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

Percentage Accurate: 66.7% → 99.5%

Time: 12.2s

Alternatives: 17

Speedup: 0.8×

• 49.0% 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: 66.7% 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: 99.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{1}{{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}}} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (/ 1.0 (/ 1.0 (+ (pow (/ x y) 2.0) (pow (/ z t) 2.0)))))

C

double code(double x, double y, double z, double t) {
	return 1.0 / (1.0 / (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 = 1.0d0 / (1.0d0 / (((x / y) ** 2.0d0) + ((z / t) ** 2.0d0)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0 / (1.0 / (Math.pow((x / y), 2.0) + Math.pow((z / t), 2.0)));
}

Python

def code(x, y, z, t):
	return 1.0 / (1.0 / (math.pow((x / y), 2.0) + math.pow((z / t), 2.0)))

Julia

function code(x, y, z, t)
	return Float64(1.0 / Float64(1.0 / Float64((Float64(x / y) ^ 2.0) + (Float64(z / t) ^ 2.0))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0 / (1.0 / (((x / y) ^ 2.0) + ((z / t) ^ 2.0)));
end

Wolfram

code[x_, y_, z_, t_] := N[(1.0 / N[(1.0 / N[(N[Power[N[(x / y), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(z / t), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 64.8%

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

   1. lift-+.f64 N/A

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

   2. flip-+ N/A

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

   3. clear-num N/A

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

   4. lower-/.f64 N/A

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

   5. clear-num N/A

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

   6. flip-+ N/A

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

   7. lift-+.f64 N/A

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

   8. lower-/.f64 64.7

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

4. Applied rewrites 99.6%

   \[\leadsto \color{blue}{\frac{1}{\frac{1}{{\left(\frac{z}{t}\right)}^{2} + {\left(\frac{x}{y}\right)}^{2}}}} \]

5. Final simplification 99.6%

   \[\leadsto \frac{1}{\frac{1}{{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}}} \]
6. Add Preprocessing

Alternative 2: 96.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 7 \cdot 10^{-243}:\\ \;\;\;\;\frac{\frac{z}{t} \cdot z}{t} + \frac{\frac{x}{y} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, {t}^{-1} \cdot \frac{z}{t}, {\left(\frac{x}{y}\right)}^{2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 7e-243)
   (+ (/ (* (/ z t) z) t) (/ (* (/ x y) x) y))
   (fma z (* (pow t -1.0) (/ z t)) (pow (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 7e-243) {
		tmp = (((z / t) * z) / t) + (((x / y) * x) / y);
	} else {
		tmp = fma(z, (pow(t, -1.0) * (z / t)), pow((x / y), 2.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 7e-243)
		tmp = Float64(Float64(Float64(Float64(z / t) * z) / t) + Float64(Float64(Float64(x / y) * x) / y));
	else
		tmp = fma(z, Float64((t ^ -1.0) * Float64(z / t)), (Float64(x / y) ^ 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 7e-243], N[(N[(N[(N[(z / t), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision] + N[(N[(N[(x / y), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[Power[t, -1.0], $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision] + N[Power[N[(x / y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 6.99999999999999958e-243

   1. Initial program 59.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 76.5

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

   4. Applied rewrites 76.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 95.3

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

   6. Applied rewrites 95.3%

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

   if 6.99999999999999958e-243 < t

   1. Initial program 71.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. times-frac N/A

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

      7. div-inv N/A

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

      8. associate-*l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. inv-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. lower-/.f64 84.0

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

      14. lift-/.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. times-frac N/A

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

      18. pow2 N/A

          \[\leadsto \mathsf{fma}\left(z, {t}^{-1} \cdot \frac{z}{t}, \color{blue}{{\left(\frac{x}{y}\right)}^{2}}\right) \]

      19. lower-pow.f64 N/A

          \[\leadsto \mathsf{fma}\left(z, {t}^{-1} \cdot \frac{z}{t}, \color{blue}{{\left(\frac{x}{y}\right)}^{2}}\right) \]

