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

Percentage Accurate: 66.7% → 96.7%

Time: 8.4s

Alternatives: 11

Speedup: 1.0×

• 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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: 96.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 66.7%

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

3. Applied rewrites 88.9%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. associate-*l/ N/A

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

   5. pow2 N/A

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

   6. associate-/r* N/A

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

   7. lower-/.f64 N/A

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

   8. pow2 N/A

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

   9. associate-*l/ N/A

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

   10. lower-*.f64 N/A

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

   11. lift-/.f64 96.7

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

5. Applied rewrites 96.7%

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

Alternative 2: 96.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 66.7%

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

3. Applied rewrites 88.9%

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

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. associate-/r* N/A

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

   4. lower-/.f64 N/A

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

   5. lift-/.f64 96.5

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

5. Applied rewrites 96.5%

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

Alternative 3: 96.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 2 \cdot 10^{+283}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, \frac{x}{y \cdot y} \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \frac{z}{t \cdot t} \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* x x) (* y y)) 2e+283)
   (fma (/ z t) (/ z t) (* (/ x (* y y)) x))
   (fma (/ x y) (/ x y) (* (/ z (* t t)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * x) / (y * y)) <= 2e+283) {
		tmp = fma((z / t), (z / t), ((x / (y * y)) * x));
	} else {
		tmp = fma((x / y), (x / y), ((z / (t * t)) * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x * x) / Float64(y * y)) <= 2e+283)
		tmp = fma(Float64(z / t), Float64(z / t), Float64(Float64(x / Float64(y * y)) * x));
	else
		tmp = fma(Float64(x / y), Float64(x / y), Float64(Float64(z / Float64(t * t)) * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision], 2e+283], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision] + N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision] + N[(N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 1.99999999999999991e283

   1. Initial program 73.6%

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

   3. Applied rewrites 97.6%

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

   if 1.99999999999999991e283 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 58.7%

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

   3. Applied rewrites 95.4%

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

Alternative 4: 91.1% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 70.7%

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

   2. Taylor expanded in x around 0

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

      1. pow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. pow2 N/A

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

      6. lift-*.f64 75.5

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

   4. Applied rewrites 75.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. pow2 N/A

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

      4. frac-2neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(z\right)}{\mathsf{neg}\left({t}^{2}\right)} \cdot z \]

      5. frac-2neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)}{\mathsf{neg}\left(\left(\mathsf{neg}\left({t}^{2}\right)\right)\right)} \cdot z \]

      6. remove-double-neg N/A

         \[\leadsto \frac{z}{\mathsf{neg}\left(\left(\mathsf{neg}\left({t}^{2}\right)\right)\right)} \cdot z \]

      7. *-lft-identity N/A

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

      8. remove-double-neg N/A

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

      9. associate-*l/ N/A

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

      10. pow2 N/A

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

      11. associate-/r* N/A

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

      12. associate-*l/ N/A

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

      13. lower-/.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 88.1

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

   6. Applied rewrites 88.1%

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

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

   1. Initial program 64.6%

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

   3. Applied rewrites 92.7%

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

Alternative 5: 81.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-158}:\\ \;\;\;\;\left(\frac{1}{y} \cdot \frac{x}{y}\right) \cdot x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+154}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t \cdot t}, z, \frac{x}{y \cdot y} \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 7.5e-158)
   (* (* (/ 1.0 y) (/ x y)) x)
   (if (<= y 1.25e+154)
     (fma (/ z (* t t)) z (* (/ x (* y y)) x))
     (* (/ (/ z t) t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 7.5e-158) {
		tmp = ((1.0 / y) * (x / y)) * x;
	} else if (y <= 1.25e+154) {
		tmp = fma((z / (t * t)), z, ((x / (y * y)) * x));
	} else {
		tmp = ((z / t) / t) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 7.5e-158)
		tmp = Float64(Float64(Float64(1.0 / y) * Float64(x / y)) * x);
	elseif (y <= 1.25e+154)
		tmp = fma(Float64(z / Float64(t * t)), z, Float64(Float64(x / Float64(y * y)) * x));
	else
		tmp = Float64(Float64(Float64(z / t) / t) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 7.5e-158], N[(N[(N[(1.0 / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 1.25e+154], N[(N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision] * z + N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / t), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 7.5e-158

