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

Percentage Accurate: 66.1% → 93.4%

Time: 10.0s

Alternatives: 12

Speedup: 0.8×

• 49.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{+248}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}} + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t \cdot t}{z}} + \frac{\frac{x}{y} \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))))
   (if (<= t_1 4e+248)
     (+ (/ (/ z t) (/ t z)) t_1)
     (+ (/ z (/ (* t t) z)) (/ (* (/ x y) x) y)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if (t_1 <= 4e+248) {
		tmp = ((z / t) / (t / z)) + t_1;
	} else {
		tmp = (z / ((t * t) / z)) + (((x / y) * x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * x) / (y * y)
    if (t_1 <= 4d+248) then
        tmp = ((z / t) / (t / z)) + t_1
    else
        tmp = (z / ((t * t) / z)) + (((x / y) * x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if (t_1 <= 4e+248) {
		tmp = ((z / t) / (t / z)) + t_1;
	} else {
		tmp = (z / ((t * t) / z)) + (((x / y) * x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * x) / (y * y)
	tmp = 0
	if t_1 <= 4e+248:
		tmp = ((z / t) / (t / z)) + t_1
	else:
		tmp = (z / ((t * t) / z)) + (((x / y) * x) / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) / Float64(y * y))
	tmp = 0.0
	if (t_1 <= 4e+248)
		tmp = Float64(Float64(Float64(z / t) / Float64(t / z)) + t_1);
	else
		tmp = Float64(Float64(z / Float64(Float64(t * t) / z)) + Float64(Float64(Float64(x / y) * x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * x) / (y * y);
	tmp = 0.0;
	if (t_1 <= 4e+248)
		tmp = ((z / t) / (t / z)) + t_1;
	else
		tmp = (z / ((t * t) / z)) + (((x / y) * x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e+248], N[(N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(z / N[(N[(t * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x / y), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 4.00000000000000018e248

   1. Initial program 67.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. clear-num N/A

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

      6. un-div-inv N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 94.7

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

   4. Applied rewrites 94.7%

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

   if 4.00000000000000018e248 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 56.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 63.7

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

   4. Applied rewrites 63.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 95.8

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

   6. Applied rewrites 95.8%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 4 \cdot 10^{+248}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}} + \frac{x \cdot x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t \cdot t}{z}} + \frac{\frac{x}{y} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+248}:\\ \;\;\;\;\frac{\frac{z}{t} \cdot z}{t} + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t \cdot t} \cdot z + \frac{\frac{x}{y} \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))))
   (if (<= t_1 0.0)
     (/ (/ z t) (/ t z))
     (if (<= t_1 4e+248)
       (+ (/ (* (/ z t) z) t) t_1)
       (+ (* (/ z (* t t)) z) (/ (* (/ x y) x) y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if (t_1 <= 0.0) {
		tmp = (z / t) / (t / z);
	} else if (t_1 <= 4e+248) {
		tmp = (((z / t) * z) / t) + t_1;
	} else {
		tmp = ((z / (t * t)) * z) + (((x / y) * x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * x) / (y * y)
    if (t_1 <= 0.0d0) then
        tmp = (z / t) / (t / z)
    else if (t_1 <= 4d+248) then
        tmp = (((z / t) * z) / t) + t_1
    else
        tmp = ((z / (t * t)) * z) + (((x / y) * x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if (t_1 <= 0.0) {
		tmp = (z / t) / (t / z);
	} else if (t_1 <= 4e+248) {
		tmp = (((z / t) * z) / t) + t_1;
	} else {
		tmp = ((z / (t * t)) * z) + (((x / y) * x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * x) / (y * y)
	tmp = 0
	if t_1 <= 0.0:
		tmp = (z / t) / (t / z)
	elif t_1 <= 4e+248:
		tmp = (((z / t) * z) / t) + t_1
	else:
		tmp = ((z / (t * t)) * z) + (((x / y) * x) / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) / Float64(y * y))
	tmp = 0.0
	if (t_1 <= 0.0)
		tmp = Float64(Float64(z / t) / Float64(t / z));
	elseif (t_1 <= 4e+248)
		tmp = Float64(Float64(Float64(Float64(z / t) * z) / t) + t_1);
	else
		tmp = Float64(Float64(Float64(z / Float64(t * t)) * z) + Float64(Float64(Float64(x / y) * x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * x) / (y * y);
	tmp = 0.0;
	if (t_1 <= 0.0)
		tmp = (z / t) / (t / z);
	elseif (t_1 <= 4e+248)
		tmp = (((z / t) * z) / t) + t_1;
	else
		tmp = ((z / (t * t)) * z) + (((x / y) * x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.0], N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+248], N[(N[(N[(N[(z / t), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] + N[(N[(N[(x / y), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 65.8%

