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

Percentage Accurate: 66.7% → 94.7%

Time: 11.5s

Alternatives: 11

Speedup: 0.9×

• 48.4% 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: 94.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \cdot t \leq 0:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, x \cdot \frac{x}{y \cdot y}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{1}{y} \cdot \frac{x}{y}, \frac{1}{\frac{t \cdot \frac{t}{z}}{z}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* t t) 0.0)
   (fma (/ z t) (/ z t) (* x (/ x (* y y))))
   (fma x (* (/ 1.0 y) (/ x y)) (/ 1.0 (/ (* t (/ t z)) z)))))

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(t * t), $MachinePrecision], 0.0], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision] + N[(x * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(1.0 / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(N[(t * N[(t / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 t t) < 0.0

   1. Initial program 66.7%

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

      1. +-commutative N/A

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

      2. times-frac N/A

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

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

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 94.9

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

   4. Applied egg-rr 94.9%

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

      1. associate-*l/ N/A

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

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

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

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

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

      4. *-lowering-*.f64 98.3

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

   6. Applied egg-rr 98.3%

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

   if 0.0 < (*.f64 t t)

   1. Initial program 70.1%

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

      1. times-frac N/A

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

      2. div-inv N/A

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

      3. associate-*l* N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      10. *-lowering-*.f64 88.0

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

   4. Applied egg-rr 88.0%

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

      1. frac-times N/A

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

      2. clear-num N/A

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

      3. frac-times N/A

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

      4. *-lft-identity N/A

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

      5. clear-num N/A

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

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

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

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

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

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

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

      9. /-lowering-/.f64 97.2

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

   6. Applied egg-rr 97.2%

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

4. Final simplification 97.4%

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

Alternative 2: 87.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 0:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+297}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y \cdot y}, x, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 0.0)
     (* (/ x y) (/ x y))
     (if (<= t_1 2e+297) (fma (/ x (* y y)) x t_1) (* (/ 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 <= 0.0) {
		tmp = (x / y) * (x / y);
	} else if (t_1 <= 2e+297) {
		tmp = fma((x / (y * y)), x, t_1);
	} else {
		tmp = (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 <= 0.0)
		tmp = Float64(Float64(x / y) * Float64(x / y));
	elseif (t_1 <= 2e+297)
		tmp = fma(Float64(x / Float64(y * y)), x, t_1);
	else
		tmp = Float64(Float64(z / t) * Float64(z / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.0], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+297], N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] * x + t$95$1), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 0.0

   1. Initial program 68.1%

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

   3. Taylor expanded in x around inf

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

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 76.6

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

   5. Simplified 76.6%

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

      1. associate-*r/ N/A

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

      2. times-frac N/A

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

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

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

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

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

      5. /-lowering-/.f64 92.4

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

   7. Applied egg-rr 92.4%

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

   if 0.0 < (/.f64 (*.f64 z z) (*.f64 t t)) < 2e297

   1. Initial program 78.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 89.0

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

   4. Applied egg-rr 89.0%

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

   if 2e297 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 66.7%

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

   3. Taylor expanded in x around 0

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

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 81.6

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

   5. Simplified 81.6%

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

      1. associate-*r/ N/A

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

      2. times-frac N/A

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

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

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

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

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

      5. /-lowering-/.f64 86.6

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

   7. Applied egg-rr 86.6%

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

Alternative 3: 95.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+171}:\\ \;\;\;\;t\_1 + \frac{\frac{x}{y}}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, x \cdot \frac{x}{y \cdot y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 5e+171)
     (+ t_1 (/ (/ x y) (/ y x)))
     (fma (/ z t) (/ z t) (* 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 <= 5e+171) {
		tmp = t_1 + ((x / y) / (y / x));
	} else {
		tmp = fma((z / t), (z / t), (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 <= 5e+171)
		tmp = Float64(t_1 + Float64(Float64(x / y) / Float64(y / x)));
	else
		tmp = fma(Float64(z / t), Float64(z / t), Float64(x * Float64(x / Float64(y * y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+171], N[(t$95$1 + N[(N[(x / y), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision] + N[(x * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 5.0000000000000004e171

   1. Initial program 68.8%

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

      1. times-frac N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

      6. /-lowering-/.f64 94.1

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

   4. Applied egg-rr 94.1%

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

   if 5.0000000000000004e171 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 69.9%

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

      1. +-commutative N/A

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

      2. times-frac N/A

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

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

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 90.0

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

   4. Applied egg-rr 90.0%

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

      1. associate-*l/ N/A

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

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

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

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

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

      4. *-lowering-*.f64 96.0

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

   6. Applied egg-rr 96.0%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 5 \cdot 10^{+171}:\\ \;\;\;\;\frac{z \cdot z}{t \cdot t} + \frac{\frac{x}{y}}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, x \cdot \frac{x}{y \cdot y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+171}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, x \cdot \frac{x}{y \cdot y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 5e+171)
     (fma (/ x y) (/ x y) t_1)
     (fma (/ z t) (/ z t) (* 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 <= 5e+171) {
		tmp = fma((x / y), (x / y), t_1);
	} else {
		tmp = fma((z / t), (z / t), (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 <= 5e+171)
		tmp = fma(Float64(x / y), Float64(x / y), t_1);
	else
		tmp = fma(Float64(z / t), Float64(z / t), Float64(x * Float64(x / Float64(y * y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+171], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision] + N[(x * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 5.0000000000000004e171

