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

Percentage Accurate: 66.7% → 99.6%

Time: 8.6s

Alternatives: 10

Speedup: 0.8×

• 48.5% 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: 99.6% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 64.7%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. times-frac N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 N/A

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

   9. lower-/.f64 81.5

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

   10. lift-/.f64 N/A

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

   11. lift-*.f64 N/A

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

   12. lift-*.f64 N/A

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

   13. times-frac N/A

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

   14. pow2 N/A

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

   15. lower-pow.f64 N/A

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

   16. lower-/.f64 99.7

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

4. Applied rewrites 99.7%

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

   1. lift-pow.f64 N/A

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

   2. pow2 N/A

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

   3. lift-*.f64 99.7

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

6. Applied rewrites 99.7%

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

Alternative 2: 85.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 10^{-265} \lor \neg \left(t\_1 \leq \infty\right):\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + z \cdot \frac{z}{t \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))))
   (if (or (<= t_1 1e-265) (not (<= t_1 INFINITY)))
     (* (/ z t) (/ z t))
     (+ t_1 (* z (/ z (* t t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if ((t_1 <= 1e-265) || !(t_1 <= ((double) INFINITY))) {
		tmp = (z / t) * (z / t);
	} else {
		tmp = t_1 + (z * (z / (t * t)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if ((t_1 <= 1e-265) || !(t_1 <= Double.POSITIVE_INFINITY)) {
		tmp = (z / t) * (z / t);
	} else {
		tmp = t_1 + (z * (z / (t * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * x) / (y * y)
	tmp = 0
	if (t_1 <= 1e-265) or not (t_1 <= math.inf):
		tmp = (z / t) * (z / t)
	else:
		tmp = t_1 + (z * (z / (t * t)))
	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-265) || !(t_1 <= Inf))
		tmp = Float64(Float64(z / t) * Float64(z / t));
	else
		tmp = Float64(t_1 + Float64(z * Float64(z / Float64(t * t))));
	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-265) || ~((t_1 <= Inf)))
		tmp = (z / t) * (z / t);
	else
		tmp = t_1 + (z * (z / (t * t)));
	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[Or[LessEqual[t$95$1, 1e-265], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(z * N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 9.99999999999999985e-266 or +inf.0 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 53.6%

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

   3. Taylor expanded in x around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 77.7

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

   5. Applied rewrites 77.7%

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

   7. Applied rewrites 86.9%

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

   if 9.99999999999999985e-266 < (/.f64 (*.f64 x x) (*.f64 y y)) < +inf.0

   1. Initial program 74.3%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. Add Preprocessing
   3. 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. sqr-neg-rev N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. distribute-frac-neg N/A

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

      8. frac-2neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. frac-2neg-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lift-*.f64 N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. lower-neg.f64 84.7

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

   4. Applied rewrites 84.7%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 10^{-265} \lor \neg \left(\frac{x \cdot x}{y \cdot y} \leq \infty\right):\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot x}{y \cdot y} + z \cdot \frac{z}{t \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{-125} \lor \neg \left(t\_1 \leq \infty\right):\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))))
   (if (or (<= t_1 4e-125) (not (<= t_1 INFINITY)))
     (* (/ z t) (/ z t))
     (+ (* x (/ x (* y y))) (/ (* z z) (* t t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if ((t_1 <= 4e-125) || !(t_1 <= ((double) INFINITY))) {
		tmp = (z / t) * (z / t);
	} else {
		tmp = (x * (x / (y * y))) + ((z * z) / (t * t));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if ((t_1 <= 4e-125) || !(t_1 <= Double.POSITIVE_INFINITY)) {
		tmp = (z / t) * (z / t);
	} else {
		tmp = (x * (x / (y * y))) + ((z * z) / (t * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * x) / (y * y)
	tmp = 0
	if (t_1 <= 4e-125) or not (t_1 <= math.inf):
		tmp = (z / t) * (z / t)
	else:
		tmp = (x * (x / (y * y))) + ((z * z) / (t * t))
	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-125) || !(t_1 <= Inf))
		tmp = Float64(Float64(z / t) * Float64(z / t));
	else
		tmp = Float64(Float64(x * Float64(x / Float64(y * y))) + Float64(Float64(z * z) / Float64(t * t)));
	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-125) || ~((t_1 <= Inf)))
		tmp = (z / t) * (z / t);
	else
		tmp = (x * (x / (y * y))) + ((z * z) / (t * t));
	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[Or[LessEqual[t$95$1, 4e-125], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 4.00000000000000005e-125 or +inf.0 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 54.3%

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

   3. Taylor expanded in x around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 77.2

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

   5. Applied rewrites 77.2%

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

   7. Applied rewrites 85.7%

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

   if 4.00000000000000005e-125 < (/.f64 (*.f64 x x) (*.f64 y y)) < +inf.0

   1. Initial program 75.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. sqr-neg-rev N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. frac-2neg N/A

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

      8. remove-double-neg N/A

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

      9. lower-/.f64 N/A

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

      10. lift-*.f64 N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. lower-neg.f64 79.0