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

   3. Taylor expanded in t around 0

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

      1. unpow2 N/A

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

      2. unpow2 N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 92.7

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

   5. Applied rewrites 92.7%

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

   7. Applied rewrites 92.9%

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

   if 0.0 < (/.f64 (*.f64 x x) (*.f64 y y)) < 4.00000000000000018e248

   1. Initial program 71.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 96.4

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

   4. Applied rewrites 96.4%

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

   if 4.00000000000000018e248 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 56.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 63.7

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

   4. Applied rewrites 63.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 95.8

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

   6. Applied rewrites 95.8%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. frac-2neg N/A

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

      4. associate-/r/ N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-neg.f64 95.7

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

   8. Applied rewrites 95.7%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 0:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{x \cdot x}{y \cdot y} \leq 4 \cdot 10^{+248}:\\ \;\;\;\;\frac{\frac{z}{t} \cdot z}{t} + \frac{x \cdot x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t \cdot t} \cdot z + \frac{\frac{x}{y} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 10^{+304}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t} \cdot z}{t} + \frac{x \cdot x}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 1e+304)
     (+ (* (/ x y) (/ x y)) t_1)
     (if (<= t_1 INFINITY)
       (* (/ z t) (/ z t))
       (+ (/ (* (/ 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 <= 1e+304) {
		tmp = ((x / y) * (x / y)) + t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (z / t) * (z / t);
	} else {
		tmp = (((z / t) * z) / t) + ((x * x) / (y * y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 1e+304) {
		tmp = ((x / y) * (x / y)) + t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (z / t) * (z / t);
	} else {
		tmp = (((z / t) * z) / t) + ((x * x) / (y * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * z) / (t * t)
	tmp = 0
	if t_1 <= 1e+304:
		tmp = ((x / y) * (x / y)) + t_1
	elif t_1 <= math.inf:
		tmp = (z / t) * (z / t)
	else:
		tmp = (((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 <= 1e+304)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + t_1);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(z / t) * Float64(z / t));
	else
		tmp = Float64(Float64(Float64(Float64(z / t) * z) / t) + Float64(Float64(x * x) / Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * z) / (t * t);
	tmp = 0.0;
	if (t_1 <= 1e+304)
		tmp = ((x / y) * (x / y)) + t_1;
	elseif (t_1 <= Inf)
		tmp = (z / t) * (z / t);
	else
		tmp = (((z / t) * z) / t) + ((x * x) / (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+304], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(z / t), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision] + N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 9.9999999999999994e303

   1. Initial program 70.6%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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 95.7

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

   4. Applied rewrites 95.7%

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

   if 9.9999999999999994e303 < (/.f64 (*.f64 z z) (*.f64 t t)) < +inf.0

   1. Initial program 76.8%

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

   3. Taylor expanded in t around 0

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

      1. unpow2 N/A

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

      2. unpow2 N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 95.8

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

   5. Applied rewrites 95.8%

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

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

   1. Initial program 0.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 77.0

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

   4. Applied rewrites 77.0%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 10^{+304}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + \frac{z \cdot z}{t \cdot t}\\ \mathbf{elif}\;\frac{z \cdot z}{t \cdot t} \leq \infty:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t} \cdot z}{t} + \frac{x \cdot x}{y \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 10^{-203}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{elif}\;t\_1 \leq 10^{+50}:\\ \;\;\;\;\frac{z}{t \cdot t} \cdot z + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))))
   (if (<= t_1 1e-203)
     (/ (/ z t) (/ t z))
     (if (<= t_1 1e+50) (+ (* (/ z (* t t)) z) t_1) (* (/ (/ x y) y) x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if (t_1 <= 1e-203) {
		tmp = (z / t) / (t / z);
	} else if (t_1 <= 1e+50) {
		tmp = ((z / (t * t)) * z) + t_1;
	} else {
		tmp = ((x / y) / y) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * x) / (y * y)
    if (t_1 <= 1d-203) then
        tmp = (z / t) / (t / z)
    else if (t_1 <= 1d+50) then
        tmp = ((z / (t * t)) * z) + t_1
    else
        tmp = ((x / y) / y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if (t_1 <= 1e-203) {
		tmp = (z / t) / (t / z);
	} else if (t_1 <= 1e+50) {
		tmp = ((z / (t * t)) * z) + t_1;
	} else {
		tmp = ((x / y) / y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * x) / (y * y)
	tmp = 0
	if t_1 <= 1e-203:
		tmp = (z / t) / (t / z)
	elif t_1 <= 1e+50:
		tmp = ((z / (t * t)) * z) + t_1
	else:
		tmp = ((x / y) / y) * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) / Float64(y * y))
	tmp = 0.0
	if (t_1 <= 1e-203)
		tmp = Float64(Float64(z / t) / Float64(t / z));
	elseif (t_1 <= 1e+50)
		tmp = Float64(Float64(Float64(z / Float64(t * t)) * z) + t_1);
	else
		tmp = Float64(Float64(Float64(x / y) / y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * x) / (y * y);
	tmp = 0.0;
	if (t_1 <= 1e-203)
		tmp = (z / t) / (t / z);
	elseif (t_1 <= 1e+50)
		tmp = ((z / (t * t)) * z) + t_1;
	else
		tmp = ((x / y) / y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e-203], N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+50], N[(N[(N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 1e-203