   1. Initial program 68.8%

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

      1. times-frac N/A

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

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

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

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

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

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

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

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

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

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

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

      7. *-lowering-*.f64 94.1

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

   4. Applied egg-rr 94.1%

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

   if 5.0000000000000004e171 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 69.9%

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

      1. +-commutative N/A

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

      2. times-frac N/A

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

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

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 90.0

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

   4. Applied egg-rr 90.0%

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

      1. associate-*l/ N/A

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

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

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

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

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

      4. *-lowering-*.f64 96.0

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

   6. Applied egg-rr 96.0%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 5 \cdot 10^{+171}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \frac{z \cdot z}{t \cdot t}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, x \cdot \frac{x}{y \cdot y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+297}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 2e+297) (fma (/ x y) (/ x y) t_1) (* (/ 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 <= 2e+297) {
		tmp = fma((x / y), (x / y), t_1);
	} else {
		tmp = (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 <= 2e+297)
		tmp = fma(Float64(x / y), Float64(x / y), t_1);
	else
		tmp = Float64(Float64(z / t) * Float64(z / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+297], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision] + t$95$1), $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)) < 2e297

   1. Initial program 71.3%

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

      1. times-frac N/A

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

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

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

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

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

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

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

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

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

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

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

      7. *-lowering-*.f64 94.6

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

   4. Applied egg-rr 94.6%

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

   if 2e297 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 66.7%

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

   3. Taylor expanded in x around 0

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

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 81.6

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

   5. Simplified 81.6%

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

      1. associate-*r/ N/A

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

      2. times-frac N/A

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

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

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

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

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

      5. /-lowering-/.f64 86.6

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

   7. Applied egg-rr 86.6%

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

Alternative 6: 80.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 2 \cdot 10^{-308}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 2e-308) (* (/ 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)) <= 2e-308) {
		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)) <= 2d-308) 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)) <= 2e-308) {
		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)) <= 2e-308:
		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)) <= 2e-308)
		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)) <= 2e-308)
		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], 2e-308], 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)) < 1.9999999999999998e-308

   1. Initial program 68.3%

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

   3. Taylor expanded in x around inf

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

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 77.2

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

   5. Simplified 77.2%

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

      1. associate-*r/ N/A

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

      2. times-frac N/A

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

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

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

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

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

      5. /-lowering-/.f64 92.6

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

   7. Applied egg-rr 92.6%

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

   if 1.9999999999999998e-308 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 70.0%

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

   3. Taylor expanded in x around 0

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

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 75.5

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

   5. Simplified 75.5%

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

      1. associate-*r/ N/A

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

      2. times-frac N/A

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

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

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

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

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

      5. /-lowering-/.f64 79.1

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

   7. Applied egg-rr 79.1%

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

Alternative 7: 79.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 2 \cdot 10^{-308}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\frac{z}{t}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 2e-308) (* (/ x y) (/ x y)) (* z (/ (/ z t) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 2e-308) {
		tmp = (x / y) * (x / y);
	} else {
		tmp = z * ((z / t) / 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-308) then
        tmp = (x / y) * (x / y)
    else
        tmp = z * ((z / t) / 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-308) {
		tmp = (x / y) * (x / y);
	} else {
		tmp = z * ((z / t) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * z) / (t * t)) <= 2e-308:
		tmp = (x / y) * (x / y)
	else:
		tmp = z * ((z / t) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(z * z) / Float64(t * t)) <= 2e-308)
		tmp = Float64(Float64(x / y) * Float64(x / y));
	else
		tmp = Float64(z * Float64(Float64(z / t) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * z) / (t * t)) <= 2e-308)
		tmp = (x / y) * (x / y);
	else
		tmp = z * ((z / t) / 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-308], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(z / t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 1.9999999999999998e-308

   1. Initial program 68.3%

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

   3. Taylor expanded in x around inf

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

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 77.2

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

   5. Simplified 77.2%

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

      1. associate-*r/ N/A

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

      2. times-frac N/A

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

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

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

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

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

      5. /-lowering-/.f64 92.6

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

   7. Applied egg-rr 92.6%

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

   if 1.9999999999999998e-308 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 70.0%

