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

Percentage Accurate: 66.8% → 96.5%

Time: 8.6s

Alternatives: 12

Speedup: 0.8×

• 47.8% 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: 66.8% 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: 96.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 64.9%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-*l/ N/A

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

   4. associate-/r/ N/A

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

   5. lower-/.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. associate-*l/ N/A

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

   8. lower-*.f64 N/A

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

   9. lower-/.f64 79.0

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

4. Applied rewrites 79.0%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. times-frac N/A

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

   5. lift-/.f64 N/A

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

   6. lift-/.f64 N/A

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

   7. lower-*.f64 97.9

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

6. Applied rewrites 97.9%

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

7. Final simplification 97.9%

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

Alternative 2: 87.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{y}{x}}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x}{y \cdot y} \cdot x + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 0.0)
     (/ (/ x y) (/ y x))
     (if (<= t_1 2e+290) (+ (* (/ x (* y y)) x) 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 <= 0.0) {
		tmp = (x / y) / (y / x);
	} else if (t_1 <= 2e+290) {
		tmp = ((x / (y * y)) * x) + 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 <= 0.0d0) then
        tmp = (x / y) / (y / x)
    else if (t_1 <= 2d+290) then
        tmp = ((x / (y * y)) * x) + 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 <= 0.0) {
		tmp = (x / y) / (y / x);
	} else if (t_1 <= 2e+290) {
		tmp = ((x / (y * y)) * x) + 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 <= 0.0:
		tmp = (x / y) / (y / x)
	elif t_1 <= 2e+290:
		tmp = ((x / (y * y)) * x) + 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 <= 0.0)
		tmp = Float64(Float64(x / y) / Float64(y / x));
	elseif (t_1 <= 2e+290)
		tmp = Float64(Float64(Float64(x / Float64(y * y)) * x) + 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 <= 0.0)
		tmp = (x / y) / (y / x);
	elseif (t_1 <= 2e+290)
		tmp = ((x / (y * y)) * x) + 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, 0.0], N[(N[(x / y), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+290], N[(N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 65.3%

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

   3. Taylor expanded in y around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 92.6

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

   5. Applied rewrites 92.6%

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

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   7. 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 97.3

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

   8. Applied rewrites 97.3%

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

   10. Applied rewrites 97.4%

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

   if 0.0 < (/.f64 (*.f64 z z) (*.f64 t t)) < 2.00000000000000012e290

   1. Initial program 85.5%

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

   3. Taylor expanded in y around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.8

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

   5. Applied rewrites 99.8%

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

   7. Applied rewrites 86.0%

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

   if 2.00000000000000012e290 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 56.8%

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

   3. Taylor expanded in y around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 63.2

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

   5. Applied rewrites 63.2%

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

   6. Taylor expanded in t around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 79.8

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

   8. Applied rewrites 79.8%

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

   10. Applied rewrites 86.1%

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

Alternative 3: 80.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ t_2 := \frac{x}{y} \cdot \frac{x}{y}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+101}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{z}{t \cdot t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))) (t_2 (* (/ x y) (/ x y))))
   (if (<= t_1 5e+101) t_2 (if (<= t_1 INFINITY) (* (/ z (* t t)) z) 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) * (x / y);
	double tmp;
	if (t_1 <= 5e+101) {
		tmp = t_2;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (z / (t * t)) * z;
	} 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) * (x / y);
	double tmp;
	if (t_1 <= 5e+101) {
		tmp = t_2;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (z / (t * t)) * z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * z) / (t * t)
	t_2 = (x / y) * (x / y)
	tmp = 0
	if t_1 <= 5e+101:
		tmp = t_2
	elif t_1 <= math.inf:
		tmp = (z / (t * t)) * z
	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 / y) * Float64(x / y))
	tmp = 0.0
	if (t_1 <= 5e+101)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(z / Float64(t * t)) * z);
	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) * (x / y);
	tmp = 0.0;
	if (t_1 <= 5e+101)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = (z / (t * t)) * z;
	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 / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+101], t$95$2, If[LessEqual[t$95$1, Infinity], N[(N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 4.99999999999999989e101 or +inf.0 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 58.1%