   1. Initial program 64.4%

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

   3. Taylor expanded in t around 0

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

      1. unpow2 N/A

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

      2. unpow2 N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 92.2

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

   5. Applied rewrites 92.2%

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

   7. Applied rewrites 92.3%

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

   if 1e-203 < (/.f64 (*.f64 x x) (*.f64 y y)) < 1.0000000000000001e50

   1. Initial program 89.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. clear-num N/A

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

      6. un-div-inv N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 97.2

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

   4. Applied rewrites 97.2%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*l/ N/A

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

      6. lift-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. associate-/r/ N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. lower-*.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. lower-neg.f64 93.5

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

   6. Applied rewrites 93.5%

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

   if 1.0000000000000001e50 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 56.3%

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

   3. Taylor expanded in t around inf

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 77.5

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

   5. Applied rewrites 77.5%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 10^{-203}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{x \cdot x}{y \cdot y} \leq 10^{+50}:\\ \;\;\;\;\frac{z}{t \cdot t} \cdot z + \frac{x \cdot x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 10^{-203}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{elif}\;t\_1 \leq 10^{+50}:\\ \;\;\;\;\frac{z \cdot z}{t \cdot t} + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))))
   (if (<= t_1 1e-203)
     (/ (/ z t) (/ t z))
     (if (<= t_1 1e+50) (+ (/ (* z z) (* t t)) t_1) (* (/ (/ x y) y) x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if (t_1 <= 1e-203) {
		tmp = (z / t) / (t / z);
	} else if (t_1 <= 1e+50) {
		tmp = ((z * z) / (t * t)) + t_1;
	} else {
		tmp = ((x / y) / y) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * x) / (y * y)
    if (t_1 <= 1d-203) then
        tmp = (z / t) / (t / z)
    else if (t_1 <= 1d+50) then
        tmp = ((z * z) / (t * t)) + t_1
    else
        tmp = ((x / y) / y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if (t_1 <= 1e-203) {
		tmp = (z / t) / (t / z);
	} else if (t_1 <= 1e+50) {
		tmp = ((z * z) / (t * t)) + t_1;
	} else {
		tmp = ((x / y) / y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * x) / (y * y)
	tmp = 0
	if t_1 <= 1e-203:
		tmp = (z / t) / (t / z)
	elif t_1 <= 1e+50:
		tmp = ((z * z) / (t * t)) + t_1
	else:
		tmp = ((x / y) / y) * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) / Float64(y * y))
	tmp = 0.0
	if (t_1 <= 1e-203)
		tmp = Float64(Float64(z / t) / Float64(t / z));
	elseif (t_1 <= 1e+50)
		tmp = Float64(Float64(Float64(z * z) / Float64(t * t)) + t_1);
	else
		tmp = Float64(Float64(Float64(x / y) / y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * x) / (y * y);
	tmp = 0.0;
	if (t_1 <= 1e-203)
		tmp = (z / t) / (t / z);
	elseif (t_1 <= 1e+50)
		tmp = ((z * z) / (t * t)) + t_1;
	else
		tmp = ((x / y) / y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e-203], N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+50], N[(N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 1e-203

   1. Initial program 64.4%

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

   3. Taylor expanded in t around 0

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

      1. unpow2 N/A

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

      2. unpow2 N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 92.2

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

   5. Applied rewrites 92.2%

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

   7. Applied rewrites 92.3%

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

   if 1e-203 < (/.f64 (*.f64 x x) (*.f64 y y)) < 1.0000000000000001e50

   1. Initial program 89.7%

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

   if 1.0000000000000001e50 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 56.3%