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

   3. Taylor expanded in x around 0

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

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 75.5

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

   5. Simplified 75.5%

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

      1. associate-/r* N/A

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

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

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

      3. /-lowering-/.f64 78.1

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

   7. Applied egg-rr 78.1%

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

Alternative 8: 77.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 2 \cdot 10^{-308}:\\ \;\;\;\;x \cdot \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\frac{z}{t}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 2e-308) (* x (/ (/ x y) y)) (* z (/ (/ z t) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 2e-308) {
		tmp = x * ((x / y) / y);
	} else {
		tmp = z * ((z / t) / 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-308) then
        tmp = x * ((x / y) / y)
    else
        tmp = z * ((z / t) / 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-308) {
		tmp = x * ((x / y) / y);
	} else {
		tmp = z * ((z / t) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * z) / (t * t)) <= 2e-308:
		tmp = x * ((x / y) / y)
	else:
		tmp = z * ((z / t) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(z * z) / Float64(t * t)) <= 2e-308)
		tmp = Float64(x * Float64(Float64(x / y) / y));
	else
		tmp = Float64(z * Float64(Float64(z / t) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * z) / (t * t)) <= 2e-308)
		tmp = x * ((x / y) / y);
	else
		tmp = z * ((z / t) / 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-308], N[(x * N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(z / t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 1.9999999999999998e-308

   1. Initial program 68.3%

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

   3. Taylor expanded in x around inf

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

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 77.2

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

   5. Simplified 77.2%

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

      1. associate-/r* N/A

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

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

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

      3. /-lowering-/.f64 89.7

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

   7. Applied egg-rr 89.7%

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

   if 1.9999999999999998e-308 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 70.0%

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

   3. Taylor expanded in x around 0

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

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 75.5

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

   5. Simplified 75.5%

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

      1. associate-/r* N/A

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

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

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

      3. /-lowering-/.f64 78.1

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

   7. Applied egg-rr 78.1%

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

Alternative 9: 73.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 2 \cdot 10^{-308}:\\ \;\;\;\;x \cdot \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{z}{t \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 2e-308) (* x (/ (/ x y) y)) (* z (/ z (* t t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 2e-308) {
		tmp = x * ((x / y) / y);
	} else {
		tmp = z * (z / (t * 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-308) then
        tmp = x * ((x / y) / y)
    else
        tmp = z * (z / (t * 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-308) {
		tmp = x * ((x / y) / y);
	} else {
		tmp = z * (z / (t * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * z) / (t * t)) <= 2e-308:
		tmp = x * ((x / y) / y)
	else:
		tmp = z * (z / (t * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(z * z) / Float64(t * t)) <= 2e-308)
		tmp = Float64(x * Float64(Float64(x / y) / y));
	else
		tmp = Float64(z * Float64(z / Float64(t * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * z) / (t * t)) <= 2e-308)
		tmp = x * ((x / y) / y);
	else
		tmp = z * (z / (t * 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-308], N[(x * N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(z * N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 1.9999999999999998e-308

   1. Initial program 68.3%

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

   3. Taylor expanded in x around inf

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

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 77.2

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

   5. Simplified 77.2%

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

      1. associate-/r* N/A

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

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

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

      3. /-lowering-/.f64 89.7

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

   7. Applied egg-rr 89.7%

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

   if 1.9999999999999998e-308 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 70.0%

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

   3. Taylor expanded in x around 0

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

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 75.5

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

   5. Simplified 75.5%

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

Alternative 10: 69.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 2 \cdot 10^{-308}:\\ \;\;\;\;x \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{z}{t \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 2e-308) (* x (/ x (* y y))) (* z (/ z (* t t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 2e-308) {
		tmp = x * (x / (y * y));
	} else {
		tmp = z * (z / (t * 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-308) then
        tmp = x * (x / (y * y))
    else
        tmp = z * (z / (t * 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-308) {
		tmp = x * (x / (y * y));
	} else {
		tmp = z * (z / (t * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * z) / (t * t)) <= 2e-308:
		tmp = x * (x / (y * y))
	else:
		tmp = z * (z / (t * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(z * z) / Float64(t * t)) <= 2e-308)
		tmp = Float64(x * Float64(x / Float64(y * y)));
	else
		tmp = Float64(z * Float64(z / Float64(t * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * z) / (t * t)) <= 2e-308)
		tmp = x * (x / (y * y));
	else
		tmp = z * (z / (t * 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-308], N[(x * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 1.9999999999999998e-308

   1. Initial program 68.3%

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

   3. Taylor expanded in x around inf

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

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 77.2

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

   5. Simplified 77.2%

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

   if 1.9999999999999998e-308 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 70.0%

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

   3. Taylor expanded in x around 0

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

      1. unpow2 N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 75.5

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

   5. Simplified 75.5%

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

Alternative 11: 52.8% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.3%

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

3. Taylor expanded in x around inf

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

   1. unpow2 N/A

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

   2. associate-/l* N/A

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

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

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

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

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

   5. unpow2 N/A

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

   6. *-lowering-*.f64 50.5

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

5. Simplified 50.5%

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

Developer Target 1: 99.7% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024199 
(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))))