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

   3. Taylor expanded in y around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 77.0

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

   5. Applied rewrites 77.0%

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

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   7. 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 80.9

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

   8. Applied rewrites 80.9%

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

   if 4.99999999999999989e101 < (/.f64 (*.f64 z z) (*.f64 t t)) < +inf.0

   1. Initial program 74.2%

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

   3. Taylor expanded in y around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 82.7

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

   5. Applied rewrites 82.7%

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

   6. Taylor expanded in t around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 87.0

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

   8. Applied rewrites 87.0%

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

   10. Applied rewrites 86.1%

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

Alternative 4: 95.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot y} \cdot x + \frac{z}{t} \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 2e+290)
     (+ (* (/ x y) (/ x y)) t_1)
     (+ (* (/ x (* y y)) x) (* (/ 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+290) {
		tmp = ((x / y) * (x / y)) + t_1;
	} else {
		tmp = ((x / (y * y)) * x) + ((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) :: t_1
    real(8) :: tmp
    t_1 = (z * z) / (t * t)
    if (t_1 <= 2d+290) then
        tmp = ((x / y) * (x / y)) + t_1
    else
        tmp = ((x / (y * y)) * x) + ((z / t) * (z / t))
    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+290) {
		tmp = ((x / y) * (x / y)) + t_1;
	} else {
		tmp = ((x / (y * y)) * x) + ((z / t) * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * z) / (t * t)
	tmp = 0
	if t_1 <= 2e+290:
		tmp = ((x / y) * (x / y)) + t_1
	else:
		tmp = ((x / (y * y)) * x) + ((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+290)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + t_1);
	else
		tmp = Float64(Float64(Float64(x / Float64(y * y)) * x) + Float64(Float64(z / t) * Float64(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 <= 2e+290)
		tmp = ((x / y) * (x / y)) + t_1;
	else
		tmp = ((x / (y * y)) * x) + ((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, 2e+290], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 2.00000000000000012e290

   1. Initial program 72.8%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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. 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 98.2

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

   4. Applied rewrites 98.2%

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

   if 2.00000000000000012e290 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 56.8%

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

   3. Taylor expanded in y around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 63.2

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

   5. Applied rewrites 63.2%

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

   7. Applied rewrites 63.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. frac-times N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift-*.f64 97.3

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

   9. Applied rewrites 97.3%

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

Alternative 5: 92.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{\frac{x}{y}}{y} \cdot x + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot y} \cdot x + \frac{z}{t} \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 2e+290)
     (+ (* (/ (/ x y) y) x) t_1)
     (+ (* (/ x (* y y)) x) (* (/ 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+290) {
		tmp = (((x / y) / y) * x) + t_1;
	} else {
		tmp = ((x / (y * y)) * x) + ((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) :: t_1
    real(8) :: tmp
    t_1 = (z * z) / (t * t)
    if (t_1 <= 2d+290) then
        tmp = (((x / y) / y) * x) + t_1
    else
        tmp = ((x / (y * y)) * x) + ((z / t) * (z / t))
    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+290) {
		tmp = (((x / y) / y) * x) + t_1;
	} else {
		tmp = ((x / (y * y)) * x) + ((z / t) * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * z) / (t * t)
	tmp = 0
	if t_1 <= 2e+290:
		tmp = (((x / y) / y) * x) + t_1
	else:
		tmp = ((x / (y * y)) * x) + ((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+290)
		tmp = Float64(Float64(Float64(Float64(x / y) / y) * x) + t_1);
	else
		tmp = Float64(Float64(Float64(x / Float64(y * y)) * x) + Float64(Float64(z / t) * Float64(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 <= 2e+290)
		tmp = (((x / y) / y) * x) + t_1;
	else
		tmp = ((x / (y * y)) * x) + ((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, 2e+290], N[(N[(N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 2.00000000000000012e290

   1. Initial program 72.8%

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

   3. Taylor expanded in y around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 95.3

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

   5. Applied rewrites 95.3%

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

   if 2.00000000000000012e290 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 56.8%