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

   4. Applied rewrites 79.0%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 4 \cdot 10^{-125} \lor \neg \left(\frac{x \cdot x}{y \cdot y} \leq \infty\right):\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{-125} \lor \neg \left(t\_1 \leq \infty\right):\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{z \cdot z}{t \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))))
   (if (or (<= t_1 4e-125) (not (<= t_1 INFINITY)))
     (* (/ z t) (/ z t))
     (+ t_1 (/ (* z z) (* t t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if ((t_1 <= 4e-125) || !(t_1 <= ((double) INFINITY))) {
		tmp = (z / t) * (z / t);
	} else {
		tmp = t_1 + ((z * z) / (t * t));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double tmp;
	if ((t_1 <= 4e-125) || !(t_1 <= Double.POSITIVE_INFINITY)) {
		tmp = (z / t) * (z / t);
	} else {
		tmp = t_1 + ((z * z) / (t * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * x) / (y * y)
	tmp = 0
	if (t_1 <= 4e-125) or not (t_1 <= math.inf):
		tmp = (z / t) * (z / t)
	else:
		tmp = t_1 + ((z * z) / (t * t))
	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-125) || !(t_1 <= Inf))
		tmp = Float64(Float64(z / t) * Float64(z / t));
	else
		tmp = Float64(t_1 + Float64(Float64(z * z) / Float64(t * t)));
	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-125) || ~((t_1 <= Inf)))
		tmp = (z / t) * (z / t);
	else
		tmp = t_1 + ((z * z) / (t * t));
	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[Or[LessEqual[t$95$1, 4e-125], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 4.00000000000000005e-125 or +inf.0 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 54.3%

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

   3. Taylor expanded in x around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 77.2

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

   5. Applied rewrites 77.2%

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

   7. Applied rewrites 85.7%

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

   if 4.00000000000000005e-125 < (/.f64 (*.f64 x x) (*.f64 y y)) < +inf.0

   1. Initial program 75.3%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 4 \cdot 10^{-125} \lor \neg \left(\frac{x \cdot x}{y \cdot y} \leq \infty\right):\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, x \cdot \frac{x}{y \cdot y}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{z}{t}}{t}, z, \frac{\frac{x}{y}}{y} \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* x x) (* y y)) 1e+82)
   (fma (/ z t) (/ z t) (* x (/ x (* y y))))
   (fma (/ (/ z t) t) z (* (/ (/ x y) y) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * x) / (y * y)) <= 1e+82) {
		tmp = fma((z / t), (z / t), (x * (x / (y * y))));
	} else {
		tmp = fma(((z / t) / t), z, (((x / y) / y) * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x * x) / Float64(y * y)) <= 1e+82)
		tmp = fma(Float64(z / t), Float64(z / t), Float64(x * Float64(x / Float64(y * y))));
	else
		tmp = fma(Float64(Float64(z / t) / t), z, Float64(Float64(Float64(x / y) / y) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision], 1e+82], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision] + N[(x * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / t), $MachinePrecision] / t), $MachinePrecision] * z + N[(N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 9.9999999999999996e81

   1. Initial program 72.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. times-frac N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 96.5

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

      10. lift-/.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. times-frac N/A

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

      14. pow2 N/A

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

      15. lower-pow.f64 N/A

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

      16. lower-/.f64 99.5

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

   4. Applied rewrites 99.5%

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

      1. lift-pow.f64 N/A

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

      2. pow2 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. frac-times N/A

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

      6. sqr-neg-rev N/A

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

      7. lift-*.f64 N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. sqr-neg-rev N/A

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

      13. distribute-lft-neg-out N/A

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

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

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

      15. lift-*.f64 N/A

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

      16. frac-2neg-rev N/A

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

      17. lower-/.f64 N/A

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

      18. lift-*.f64 N/A

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

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

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

      20. lower-*.f64 N/A

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

      21. lower-neg.f64 97.4

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

   6. Applied rewrites 97.4%

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

   if 9.9999999999999996e81 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 57.3%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. unpow2 N/A

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

      3. associate-/l* N/A

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

      4. unpow2 N/A

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

      5. associate-*l/ N/A

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

      6. associate-/l* N/A

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

      7. unpow2 N/A

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

      8. lower-fma.f64 N/A

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

      9. unpow2 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. unpow2 N/A

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

      14. associate-*l/ N/A

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

      15. lower-*.f64 N/A

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

      16. unpow2 N/A

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

      17. associate-/r* N/A

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

      18. lower-/.f64 N/A

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

      19. lower-/.f64 92.8

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

   5. Applied rewrites 92.8%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, x \cdot \frac{x}{y \cdot y}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{z}{t}}{t}, z, \frac{\frac{x}{y}}{y} \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{+159}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, x \cdot \frac{x}{y \cdot y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 4e+159)
     (+ (* (/ x y) (/ x y)) t_1)
     (fma (/ z t) (/ z t) (* x (/ x (* y y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 4e+159) {
		tmp = ((x / y) * (x / y)) + t_1;
	} else {
		tmp = fma((z / t), (z / t), (x * (x / (y * y))));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * z) / Float64(t * t))
	tmp = 0.0
	if (t_1 <= 4e+159)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + t_1);
	else
		tmp = fma(Float64(z / t), Float64(z / t), Float64(x * Float64(x / Float64(y * y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e+159], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision] + N[(x * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 3.9999999999999997e159