      20. lower-/.f64 99.8

          \[\leadsto \mathsf{fma}\left(z, {t}^{-1} \cdot \frac{z}{t}, {\color{blue}{\left(\frac{x}{y}\right)}}^{2}\right) \]

   4. Applied rewrites 99.8%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7 \cdot 10^{-243}:\\ \;\;\;\;\frac{\frac{z}{t} \cdot z}{t} + \frac{\frac{x}{y} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, {t}^{-1} \cdot \frac{z}{t}, {\left(\frac{x}{y}\right)}^{2}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{-1}{t}, \frac{-z}{t} \cdot z, {\left(\frac{x}{y}\right)}^{2}\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (fma (/ -1.0 t) (* (/ (- z) t) z) (pow (/ x y) 2.0)))

C

double code(double x, double y, double z, double t) {
	return fma((-1.0 / t), ((-z / t) * z), pow((x / y), 2.0));
}

Julia

function code(x, y, z, t)
	return fma(Float64(-1.0 / t), Float64(Float64(Float64(-z) / t) * z), (Float64(x / y) ^ 2.0))
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(-1.0 / t), $MachinePrecision] * N[(N[((-z) / t), $MachinePrecision] * z), $MachinePrecision] + N[Power[N[(x / y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 64.8%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. frac-2neg N/A

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

   5. neg-mul-1 N/A

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

   6. lift-*.f64 N/A

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

   7. distribute-rgt-neg-in N/A

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

   8. times-frac N/A

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

   9. distribute-neg-frac2 N/A

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

   10. lower-fma.f64 N/A

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

   11. lower-/.f64 N/A

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

   12. lift-*.f64 N/A

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

   13. associate-/l* N/A

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

   14. distribute-lft-neg-in N/A

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

   15. lower-*.f64 N/A

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

   16. lower-neg.f64 N/A

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

   17. lower-/.f64 77.5

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

   18. lift-/.f64 N/A

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

   19. lift-*.f64 N/A

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

   20. lift-*.f64 N/A

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

   21. times-frac N/A

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

   22. pow2 N/A

       \[\leadsto \mathsf{fma}\left(\frac{-1}{t}, \left(-z\right) \cdot \frac{z}{t}, \color{blue}{{\left(\frac{x}{y}\right)}^{2}}\right) \]

   23. lower-pow.f64 N/A

       \[\leadsto \mathsf{fma}\left(\frac{-1}{t}, \left(-z\right) \cdot \frac{z}{t}, \color{blue}{{\left(\frac{x}{y}\right)}^{2}}\right) \]

   24. lower-/.f64 96.4

       \[\leadsto \mathsf{fma}\left(\frac{-1}{t}, \left(-z\right) \cdot \frac{z}{t}, {\color{blue}{\left(\frac{x}{y}\right)}}^{2}\right) \]

4. Applied rewrites 96.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{t}, \left(-z\right) \cdot \frac{z}{t}, {\left(\frac{x}{y}\right)}^{2}\right)} \]

5. Final simplification 96.4%

   \[\leadsto \mathsf{fma}\left(\frac{-1}{t}, \frac{-z}{t} \cdot z, {\left(\frac{x}{y}\right)}^{2}\right) \]
6. Add Preprocessing