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

   3. Taylor expanded in t around inf

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 77.5

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

   5. Applied rewrites 77.5%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 10^{-203}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{x \cdot x}{y \cdot y} \leq 10^{+50}:\\ \;\;\;\;\frac{z \cdot z}{t \cdot t} + \frac{x \cdot x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{+248}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}} + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t \cdot t} \cdot z + \frac{\frac{x}{y} \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))))
   (if (<= t_1 4e+248)
     (+ (/ (/ z t) (/ t z)) t_1)
     (+ (* (/ z (* t t)) z) (/ (* (/ x y) x) y)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if (t_1 <= 4e+248) {
		tmp = ((z / t) / (t / z)) + t_1;
	} else {
		tmp = ((z / (t * t)) * z) + (((x / y) * x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * x) / (y * y)
    if (t_1 <= 4d+248) then
        tmp = ((z / t) / (t / z)) + t_1
    else
        tmp = ((z / (t * t)) * z) + (((x / y) * x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if (t_1 <= 4e+248) {
		tmp = ((z / t) / (t / z)) + t_1;
	} else {
		tmp = ((z / (t * t)) * z) + (((x / y) * x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * x) / (y * y)
	tmp = 0
	if t_1 <= 4e+248:
		tmp = ((z / t) / (t / z)) + t_1
	else:
		tmp = ((z / (t * t)) * z) + (((x / y) * x) / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) / Float64(y * y))
	tmp = 0.0
	if (t_1 <= 4e+248)
		tmp = Float64(Float64(Float64(z / t) / Float64(t / z)) + t_1);
	else
		tmp = Float64(Float64(Float64(z / Float64(t * t)) * z) + Float64(Float64(Float64(x / y) * x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * x) / (y * y);
	tmp = 0.0;
	if (t_1 <= 4e+248)
		tmp = ((z / t) / (t / z)) + t_1;
	else
		tmp = ((z / (t * t)) * z) + (((x / y) * x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e+248], N[(N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] + N[(N[(N[(x / y), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 4.00000000000000018e248

   1. Initial program 67.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. clear-num N/A

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

      6. un-div-inv N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 94.7

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

   4. Applied rewrites 94.7%

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

   if 4.00000000000000018e248 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 56.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 63.7

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

   4. Applied rewrites 63.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 95.8

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

   6. Applied rewrites 95.8%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. frac-2neg N/A

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

      4. associate-/r/ N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-neg.f64 95.7

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

   8. Applied rewrites 95.7%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 4 \cdot 10^{+248}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}} + \frac{x \cdot x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t \cdot t} \cdot z + \frac{\frac{x}{y} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 10^{+304}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 1e+304) (+ (* (/ x y) (/ x y)) t_1) (/ (/ z t) (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 1e+304) {
		tmp = ((x / y) * (x / y)) + t_1;
	} else {
		tmp = (z / t) / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * z) / (t * t)
    if (t_1 <= 1d+304) then
        tmp = ((x / y) * (x / y)) + t_1
    else
        tmp = (z / t) / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 1e+304) {
		tmp = ((x / y) * (x / y)) + t_1;
	} else {
		tmp = (z / t) / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * z) / (t * t)
	tmp = 0
	if t_1 <= 1e+304:
		tmp = ((x / y) * (x / y)) + t_1
	else:
		tmp = (z / t) / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * z) / Float64(t * t))
	tmp = 0.0
	if (t_1 <= 1e+304)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + t_1);
	else
		tmp = Float64(Float64(z / t) / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * z) / (t * t);
	tmp = 0.0;
	if (t_1 <= 1e+304)
		tmp = ((x / y) * (x / y)) + t_1;
	else
		tmp = (z / t) / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+304], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 9.9999999999999994e303

   1. Initial program 70.6%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   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 95.7

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

   4. Applied rewrites 95.7%

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

   if 9.9999999999999994e303 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 54.5%

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

   3. Taylor expanded in t around 0

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

      1. unpow2 N/A

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

      2. unpow2 N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 84.5

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

   5. Applied rewrites 84.5%

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

   7. Applied rewrites 84.6%

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

Alternative 8: 80.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 2 \cdot 10^{-41}:\\ \;\;\;\;\frac{\frac{x}{y}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 2e-41) (* (/ (/ x y) y) x) (/ (/ z t) (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 2e-41) {
		tmp = ((x / y) / y) * x;
	} else {
		tmp = (z / t) / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * z) / (t * t)) <= 2d-41) then
        tmp = ((x / y) / y) * x
    else
        tmp = (z / t) / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 2e-41) {
		tmp = ((x / y) / y) * x;
	} else {
		tmp = (z / t) / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * z) / (t * t)) <= 2e-41:
		tmp = ((x / y) / y) * x
	else:
		tmp = (z / t) / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(z * z) / Float64(t * t)) <= 2e-41)
		tmp = Float64(Float64(Float64(x / y) / y) * x);
	else
		tmp = Float64(Float64(z / t) / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * z) / (t * t)) <= 2e-41)
		tmp = ((x / y) / y) * x;
	else
		tmp = (z / t) / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision], 2e-41], N[(N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision] * x), $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)) < 2.00000000000000001e-41