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

   3. Taylor expanded in y around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 63.2

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

   5. Applied rewrites 63.2%

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

   7. Applied rewrites 63.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. frac-times N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift-*.f64 97.3

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

   9. Applied rewrites 97.3%

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

Alternative 6: 93.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 0:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot y} \cdot x + \frac{z}{t} \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 0.0)
   (/ (/ x y) (/ y x))
   (+ (* (/ 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)) <= 0.0) {
		tmp = (x / y) / (y / x);
	} else {
		tmp = ((x / (y * y)) * x) + ((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)) <= 0.0d0) then
        tmp = (x / y) / (y / x)
    else
        tmp = ((x / (y * y)) * x) + ((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)) <= 0.0) {
		tmp = (x / y) / (y / x);
	} else {
		tmp = ((x / (y * y)) * x) + ((z / t) * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * z) / (t * t)) <= 0.0:
		tmp = (x / y) / (y / x)
	else:
		tmp = ((x / (y * y)) * x) + ((z / t) * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(z * z) / Float64(t * t)) <= 0.0)
		tmp = Float64(Float64(x / y) / Float64(y / x));
	else
		tmp = Float64(Float64(Float64(x / Float64(y * y)) * x) + 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)) <= 0.0)
		tmp = (x / y) / (y / x);
	else
		tmp = ((x / (y * y)) * x) + ((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], 0.0], N[(N[(x / y), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 65.3%

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

   3. Taylor expanded in y around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 92.6

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

   5. Applied rewrites 92.6%

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

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   7. 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 97.3

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

   8. Applied rewrites 97.3%

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

   10. Applied rewrites 97.4%

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

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

   1. Initial program 64.7%

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

   3. Taylor expanded in y around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 73.3

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

   5. Applied rewrites 73.3%

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

   7. Applied rewrites 69.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. frac-times N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift-*.f64 94.2

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

   9. Applied rewrites 94.2%

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

Alternative 7: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ t_2 := \frac{x}{y \cdot y} \cdot x\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+101}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{z}{t \cdot t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))) (t_2 (* (/ x (* y y)) x)))
   (if (<= t_1 5e+101) t_2 (if (<= t_1 INFINITY) (* (/ z (* t t)) z) 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 <= 5e+101) {
		tmp = t_2;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (z / (t * t)) * z;
	} 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 <= 5e+101) {
		tmp = t_2;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (z / (t * t)) * z;
	} 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 <= 5e+101:
		tmp = t_2
	elif t_1 <= math.inf:
		tmp = (z / (t * t)) * z
	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 <= 5e+101)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(z / Float64(t * t)) * z);
	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 <= 5e+101)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = (z / (t * t)) * z;
	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, 5e+101], t$95$2, If[LessEqual[t$95$1, Infinity], N[(N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 4.99999999999999989e101 or +inf.0 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 58.1%

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

   3. Taylor expanded in y around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 77.0

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

   5. Applied rewrites 77.0%

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

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   7. 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 80.9

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

   8. Applied rewrites 80.9%

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

   10. Applied rewrites 58.1%

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

   12. Applied rewrites 66.1%

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

   if 4.99999999999999989e101 < (/.f64 (*.f64 z z) (*.f64 t t)) < +inf.0

   1. Initial program 74.2%

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

   3. Taylor expanded in y around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 82.7

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

   5. Applied rewrites 82.7%

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

   6. Taylor expanded in t around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 87.0

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

   8. Applied rewrites 87.0%

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

   10. Applied rewrites 86.1%

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

Alternative 8: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 5 \cdot 10^{+101}:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 5e+101) (/ (/ 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)) <= 5e+101) {
		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)) <= 5d+101) 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)) <= 5e+101) {
		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)) <= 5e+101:
		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)) <= 5e+101)
		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)) <= 5e+101)
		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], 5e+101], 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)) < 4.99999999999999989e101

   1. Initial program 71.6%

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

   3. Taylor expanded in y around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 94.9

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

   5. Applied rewrites 94.9%

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

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   7. 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 88.5

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

   8. Applied rewrites 88.5%

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

   10. Applied rewrites 88.6%

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

   if 4.99999999999999989e101 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 58.9%