Alternative 4: 87.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 10^{-231}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+255}:\\ \;\;\;\;\frac{z}{t \cdot t} \cdot z + t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{t} \cdot \left(\frac{-1}{t} \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))))
   (if (<= t_1 1e-231)
     (/ (/ z t) (/ t z))
     (if (<= t_1 2e+255)
       (+ (* (/ z (* t t)) z) t_1)
       (if (<= t_1 INFINITY)
         (/ (/ x y) (/ y x))
         (* (/ (- z) t) (* (/ -1.0 t) z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if (t_1 <= 1e-231) {
		tmp = (z / t) / (t / z);
	} else if (t_1 <= 2e+255) {
		tmp = ((z / (t * t)) * z) + t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (x / y) / (y / x);
	} else {
		tmp = (-z / t) * ((-1.0 / t) * z);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if (t_1 <= 1e-231) {
		tmp = (z / t) / (t / z);
	} else if (t_1 <= 2e+255) {
		tmp = ((z / (t * t)) * z) + t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (x / y) / (y / x);
	} else {
		tmp = (-z / t) * ((-1.0 / t) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * x) / (y * y)
	tmp = 0
	if t_1 <= 1e-231:
		tmp = (z / t) / (t / z)
	elif t_1 <= 2e+255:
		tmp = ((z / (t * t)) * z) + t_1
	elif t_1 <= math.inf:
		tmp = (x / y) / (y / x)
	else:
		tmp = (-z / t) * ((-1.0 / t) * z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) / Float64(y * y))
	tmp = 0.0
	if (t_1 <= 1e-231)
		tmp = Float64(Float64(z / t) / Float64(t / z));
	elseif (t_1 <= 2e+255)
		tmp = Float64(Float64(Float64(z / Float64(t * t)) * z) + t_1);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(x / y) / Float64(y / x));
	else
		tmp = Float64(Float64(Float64(-z) / t) * Float64(Float64(-1.0 / t) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * x) / (y * y);
	tmp = 0.0;
	if (t_1 <= 1e-231)
		tmp = (z / t) / (t / z);
	elseif (t_1 <= 2e+255)
		tmp = ((z / (t * t)) * z) + t_1;
	elseif (t_1 <= Inf)
		tmp = (x / y) / (y / x);
	else
		tmp = (-z / t) * ((-1.0 / t) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e-231], N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+255], N[(N[(N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(x / y), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], N[(N[((-z) / t), $MachinePrecision] * N[(N[(-1.0 / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 9.9999999999999999e-232

   1. Initial program 68.4%

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

   3. Taylor expanded in t 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. unpow2 N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 94.6

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

   5. Applied rewrites 94.6%

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

   7. Applied rewrites 94.7%

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

   if 9.9999999999999999e-232 < (/.f64 (*.f64 x x) (*.f64 y y)) < 1.99999999999999998e255

   1. Initial program 80.2%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. pow2 N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \left(\frac{1}{\color{blue}{{t}^{2}}} \cdot z\right) \cdot z \]

      10. pow-flip N/A

          \[\leadsto \frac{x \cdot x}{y \cdot y} + \left(\color{blue}{{t}^{\left(\mathsf{neg}\left(2\right)\right)}} \cdot z\right) \cdot z \]

      11. lower-pow.f64 N/A

          \[\leadsto \frac{x \cdot x}{y \cdot y} + \left(\color{blue}{{t}^{\left(\mathsf{neg}\left(2\right)\right)}} \cdot z\right) \cdot z \]

      12. metadata-eval 91.0

          \[\leadsto \frac{x \cdot x}{y \cdot y} + \left({t}^{\color{blue}{-2}} \cdot z\right) \cdot z \]

   4. Applied rewrites 91.0%

      \[\leadsto \frac{x \cdot x}{y \cdot y} + \color{blue}{\left({t}^{-2} \cdot z\right) \cdot z} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \color{blue}{\left({t}^{-2} \cdot z\right)} \cdot z \]

      2. *-commutative N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \color{blue}{\left(z \cdot {t}^{-2}\right)} \cdot z \]

      3. lift-pow.f64 N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \left(z \cdot \color{blue}{{t}^{-2}}\right) \cdot z \]

      4. metadata-eval N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \left(z \cdot {t}^{\color{blue}{\left(\mathsf{neg}\left(2\right)\right)}}\right) \cdot z \]

      5. pow-flip N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \left(z \cdot \color{blue}{\frac{1}{{t}^{2}}}\right) \cdot z \]