   1. Initial program 71.2%

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

   3. Taylor expanded in t around inf

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 83.5

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

   5. Applied rewrites 83.5%

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

   if 2.00000000000000001e-41 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 56.6%

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

   3. Taylor expanded in t around 0

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

      1. unpow2 N/A

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

      2. unpow2 N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 81.8

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

   5. Applied rewrites 81.8%

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

   7. Applied rewrites 81.9%

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

Alternative 9: 80.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 2 \cdot 10^{-41}:\\ \;\;\;\;\frac{\frac{x}{y}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 2e-41) (* (/ (/ x y) y) x) (* (/ z t) (/ z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 2e-41) {
		tmp = ((x / y) / y) * x;
	} else {
		tmp = (z / t) * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * z) / (t * t)) <= 2d-41) then
        tmp = ((x / y) / y) * x
    else
        tmp = (z / t) * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 2e-41) {
		tmp = ((x / y) / y) * x;
	} else {
		tmp = (z / t) * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * z) / (t * t)) <= 2e-41:
		tmp = ((x / y) / y) * x
	else:
		tmp = (z / t) * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(z * z) / Float64(t * t)) <= 2e-41)
		tmp = Float64(Float64(Float64(x / y) / y) * x);
	else
		tmp = Float64(Float64(z / t) * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * z) / (t * t)) <= 2e-41)
		tmp = ((x / y) / y) * x;
	else
		tmp = (z / t) * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision], 2e-41], N[(N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 2.00000000000000001e-41

   1. Initial program 71.2%

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

   3. Taylor expanded in t around inf

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 83.5

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

   5. Applied rewrites 83.5%

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

   if 2.00000000000000001e-41 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 56.6%

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

   3. Taylor expanded in t around 0

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

      1. unpow2 N/A

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

      2. unpow2 N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 81.8

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

   5. Applied rewrites 81.8%

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

Alternative 10: 59.6% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 62.8%

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

3. Taylor expanded in t around 0

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

   1. unpow2 N/A

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

   2. unpow2 N/A

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

   3. times-frac N/A

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

   4. lower-*.f64 N/A

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

   5. lower-/.f64 N/A

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

   6. lower-/.f64 60.0

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

5. Applied rewrites 60.0%

   \[\leadsto \color{blue}{\frac{z}{t} \cdot \frac{z}{t}} \]
6. Add Preprocessing

Alternative 11: 52.7% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

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 * t)) * z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 62.8%

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

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

   6. un-div-inv N/A

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

   7. lower-/.f64 N/A

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

   8. lower-/.f64 N/A

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

   9. lower-/.f64 80.1

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

4. Applied rewrites 80.1%

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

5. Taylor expanded in t around 0

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

   1. *-lft-identity N/A

      \[\leadsto \frac{\color{blue}{1 \cdot {z}^{2}}}{{t}^{2}} \]

   2. associate-*l/ N/A

      \[\leadsto \color{blue}{\frac{1}{{t}^{2}} \cdot {z}^{2}} \]

   3. unpow2 N/A

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

   4. associate-*r* N/A

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

   5. lower-*.f64 N/A

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

   6. associate-*l/ N/A

      \[\leadsto \color{blue}{\frac{1 \cdot z}{{t}^{2}}} \cdot z \]

   7. *-lft-identity N/A

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

   8. unpow2 N/A

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

   9. associate-/r* N/A

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

   10. lower-/.f64 N/A

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

   11. lower-/.f64 56.4

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

7. Applied rewrites 56.4%

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

9. Applied rewrites 51.2%

   \[\leadsto \frac{z}{t \cdot t} \cdot z \]
10. Add Preprocessing

Alternative 12: 48.7% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 62.8%

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

3. Taylor expanded in t around 0

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

   1. unpow2 N/A

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

   2. unpow2 N/A

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

   3. times-frac N/A

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

   4. lower-*.f64 N/A

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

   5. lower-/.f64 N/A

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

   6. lower-/.f64 60.0

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

5. Applied rewrites 60.0%

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

7. Applied rewrites 47.8%

   \[\leadsto \frac{z \cdot z}{\color{blue}{t \cdot t}} \]
8. Add Preprocessing

Developer Target 1: 99.7% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024276 
(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))))