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

   3. Taylor expanded in y around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 65.6

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

   5. Applied rewrites 65.6%

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

   6. Taylor expanded in t around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 78.4

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

   8. Applied rewrites 78.4%

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

   10. Applied rewrites 84.2%

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

Alternative 9: 80.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 5 \cdot 10^{+101}:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t} \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 5e+101) (/ (/ 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+101) {
		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+101) 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+101) {
		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+101:
		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+101)
		tmp = Float64(Float64(x / y) / Float64(y / x));
	else
		tmp = Float64(Float64(Float64(z / t) * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * z) / (t * t)) <= 5e+101)
		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+101], N[(N[(x / y), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / t), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 4.99999999999999989e101

   1. Initial program 71.6%

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

   3. Taylor expanded in y around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 94.9

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

   5. Applied rewrites 94.9%

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

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   7. 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 88.5

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

   8. Applied rewrites 88.5%

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

   10. Applied rewrites 88.6%

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

   if 4.99999999999999989e101 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 58.9%

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

   3. Taylor expanded in y around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 65.6

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

   5. Applied rewrites 65.6%

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

   6. Taylor expanded in t around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 78.4

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

   8. Applied rewrites 78.4%

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

   10. Applied rewrites 81.5%

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

Alternative 10: 80.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 5 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t} \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 5e+101) (* (/ 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+101) {
		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+101) 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+101) {
		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+101:
		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+101)
		tmp = Float64(Float64(x / y) * Float64(x / y));
	else
		tmp = Float64(Float64(Float64(z / t) * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * z) / (t * t)) <= 5e+101)
		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+101], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / t), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 4.99999999999999989e101

   1. Initial program 71.6%

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

   3. Taylor expanded in y around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 94.9

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

   5. Applied rewrites 94.9%

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

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   7. 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 88.5

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

   8. Applied rewrites 88.5%

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

   if 4.99999999999999989e101 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 58.9%

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

   3. Taylor expanded in y around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 65.6

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

   5. Applied rewrites 65.6%

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

   6. Taylor expanded in t around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 78.4

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

   8. Applied rewrites 78.4%

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

   10. Applied rewrites 81.5%

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

Alternative 11: 80.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 5 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 5e+101) (* (/ x y) (/ x y)) (* (/ (/ z t) t) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 5e+101) {
		tmp = (x / y) * (x / y);
	} 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)) <= 5d+101) then
        tmp = (x / y) * (x / y)
    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)) <= 5e+101) {
		tmp = (x / y) * (x / y);
	} else {
		tmp = ((z / t) / t) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * z) / (t * t)) <= 5e+101:
		tmp = (x / y) * (x / y)
	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)) <= 5e+101)
		tmp = Float64(Float64(x / y) * Float64(x / y));
	else
		tmp = Float64(Float64(Float64(z / t) / t) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * z) / (t * t)) <= 5e+101)
		tmp = (x / y) * (x / y);
	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], 5e+101], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / t), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 4.99999999999999989e101

   1. Initial program 71.6%

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

   3. Taylor expanded in y around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 94.9

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

   5. Applied rewrites 94.9%

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

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
   7. 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 88.5

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

   8. Applied rewrites 88.5%

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

   if 4.99999999999999989e101 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 58.9%

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

   3. Taylor expanded in y around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 65.6

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

   5. Applied rewrites 65.6%

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

   6. Taylor expanded in t around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 78.4

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

   8. Applied rewrites 78.4%

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

Alternative 12: 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 64.9%

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

3. Taylor expanded in y around 0

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

   1. unpow2 N/A

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

   2. associate-*l/ N/A

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

   3. lower-*.f64 N/A

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

   4. unpow2 N/A

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

   5. associate-/r* N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 79.4

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

5. Applied rewrites 79.4%

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

6. Taylor expanded in t around inf

   \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} \]
7. 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 59.7

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

8. Applied rewrites 59.7%

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

10. Applied rewrites 47.5%

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

12. Applied rewrites 54.1%

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

Developer Target 1: 99.6% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024249 
(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))))