      6. pow2 N/A

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

      7. div-inv N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 91.4

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

   6. Applied rewrites 91.4%

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

   if 1.99999999999999998e255 < (/.f64 (*.f64 x x) (*.f64 y y)) < +inf.0

   1. Initial program 74.3%

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

   3. Taylor expanded in t 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

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 90.6

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

   5. Applied rewrites 90.6%

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

   7. Applied rewrites 94.8%

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

   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. Taylor expanded in t 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. unpow2 N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 58.6

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

   5. Applied rewrites 58.6%

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

   7. Applied rewrites 38.6%

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

   9. Applied rewrites 48.2%

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

   11. Applied rewrites 58.8%

       \[\leadsto \frac{z}{t} \cdot \color{blue}{\left(\frac{-1}{t} \cdot \left(-z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 10^{-231}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{x \cdot x}{y \cdot y} \leq 2 \cdot 10^{+255}:\\ \;\;\;\;\frac{z}{t \cdot t} \cdot z + \frac{x \cdot x}{y \cdot y}\\ \mathbf{elif}\;\frac{x \cdot x}{y \cdot y} \leq \infty:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{t} \cdot \left(\frac{-1}{t} \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+255}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}} + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t} \cdot z}{t} + \frac{\frac{x}{y} \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))))
   (if (<= t_1 2e+255)
     (+ (/ (/ z t) (/ t z)) t_1)
     (+ (/ (* (/ z t) z) t) (/ (* (/ x y) x) y)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if (t_1 <= 2e+255) {
		tmp = ((z / t) / (t / z)) + t_1;
	} else {
		tmp = (((z / t) * z) / t) + (((x / y) * x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * x) / (y * y)
    if (t_1 <= 2d+255) then
        tmp = ((z / t) / (t / z)) + t_1
    else
        tmp = (((z / t) * z) / t) + (((x / y) * x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if (t_1 <= 2e+255) {
		tmp = ((z / t) / (t / z)) + t_1;
	} else {
		tmp = (((z / t) * z) / t) + (((x / y) * x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * x) / (y * y)
	tmp = 0
	if t_1 <= 2e+255:
		tmp = ((z / t) / (t / z)) + t_1
	else:
		tmp = (((z / t) * z) / t) + (((x / y) * x) / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) / Float64(y * y))
	tmp = 0.0
	if (t_1 <= 2e+255)
		tmp = Float64(Float64(Float64(z / t) / Float64(t / z)) + t_1);
	else
		tmp = Float64(Float64(Float64(Float64(z / t) * z) / t) + Float64(Float64(Float64(x / y) * x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * x) / (y * y);
	tmp = 0.0;
	if (t_1 <= 2e+255)
		tmp = ((z / t) / (t / z)) + t_1;
	else
		tmp = (((z / t) * z) / t) + (((x / y) * x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+255], N[(N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(N[(z / t), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision] + N[(N[(N[(x / y), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 1.99999999999999998e255

   1. Initial program 72.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. clear-num N/A

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

      6. un-div-inv N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 96.3

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

   4. Applied rewrites 96.3%

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

   if 1.99999999999999998e255 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 56.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 63.0

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

   4. Applied rewrites 63.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 96.6

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

   6. Applied rewrites 96.6%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 2 \cdot 10^{+255}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}} + \frac{x \cdot x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t} \cdot z}{t} + \frac{\frac{x}{y} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z, t):
	t_1 = (z * z) / (t * t)
	tmp = 0
	if t_1 <= math.inf:
		tmp = ((x / y) * (x / y)) + t_1
	else:
		tmp = ((z / t) / (t / z)) + ((x * x) / (y * y))
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 75.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 93.1

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

   4. Applied rewrites 93.1%

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

   if +inf.0 < (/.f64 (*.f64 z z) (*.f64 t t))

   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. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. clear-num N/A