   1. Initial program 65.2%

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

   2. Taylor expanded in x around inf

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

      1. pow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. pow2 N/A

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

      6. lift-*.f64 56.4

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

   4. Applied rewrites 56.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. remove-double-neg N/A

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

      4. pow2 N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{{y}^{2}}\right)\right)\right)\right) \cdot x \]

      5. distribute-neg-frac2 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{x}{\mathsf{neg}\left({y}^{2}\right)}\right)\right) \cdot x \]

      6. *-lft-identity N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{1 \cdot x}{\mathsf{neg}\left({y}^{2}\right)}\right)\right) \cdot x \]

      7. distribute-neg-frac2 N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{1 \cdot x}{{y}^{2}}\right)\right)\right)\right) \cdot x \]

      8. pow2 N/A

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

      9. frac-times N/A

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

      10. lift-/.f64 N/A

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

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

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

      12. distribute-rgt-neg-out N/A

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

      13. remove-double-neg N/A

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

      14. lower-*.f64 N/A

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

      15. lift-/.f64 60.8

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

   6. Applied rewrites 60.8%

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

   if 7.5e-158 < y < 1.25000000000000001e154

   1. Initial program 76.5%

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

   3. Applied rewrites 88.7%

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

   if 1.25000000000000001e154 < y

   1. Initial program 54.0%

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

   2. Taylor expanded in x around 0

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

      1. pow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. pow2 N/A

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

      6. lift-*.f64 68.2

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

   4. Applied rewrites 68.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 79.6

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

   6. Applied rewrites 79.6%

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

Alternative 6: 81.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\frac{1}{t} \cdot z}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 2e+80)
     (* (/ x y) (/ x y))
     (if (<= t_1 INFINITY) (* (/ (* (/ 1.0 t) z) t) z) (* (/ (/ x y) y) x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 2e+80) {
		tmp = (x / y) * (x / y);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (((1.0 / t) * z) / t) * z;
	} else {
		tmp = ((x / y) / y) * x;
	}
	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 <= 2e+80) {
		tmp = (x / y) * (x / y);
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (((1.0 / t) * z) / t) * z;
	} else {
		tmp = ((x / y) / y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * z) / (t * t)
	tmp = 0
	if t_1 <= 2e+80:
		tmp = (x / y) * (x / y)
	elif t_1 <= math.inf:
		tmp = (((1.0 / t) * z) / t) * z
	else:
		tmp = ((x / y) / y) * x
	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+80)
		tmp = Float64(Float64(x / y) * Float64(x / y));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(Float64(Float64(1.0 / t) * z) / t) * z);
	else
		tmp = Float64(Float64(Float64(x / y) / y) * x);
	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+80)
		tmp = (x / y) * (x / y);
	elseif (t_1 <= Inf)
		tmp = (((1.0 / t) * z) / t) * z;
	else
		tmp = ((x / y) / y) * x;
	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+80], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(N[(1.0 / t), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 2e80

   1. Initial program 73.8%

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

   2. Taylor expanded in x around inf

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

      1. pow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. pow2 N/A

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

      6. lift-*.f64 69.3

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

   4. Applied rewrites 69.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. pow2 N/A

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

      5. pow2 N/A

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

      6. associate-/r* N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift-/.f64 84.7

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

   6. Applied rewrites 84.7%

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

   if 2e80 < (/.f64 (*.f64 z z) (*.f64 t t)) < +inf.0

   1. Initial program 78.7%

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

   2. Taylor expanded in x around 0

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

      1. pow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. pow2 N/A

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

      6. lift-*.f64 86.4

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

   4. Applied rewrites 86.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. pow2 N/A

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

      4. frac-2neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(z\right)}{\mathsf{neg}\left({t}^{2}\right)} \cdot z \]