   1. Initial program 74.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. 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 95.5

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

   4. Applied rewrites 95.5%

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

   if 3.9999999999999997e159 < (/.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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. times-frac N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 84.5

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

      10. lift-/.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. times-frac N/A

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

      14. pow2 N/A

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

      15. lower-pow.f64 N/A

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

      16. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-pow.f64 N/A

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

      2. pow2 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. frac-times N/A

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

      6. sqr-neg-rev N/A

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

      7. lift-*.f64 N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. sqr-neg-rev N/A

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

      13. distribute-lft-neg-out N/A

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

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

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

      15. lift-*.f64 N/A

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

      16. frac-2neg-rev N/A

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

      17. lower-/.f64 N/A

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

      18. lift-*.f64 N/A

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

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

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

      20. lower-*.f64 N/A

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

      21. lower-neg.f64 92.4

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

   6. Applied rewrites 92.4%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 4 \cdot 10^{+159}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + \frac{z \cdot z}{t \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, x \cdot \frac{x}{y \cdot y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 90.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 2.5 \cdot 10^{+228}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, \frac{x \cdot x}{y \cdot y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 2.5e+228)
     (+ (* (/ x y) (/ x y)) t_1)
     (fma (/ z t) (/ z t) (/ (* x x) (* y y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 2.5e+228) {
		tmp = ((x / y) * (x / y)) + t_1;
	} else {
		tmp = fma((z / t), (z / t), ((x * x) / (y * y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * z) / Float64(t * t))
	tmp = 0.0
	if (t_1 <= 2.5e+228)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + t_1);
	else
		tmp = fma(Float64(z / t), Float64(z / t), Float64(Float64(x * x) / Float64(y * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2.5e+228], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision] + N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 2.5e228

   1. Initial program 74.4%

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

      1. lift-/.f64 N/A

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

      2. 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 95.6

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

   4. Applied rewrites 95.6%

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

   if 2.5e228 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 54.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. times-frac N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 85.4

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

      10. lift-/.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. times-frac N/A

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

      14. pow2 N/A

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

      15. lower-pow.f64 N/A

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

      16. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-pow.f64 N/A

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

      2. pow2 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. frac-times N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-/.f64 85.4

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

   6. Applied rewrites 85.4%

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

Alternative 8: 87.4% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 72.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. times-frac N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 90.8

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

      10. lift-/.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. times-frac N/A

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

      14. pow2 N/A

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

      15. lower-pow.f64 N/A

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

      16. lower-/.f64 99.7

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

   4. Applied rewrites 99.7%

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

      1. lift-pow.f64 N/A

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

      2. pow2 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. frac-times N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-/.f64 90.8

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

   6. Applied rewrites 90.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 44.6

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

   5. Applied rewrites 44.6%

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

   7. Applied rewrites 59.1%

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

Alternative 9: 59.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 9 \cdot 10^{+61}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t \cdot t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 9e+61) (* (/ z t) (/ z t)) (* (/ z (* t t)) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 9e+61) {
		tmp = (z / t) * (z / t);
	} else {
		tmp = (z / (t * t)) * z;
	}
	return tmp;
}

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
    real(8) :: tmp
    if (x <= 9d+61) then
        tmp = (z / t) * (z / t)
    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 (x <= 9e+61) {
		tmp = (z / t) * (z / t);
	} else {
		tmp = (z / (t * t)) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 9e+61:
		tmp = (z / t) * (z / t)
	else:
		tmp = (z / (t * t)) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 9e+61)
		tmp = Float64(Float64(z / t) * Float64(z / t));
	else
		tmp = Float64(Float64(z / Float64(t * t)) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 9e+61)
		tmp = (z / t) * (z / t);
	else
		tmp = (z / (t * t)) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 9e+61], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 9e61

   1. Initial program 63.5%

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

   3. Taylor expanded in x around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 59.3

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

   5. Applied rewrites 59.3%

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

   7. Applied rewrites 63.6%

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

   if 9e61 < x

   1. Initial program 70.0%

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

   3. Taylor expanded in x around 0

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

      1. unpow2 N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 42.9

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

   5. Applied rewrites 42.9%

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

   7. Applied rewrites 40.7%

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

Alternative 10: 52.6% 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

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 = (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 64.7%

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

3. Taylor expanded in x around 0

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

   1. unpow2 N/A

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

   2. associate-*l/ N/A

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

   3. lower-*.f64 N/A

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

   4. unpow2 N/A

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

   5. associate-/r* N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 56.3

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

5. Applied rewrites 56.3%

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

7. Applied rewrites 51.1%

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

Developer Target 1: 99.6% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Fortran

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) ** 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 2024352 
(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))))