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

      6. un-div-inv N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 85.5

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

   4. Applied rewrites 85.5%

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

4. Final simplification 92.0%

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

Alternative 7: 80.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ t_2 := \frac{z}{t} \cdot \frac{z}{t}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-180}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{x}{y \cdot y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))) (t_2 (* (/ z t) (/ z t))))
   (if (<= t_1 5e-180) t_2 (if (<= t_1 INFINITY) (* (/ x (* y y)) x) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double t_2 = (z / t) * (z / t);
	double tmp;
	if (t_1 <= 5e-180) {
		tmp = t_2;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (x / (y * y)) * x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double t_2 = (z / t) * (z / t);
	double tmp;
	if (t_1 <= 5e-180) {
		tmp = t_2;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (x / (y * y)) * x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * x) / (y * y)
	t_2 = (z / t) * (z / t)
	tmp = 0
	if t_1 <= 5e-180:
		tmp = t_2
	elif t_1 <= math.inf:
		tmp = (x / (y * y)) * x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) / Float64(y * y))
	t_2 = Float64(Float64(z / t) * Float64(z / t))
	tmp = 0.0
	if (t_1 <= 5e-180)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(x / Float64(y * y)) * x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * x) / (y * y);
	t_2 = (z / t) * (z / t);
	tmp = 0.0;
	if (t_1 <= 5e-180)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = (x / (y * y)) * x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-180], t$95$2, If[LessEqual[t$95$1, Infinity], N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 5.0000000000000001e-180 or +inf.0 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 52.9%

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

   3. Taylor expanded in t 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. unpow2 N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 85.5

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

   5. Applied rewrites 85.5%

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

   if 5.0000000000000001e-180 < (/.f64 (*.f64 x x) (*.f64 y y)) < +inf.0

   1. Initial program 75.9%

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

   3. Taylor expanded in t 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

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 80.6

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

   5. Applied rewrites 80.6%

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

   7. Applied rewrites 80.7%

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

Alternative 8: 89.6% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z, t):
	t_1 = (z * z) / (t * t)
	tmp = 0
	if t_1 <= math.inf:
		tmp = ((x / y) * (x / y)) + t_1
	else:
		tmp = ((x * x) / (y * y)) + (((z / t) * z) / t)
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 75.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 93.1

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

   4. Applied rewrites 93.1%

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

   if +inf.0 < (/.f64 (*.f64 z z) (*.f64 t t))

   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. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 74.9

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

   4. Applied rewrites 74.9%

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

Alternative 9: 89.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+271}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 2e+271) (+ (* (/ x y) (/ x y)) t_1) (/ (/ z t) (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 2e+271) {
		tmp = ((x / y) * (x / y)) + t_1;
	} else {
		tmp = (z / t) / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * z) / (t * t)
    if (t_1 <= 2d+271) then
        tmp = ((x / y) * (x / y)) + t_1
    else
        tmp = (z / t) / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 2e+271) {
		tmp = ((x / y) * (x / y)) + t_1;
	} else {
		tmp = (z / t) / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * z) / (t * t)
	tmp = 0
	if t_1 <= 2e+271:
		tmp = ((x / y) * (x / y)) + t_1
	else:
		tmp = (z / t) / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * z) / Float64(t * t))
	tmp = 0.0
	if (t_1 <= 2e+271)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + t_1);
	else
		tmp = Float64(Float64(z / t) / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * z) / (t * t);
	tmp = 0.0;
	if (t_1 <= 2e+271)
		tmp = ((x / y) * (x / y)) + t_1;
	else
		tmp = (z / t) / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+271], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 1.99999999999999991e271

   1. Initial program 72.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 94.3

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

   4. Applied rewrites 94.3%

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

   if 1.99999999999999991e271 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 55.8%

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

   3. Taylor expanded in t 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. unpow2 N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 83.8