      5. frac-2neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)}{\mathsf{neg}\left(\left(\mathsf{neg}\left({t}^{2}\right)\right)\right)} \cdot z \]

      6. remove-double-neg N/A

         \[\leadsto \frac{z}{\mathsf{neg}\left(\left(\mathsf{neg}\left({t}^{2}\right)\right)\right)} \cdot z \]

      7. *-lft-identity N/A

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

      8. remove-double-neg N/A

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

      9. associate-*l/ N/A

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

      10. pow2 N/A

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

      11. associate-/r* N/A

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

      12. associate-*l/ N/A

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

      13. lower-/.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 87.8

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

   6. Applied rewrites 87.8%

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

   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. Taylor expanded in x around inf

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

      1. pow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. pow2 N/A

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

      6. lift-*.f64 41.8

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

   4. Applied rewrites 41.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lift-/.f64 47.1

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

   6. Applied rewrites 47.1%

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

Alternative 7: 81.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\frac{z}{t}}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 2e+80)
     (* (/ x y) (/ x y))
     (if (<= t_1 INFINITY) (* (/ (/ z t) t) z) (* (/ (/ x y) y) x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 2e+80) {
		tmp = (x / y) * (x / y);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = ((z / t) / t) * z;
	} else {
		tmp = ((x / y) / y) * x;
	}
	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 <= 2e+80) {
		tmp = (x / y) * (x / y);
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = ((z / t) / t) * z;
	} else {
		tmp = ((x / y) / y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * z) / (t * t)
	tmp = 0
	if t_1 <= 2e+80:
		tmp = (x / y) * (x / y)
	elif t_1 <= math.inf:
		tmp = ((z / t) / t) * z
	else:
		tmp = ((x / y) / y) * x
	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+80)
		tmp = Float64(Float64(x / y) * Float64(x / y));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(Float64(z / t) / t) * z);
	else
		tmp = Float64(Float64(Float64(x / y) / y) * x);
	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+80)
		tmp = (x / y) * (x / y);
	elseif (t_1 <= Inf)
		tmp = ((z / t) / t) * z;
	else
		tmp = ((x / y) / y) * x;
	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+80], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(z / t), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 2e80

   1. Initial program 73.8%

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

   2. Taylor expanded in x around inf

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

      1. pow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. pow2 N/A

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

      6. lift-*.f64 69.3

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

   4. Applied rewrites 69.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. pow2 N/A

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

      5. pow2 N/A

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

      6. associate-/r* N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift-/.f64 84.7

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

   6. Applied rewrites 84.7%

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

   if 2e80 < (/.f64 (*.f64 z z) (*.f64 t t)) < +inf.0

   1. Initial program 78.7%

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

   2. Taylor expanded in x around 0

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

      1. pow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. pow2 N/A

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

      6. lift-*.f64 86.4

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

   4. Applied rewrites 86.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 87.9

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

   6. Applied rewrites 87.9%

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

   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. Taylor expanded in x around inf

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

      1. pow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. pow2 N/A

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

      6. lift-*.f64 41.8

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

   4. Applied rewrites 41.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lift-/.f64 47.1

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

   6. Applied rewrites 47.1%

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

Alternative 8: 80.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{z}{t \cdot t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 2e+80)
     (* (/ x y) (/ x y))
     (if (<= t_1 INFINITY) (* (/ z (* t t)) z) (* (/ (/ x y) y) x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 2e+80) {
		tmp = (x / y) * (x / y);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (z / (t * t)) * z;
	} else {
		tmp = ((x / y) / y) * x;
	}
	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 <= 2e+80) {
		tmp = (x / y) * (x / y);
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (z / (t * t)) * z;
	} else {
		tmp = ((x / y) / y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * z) / (t * t)
	tmp = 0
	if t_1 <= 2e+80:
		tmp = (x / y) * (x / y)
	elif t_1 <= math.inf:
		tmp = (z / (t * t)) * z
	else:
		tmp = ((x / y) / y) * x
	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+80)
		tmp = Float64(Float64(x / y) * Float64(x / y));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(z / Float64(t * t)) * z);
	else
		tmp = Float64(Float64(Float64(x / y) / y) * x);
	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+80)
		tmp = (x / y) * (x / y);
	elseif (t_1 <= Inf)
		tmp = (z / (t * t)) * z;
	else
		tmp = ((x / y) / y) * x;
	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+80], N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 2e80

