t_1 <= math.inf:
		tmp = t_1
	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(x / Float64(y * y)))
	tmp = 0.0
	if (t_1 <= 4e-170)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = t_1;
	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 <= 4e-170)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = t_1;
	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[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e-170], t$95$2, If[LessEqual[t$95$1, Infinity], t$95$1, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 3.99999999999999993e-170 or +inf.0 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 63.0%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. 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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 77.8

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

   5. Simplified 77.8%

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

   if 3.99999999999999993e-170 < (/.f64 (*.f64 z z) (*.f64 t t)) < +inf.0

   1. Initial program 77.0%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. 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. lower-/.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 90.9

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

   4. Applied egg-rr 90.9%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. unpow2 N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 80.2

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

   7. Simplified 80.2%

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

Alternative 10: 73.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ t_2 := x \cdot \frac{x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{-170}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;z \cdot \frac{z}{t \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))) (t_2 (* x (/ x (* y y)))))
   (if (<= t_1 4e-170) 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 <= 4e-170) {
		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 <= 4e-170) {
		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 <= 4e-170:
		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(x / Float64(y * y)))
	tmp = 0.0
	if (t_1 <= 4e-170)
		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 <= 4e-170)
		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[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e-170], 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)) < 3.99999999999999993e-170 or +inf.0 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 63.0%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. 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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 77.8

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

   5. Simplified 77.8%

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

   if 3.99999999999999993e-170 < (/.f64 (*.f64 z z) (*.f64 t t)) < +inf.0

   1. Initial program 77.0%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 78.9

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

   5. Simplified 78.9%

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

Alternative 11: 80.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 2 \cdot 10^{+120}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{y \cdot \frac{y}{x}} \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* x x) (* y y)) 2e+120)
   (/ (/ z t) (/ t z))
   (* (/ -1.0 (* y (/ y x))) (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * x) / (y * y)) <= 2e+120) {
		tmp = (z / t) / (t / z);
	} else {
		tmp = (-1.0 / (y * (y / x))) * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x * x) / (y * y)) <= 2d+120) then
        tmp = (z / t) / (t / z)
    else
        tmp = ((-1.0d0) / (y * (y / x))) * -x
    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+120) {
		tmp = (z / t) / (t / z);
	} else {
		tmp = (-1.0 / (y * (y / x))) * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * x) / (y * y)) <= 2e+120:
		tmp = (z / t) / (t / z)
	else:
		tmp = (-1.0 / (y * (y / x))) * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x * x) / Float64(y * y)) <= 2e+120)
		tmp = Float64(Float64(z / t) / Float64(t / z));
	else
		tmp = Float64(Float64(-1.0 / Float64(y * Float64(y / x))) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * x) / (y * y)) <= 2e+120)
		tmp = (z / t) / (t / z);
	else
		tmp = (-1.0 / (y * (y / x))) * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision], 2e+120], N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 / N[(y * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 2e120

   1. Initial program 82.4%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 75.2

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

   5. Simplified 75.2%

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

      1. lift-*.f64 N/A

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

      2. associate-*r/ N/A

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

      3. lift-*.f64 N/A

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

      4. frac-times N/A

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

      5. clear-num N/A

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

      6. lift-/.f64 N/A

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

      7. un-div-inv N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 87.6

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

   7. Applied egg-rr 87.6%

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

   if 2e120 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 58.9%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 75.7

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

   5. Simplified 75.7%

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

      1. *-lft-identity N/A

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

      2. *-commutative N/A

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

      3. frac-times N/A

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

      4. clear-num N/A

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. metadata-eval N/A

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

      8. frac-times N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 83.7

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

   7. Applied egg-rr 83.7%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 2 \cdot 10^{+120}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{y \cdot \frac{y}{x}} \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 80.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 2 \cdot 10^{+120}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{x}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* x x) (* y y)) 2e+120) (/ (/ z t) (/ t z)) (* x (/ (/ x y) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * x) / (y * y)) <= 2e+120) {
		tmp = (z / t) / (t / z);
	} 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)) <= 2d+120) then
        tmp = (z / t) / (t / z)
    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)) <= 2e+120) {
		tmp = (z / t) / (t / z);
	} else {
		tmp = x * ((x / y) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * x) / (y * y)) <= 2e+120:
		tmp = (z / t) / (t / z)
	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)) <= 2e+120)
		tmp = Float64(Float64(z / t) / Float64(t / z));
	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)) <= 2e+120)
		tmp = (z / t) / (t / z);
	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], 2e+120], N[(N[(z / t), $MachinePrecision] / N[(t / z), $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)) < 2e120

   1. Initial program 82.4%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 75.2

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

   5. Simplified 75.2%

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

      1. lift-*.f64 N/A

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

      2. associate-*r/ N/A

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

      3. lift-*.f64 N/A

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

      4. frac-times N/A

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

      5. clear-num N/A

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

      6. lift-/.f64 N/A

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

      7. un-div-inv N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 87.6

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

   7. Applied egg-rr 87.6%

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

   if 2e120 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 58.9%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 75.7

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

   5. Simplified 75.7%

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

      1. associate-/r* N/A

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

      2. lift-/.f64 N/A

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

      3. lower-/.f64 83.6

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

   7. Applied egg-rr 83.6%

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

Alternative 13: 80.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 2 \cdot 10^{+120}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{x}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* x x) (* y y)) 2e+120) (* (/ z t) (/ z t)) (* x (/ (/ x y) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * x) / (y * y)) <= 2e+120) {
		tmp = (z / t) * (z / 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)) <= 2d+120) then
        tmp = (z / t) * (z / 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)) <= 2e+120) {
		tmp = (z / t) * (z / t);
	} else {
		tmp = x * ((x / y) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * x) / (y * y)) <= 2e+120:
		tmp = (z / t) * (z / 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)) <= 2e+120)
		tmp = Float64(Float64(z / t) * Float64(z / 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)) <= 2e+120)
		tmp = (z / t) * (z / 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], 2e+120], N[(N[(z / t), $MachinePrecision] * N[(z / 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)) < 2e120

   1. Initial program 82.4%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 75.2

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

   5. Simplified 75.2%

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

      1. associate-/r* N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 87.5

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

   7. Applied egg-rr 87.5%

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

   if 2e120 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 58.9%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. lower-*.f64 N/A

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

      4. lower-/.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. lower-*.f64 75.7

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

   5. Simplified 75.7%

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

      1. associate-/r* N/A

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

      2. lift-/.f64 N/A

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

      3. lower-/.f64 83.6

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

   7. Applied egg-rr 83.6%

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

Alternative 14: 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 69.4%

   \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
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. lower-*.f64 N/A

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

   4. lower-/.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. lower-*.f64 60.3

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

5. Simplified 60.3%

   \[\leadsto \color{blue}{x \cdot \frac{x}{y \cdot y}} \]
6. Add Preprocessing

Developer Target 1: 99.6% 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 2024212 
(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))))