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

   5. Applied rewrites 83.8%

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

   7. Applied rewrites 83.9%

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

Alternative 10: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ t_2 := \frac{z}{t \cdot t} \cdot z\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-180}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{x}{y \cdot y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))) (t_2 (* (/ z (* t t)) z)))
   (if (<= t_1 5e-180) t_2 (if (<= t_1 INFINITY) (* (/ x (* y y)) x) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double t_2 = (z / (t * t)) * z;
	double tmp;
	if (t_1 <= 5e-180) {
		tmp = t_2;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (x / (y * y)) * x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double t_2 = (z / (t * t)) * z;
	double tmp;
	if (t_1 <= 5e-180) {
		tmp = t_2;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (x / (y * y)) * x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * x) / (y * y)
	t_2 = (z / (t * t)) * z
	tmp = 0
	if t_1 <= 5e-180:
		tmp = t_2
	elif t_1 <= math.inf:
		tmp = (x / (y * y)) * x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) / Float64(y * y))
	t_2 = Float64(Float64(z / Float64(t * t)) * z)
	tmp = 0.0
	if (t_1 <= 5e-180)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(x / Float64(y * y)) * x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * x) / (y * y);
	t_2 = (z / (t * t)) * z;
	tmp = 0.0;
	if (t_1 <= 5e-180)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = (x / (y * y)) * x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-180], t$95$2, If[LessEqual[t$95$1, Infinity], N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 5.0000000000000001e-180 or +inf.0 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 52.9%

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

   3. Taylor expanded in t 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. unpow2 N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 85.5

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

   5. Applied rewrites 85.5%

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

   7. Applied rewrites 61.2%

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

   9. Applied rewrites 79.4%

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

   11. Applied rewrites 67.2%

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

   if 5.0000000000000001e-180 < (/.f64 (*.f64 x x) (*.f64 y y)) < +inf.0

   1. Initial program 75.9%

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

   3. Taylor expanded in t 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

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 80.6

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

   5. Applied rewrites 80.6%

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

   7. Applied rewrites 80.7%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 5 \cdot 10^{-180}:\\ \;\;\;\;\frac{z}{t \cdot t} \cdot z\\ \mathbf{elif}\;\frac{x \cdot x}{y \cdot y} \leq \infty:\\ \;\;\;\;\frac{x}{y \cdot y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t \cdot t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ t_2 := \frac{x}{y \cdot y} \cdot x\\ \mathbf{if}\;t\_1 \leq 2.2 \cdot 10^{-76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))) (t_2 (* (/ x (* y y)) x)))
   (if (<= t_1 2.2e-76) 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 / (y * y)) * x;
	double tmp;
	if (t_1 <= 2.2e-76) {
		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 / (y * y)) * x;
	double tmp;
	if (t_1 <= 2.2e-76) {
		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 / (y * y)) * x
	tmp = 0
	if t_1 <= 2.2e-76:
		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(Float64(x / Float64(y * y)) * x)
	tmp = 0.0
	if (t_1 <= 2.2e-76)
		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 / (y * y)) * x;
	tmp = 0.0;
	if (t_1 <= 2.2e-76)
		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[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, 2.2e-76], 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)) < 2.19999999999999999e-76 or +inf.0 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 53.5%

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

   3. Taylor expanded in t 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

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 73.4

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

   5. Applied rewrites 73.4%

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

   7. Applied rewrites 66.2%

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

   if 2.19999999999999999e-76 < (/.f64 (*.f64 z z) (*.f64 t t)) < +inf.0

   1. Initial program 80.2%

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

   3. Taylor expanded in t 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. unpow2 N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 84.3