   1. Initial program 73.8%

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

   2. Taylor expanded in x around inf

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

      1. pow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. pow2 N/A

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

      6. lift-*.f64 69.3

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

   4. Applied rewrites 69.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. pow2 N/A

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

      5. pow2 N/A

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

      6. associate-/r* N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift-/.f64 84.7

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

   6. Applied rewrites 84.7%

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

   if 2e80 < (/.f64 (*.f64 z z) (*.f64 t t)) < +inf.0

   1. Initial program 78.7%

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

   2. Taylor expanded in x around 0

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

      1. pow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. pow2 N/A

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

      6. lift-*.f64 86.4

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

   4. Applied rewrites 86.4%

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

   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. Taylor expanded in x around inf

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

      1. pow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. pow2 N/A

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

      6. lift-*.f64 41.8

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

   4. Applied rewrites 41.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lift-/.f64 47.1

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

   6. Applied rewrites 47.1%

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

Alternative 9: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ t_2 := \frac{x}{y} \cdot \frac{x}{y}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{z}{t \cdot t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))) (t_2 (* (/ x y) (/ x y))))
   (if (<= t_1 2e+80) 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 <= 2e+80) {
		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 <= 2e+80) {
		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 <= 2e+80:
		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 <= 2e+80)
		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 <= 2e+80)
		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, 2e+80], 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)) < 2e80 or +inf.0 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 58.5%

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

   2. Taylor expanded in x around inf

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

      1. pow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. pow2 N/A

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

      6. lift-*.f64 63.6

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

   4. Applied rewrites 63.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. pow2 N/A

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

      5. pow2 N/A

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

      6. associate-/r* N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift-/.f64 77.5

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

   6. Applied rewrites 77.5%

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

   if 2e80 < (/.f64 (*.f64 z z) (*.f64 t t)) < +inf.0

   1. Initial program 78.7%

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

   2. Taylor expanded in x around 0

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

      1. pow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. pow2 N/A

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

      6. lift-*.f64 86.4

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

   4. Applied rewrites 86.4%

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

Alternative 10: 70.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ t_2 := \frac{x}{y \cdot y} \cdot x\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{z}{t \cdot t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))) (t_2 (* (/ x (* y y)) x)))
   (if (<= t_1 2e+80) 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 <= 2e+80) {
		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 <= 2e+80) {
		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 <= 2e+80:
		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 <= 2e+80)
		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 <= 2e+80)
		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, 2e+80], 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)) < 2e80 or +inf.0 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 58.5%

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

   2. Taylor expanded in x around inf

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

      1. pow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. pow2 N/A

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

      6. lift-*.f64 63.6

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

   4. Applied rewrites 63.6%

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

   if 2e80 < (/.f64 (*.f64 z z) (*.f64 t t)) < +inf.0

   1. Initial program 78.7%

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

   2. Taylor expanded in x around 0

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

      1. pow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. pow2 N/A

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

      6. lift-*.f64 86.4

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

   4. Applied rewrites 86.4%

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

Alternative 11: 52.6% accurate, 2.2× 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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 66.7%

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

2. Taylor expanded in x around inf

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

   1. pow2 N/A

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

   2. associate-*l/ N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 N/A

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

   5. pow2 N/A

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

   6. lift-*.f64 52.6

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

4. Applied rewrites 52.6%

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

Reproduce

herbie shell --seed 2025130 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"
  :precision binary64
  (+ (/ (* x x) (* y y)) (/ (* z z) (* t t))))