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

   5. Applied rewrites 84.3%

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

   7. Applied rewrites 83.4%

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

Alternative 12: 82.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 2 \cdot 10^{-76}:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 2e-76) (/ (/ x y) (/ y x)) (/ (/ z t) (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 2e-76) {
		tmp = (x / y) / (y / x);
	} else {
		tmp = (z / t) / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * z) / (t * t)) <= 2d-76) then
        tmp = (x / y) / (y / x)
    else
        tmp = (z / t) / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 2e-76) {
		tmp = (x / y) / (y / x);
	} else {
		tmp = (z / t) / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * z) / (t * t)) <= 2e-76:
		tmp = (x / y) / (y / x)
	else:
		tmp = (z / t) / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(z * z) / Float64(t * t)) <= 2e-76)
		tmp = Float64(Float64(x / y) / Float64(y / x));
	else
		tmp = Float64(Float64(z / t) / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * z) / (t * t)) <= 2e-76)
		tmp = (x / y) / (y / x);
	else
		tmp = (z / t) / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision], 2e-76], N[(N[(x / y), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 1.99999999999999985e-76

   1. Initial program 70.1%

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

   3. Taylor expanded in t 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

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 84.8

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

   5. Applied rewrites 84.8%

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

   7. Applied rewrites 90.7%

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

   if 1.99999999999999985e-76 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 60.6%

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

   3. Taylor expanded in t 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. unpow2 N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 80.0

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

   5. Applied rewrites 80.0%

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

   7. Applied rewrites 80.1%

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

Alternative 13: 82.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 5 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 5e-50) (/ (/ x y) (/ y x)) (* (/ z t) (/ z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 5e-50) {
		tmp = (x / y) / (y / x);
	} else {
		tmp = (z / t) * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * z) / (t * t)) <= 5d-50) then
        tmp = (x / y) / (y / x)
    else
        tmp = (z / t) * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 5e-50) {
		tmp = (x / y) / (y / x);
	} else {
		tmp = (z / t) * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * z) / (t * t)) <= 5e-50:
		tmp = (x / y) / (y / x)
	else:
		tmp = (z / t) * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(z * z) / Float64(t * t)) <= 5e-50)
		tmp = Float64(Float64(x / y) / Float64(y / x));
	else
		tmp = Float64(Float64(z / t) * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * z) / (t * t)) <= 5e-50)
		tmp = (x / y) / (y / x);
	else
		tmp = (z / t) * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision], 5e-50], N[(N[(x / y), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 4.99999999999999968e-50

   1. Initial program 71.1%

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

   3. Taylor expanded in t 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

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 83.7

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

   5. Applied rewrites 83.7%

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

   7. Applied rewrites 89.4%

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

   if 4.99999999999999968e-50 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 59.5%

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

   3. Taylor expanded in t 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. unpow2 N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 80.8

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

   5. Applied rewrites 80.8%

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

Alternative 14: 82.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 5 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 5e-50) (* (/ x y) (/ x y)) (* (/ z t) (/ z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 5e-50) {
		tmp = (x / y) * (x / y);
	} else {
		tmp = (z / t) * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * z) / (t * t)) <= 5d-50) then
        tmp = (x / y) * (x / y)
    else
        tmp = (z / t) * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 5e-50) {
		tmp = (x / y) * (x / y);
	} else {
		tmp = (z / t) * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * z) / (t * t)) <= 5e-50:
		tmp = (x / y) * (x / y)
	else:
		tmp = (z / t) * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(z * z) / Float64(t * t)) <= 5e-50)
		tmp = Float64(Float64(x / y) * Float64(x / y));
	else
		tmp = Float64(Float64(z / t) * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * z) / (t * t)) <= 5e-50)
		tmp = (x / y) * (x / y);
	else
		tmp = (z / t) * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision], 5e-50], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 4.99999999999999968e-50

   1. Initial program 71.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. lift-/.f64 N/A

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

      7. frac-add N/A

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

      8. lower-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*r* N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-/l* N/A

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

      15. lower-*.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. lower-*.f64 N/A

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

      18. lower-*.f64 63.9

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

   4. Applied rewrites 63.9%

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

   5. Taylor expanded in t around inf

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

      1. unpow2 N/A

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

      2. unpow2 N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 89.3

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

   7. Applied rewrites 89.3%

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

   if 4.99999999999999968e-50 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 59.5%

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

   3. Taylor expanded in t 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. unpow2 N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 80.8

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

   5. Applied rewrites 80.8%

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

Alternative 15: 80.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 5 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{\frac{y}{x} \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 5e-50) (/ x (* (/ y x) y)) (* (/ z t) (/ z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 5e-50) {
		tmp = x / ((y / x) * y);
	} else {
		tmp = (z / t) * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * z) / (t * t)) <= 5d-50) then
        tmp = x / ((y / x) * y)
    else
        tmp = (z / t) * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 5e-50) {
		tmp = x / ((y / x) * y);
	} else {
		tmp = (z / t) * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * z) / (t * t)) <= 5e-50:
		tmp = x / ((y / x) * y)
	else:
		tmp = (z / t) * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(z * z) / Float64(t * t)) <= 5e-50)
		tmp = Float64(x / Float64(Float64(y / x) * y));
	else
		tmp = Float64(Float64(z / t) * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * z) / (t * t)) <= 5e-50)
		tmp = x / ((y / x) * y);
	else
		tmp = (z / t) * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision], 5e-50], N[(x / N[(N[(y / x), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 4.99999999999999968e-50

   1. Initial program 71.1%

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

   3. Taylor expanded in t 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

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 83.7

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

   5. Applied rewrites 83.7%

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

   7. Applied rewrites 84.6%

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

   if 4.99999999999999968e-50 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 59.5%

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

   3. Taylor expanded in t 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. unpow2 N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 80.8

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

   5. Applied rewrites 80.8%

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

Alternative 16: 80.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 2 \cdot 10^{-76}:\\ \;\;\;\;\frac{\frac{x}{y}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 2e-76) (* (/ (/ x y) y) x) (* (/ z t) (/ z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 2e-76) {
		tmp = ((x / y) / y) * x;
	} else {
		tmp = (z / t) * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * z) / (t * t)) <= 2d-76) then
        tmp = ((x / y) / y) * x
    else
        tmp = (z / t) * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 2e-76) {
		tmp = ((x / y) / y) * x;
	} else {
		tmp = (z / t) * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * z) / (t * t)) <= 2e-76:
		tmp = ((x / y) / y) * x
	else:
		tmp = (z / t) * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(z * z) / Float64(t * t)) <= 2e-76)
		tmp = Float64(Float64(Float64(x / y) / y) * x);
	else
		tmp = Float64(Float64(z / t) * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * z) / (t * t)) <= 2e-76)
		tmp = ((x / y) / y) * x;
	else
		tmp = (z / t) * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision], 2e-76], N[(N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 1.99999999999999985e-76

   1. Initial program 70.1%

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

   3. Taylor expanded in t 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

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 84.8

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

   5. Applied rewrites 84.8%

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

   if 1.99999999999999985e-76 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 60.6%

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

   3. Taylor expanded in t 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. unpow2 N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 80.0

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

   5. Applied rewrites 80.0%

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

Alternative 17: 52.1% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 64.8%

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

3. Taylor expanded in t 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

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

   3. lower-*.f64 N/A

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

   4. unpow2 N/A

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

   5. associate-/r* N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 55.9

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

5. Applied rewrites 55.9%

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

7. Applied rewrites 54.4%

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

Developer Target 1: 99.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ {\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ (pow (/ x y) 2.0) (pow (/ z t) 2.0)))

C

double code(double x, double y, double z, double t) {
	return pow((x / y), 2.0) + pow((z / t), 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x / y) ** 2.0d0) + ((z / t) ** 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return Math.pow((x / y), 2.0) + Math.pow((z / t), 2.0);
}

Python

def code(x, y, z, t):
	return math.pow((x / y), 2.0) + math.pow((z / t), 2.0)

Julia

function code(x, y, z, t)
	return Float64((Float64(x / y) ^ 2.0) + (Float64(z / t) ^ 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x / y) ^ 2.0) + ((z / t) ^ 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[Power[N[(x / y), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(z / t), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024255 
(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))))