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

Percentage Accurate: 66.7% → 96.3%

Time: 4.2s

Alternatives: 13

Speedup: 0.6×

• 48.7% 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: 96.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot x}{y \cdot y} \leq 10^{+270}:\\ \;\;\;\;\mathsf{fma}\left(-x, \frac{-x}{y \cdot y}, {\left(\frac{z}{t}\right)}^{2}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, \frac{-z}{t \cdot t}, {\left(\frac{x}{y}\right)}^{2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* x x) (* y y)) 1e+270)
   (fma (- x) (/ (- x) (* y y)) (pow (/ z t) 2.0))
   (fma (- z) (/ (- z) (* t t)) (pow (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * x) / (y * y)) <= 1e+270) {
		tmp = fma(-x, (-x / (y * y)), pow((z / t), 2.0));
	} else {
		tmp = fma(-z, (-z / (t * t)), pow((x / y), 2.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x * x) / Float64(y * y)) <= 1e+270)
		tmp = fma(Float64(-x), Float64(Float64(-x) / Float64(y * y)), (Float64(z / t) ^ 2.0));
	else
		tmp = fma(Float64(-z), Float64(Float64(-z) / Float64(t * t)), (Float64(x / y) ^ 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision], 1e+270], N[((-x) * N[((-x) / N[(y * y), $MachinePrecision]), $MachinePrecision] + N[Power[N[(z / t), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision], N[((-z) * N[((-z) / N[(t * t), $MachinePrecision]), $MachinePrecision] + N[Power[N[(x / y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 1e270

   1. Initial program 74.7%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. 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. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. sqr-neg-rev N/A

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

      9. pow2 N/A

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

      10. associate-/l* N/A

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

      11. pow2 N/A

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

      12. pow2 N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. pow2 N/A

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

      18. lift-*.f64 N/A

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

      19. pow2 N/A

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

      20. pow2 N/A

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

      21. times-frac N/A

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

      22. pow2 N/A

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

      23. lower-pow.f64 N/A

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

      24. lower-/.f64 97.8

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

   3. Applied rewrites 97.8%

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

   if 1e270 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 57.6%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. 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. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. +-commutative N/A

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

      9. sqr-neg-rev N/A

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

      10. pow2 N/A

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

      11. associate-/l* N/A

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

      12. pow2 N/A

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

      13. pow2 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-neg.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. lower-neg.f64 N/A

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

      18. pow2 N/A

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

      19. lift-*.f64 N/A

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

      20. pow2 N/A

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

      21. pow2 N/A

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

      22. times-frac N/A

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

      23. pow2 N/A

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

      24. lower-pow.f64 N/A

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

      25. lower-/.f64 94.8

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

   3. Applied rewrites 94.8%

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

Alternative 2: 95.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{+266}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-x, \frac{-x}{y \cdot y}, {\left(\frac{z}{t}\right)}^{2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 4e+266)
     (+ (* (/ x y) (/ x y)) t_1)
     (fma (- x) (/ (- x) (* y y)) (pow (/ z t) 2.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 4e+266) {
		tmp = ((x / y) * (x / y)) + t_1;
	} else {
		tmp = fma(-x, (-x / (y * y)), pow((z / t), 2.0));
	}
	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+266)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + t_1);
	else
		tmp = fma(Float64(-x), Float64(Float64(-x) / Float64(y * y)), (Float64(z / t) ^ 2.0));
	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+266], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[((-x) * N[((-x) / N[(y * y), $MachinePrecision]), $MachinePrecision] + N[Power[N[(z / t), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 4.0000000000000001e266

   1. Initial program 74.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      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 95.2

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

   3. Applied rewrites 95.2%

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

   if 4.0000000000000001e266 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 58.0%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. 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. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. sqr-neg-rev N/A

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

      9. pow2 N/A

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

      10. associate-/l* N/A

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

      11. pow2 N/A

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

      12. pow2 N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. pow2 N/A

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

      18. lift-*.f64 N/A

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

      19. pow2 N/A

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

      20. pow2 N/A

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

      21. times-frac N/A

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

      22. pow2 N/A

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

      23. lower-pow.f64 N/A

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

      24. lower-/.f64 95.1

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

   3. Applied rewrites 95.1%

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

Alternative 3: 92.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot \frac{z}{t}\\ t_2 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_2 \leq 4 \cdot 10^{+266}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot x}{y \cdot y} + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z t) (/ z t))) (t_2 (/ (* z z) (* t t))))
   (if (<= t_2 4e+266)
     (+ (* (/ x y) (/ x y)) t_2)
     (if (<= t_2 INFINITY) t_1 (+ (/ (* x x) (* y y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * (z / t);
	double t_2 = (z * z) / (t * t);
	double tmp;
	if (t_2 <= 4e+266) {
		tmp = ((x / y) * (x / y)) + t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = ((x * x) / (y * y)) + t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * (z / t);
	double t_2 = (z * z) / (t * t);
	double tmp;
	if (t_2 <= 4e+266) {
		tmp = ((x / y) * (x / y)) + t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = ((x * x) / (y * y)) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / t) * (z / t)
	t_2 = (z * z) / (t * t)
	tmp = 0
	if t_2 <= 4e+266:
		tmp = ((x / y) * (x / y)) + t_2
	elif t_2 <= math.inf:
		tmp = t_1
	else:
		tmp = ((x * x) / (y * y)) + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / t) * Float64(z / t))
	t_2 = Float64(Float64(z * z) / Float64(t * t))
	tmp = 0.0
	if (t_2 <= 4e+266)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + t_2);
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(x * x) / Float64(y * y)) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / t) * (z / t);
	t_2 = (z * z) / (t * t);
	tmp = 0.0;
	if (t_2 <= 4e+266)
		tmp = ((x / y) * (x / y)) + t_2;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = ((x * x) / (y * y)) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 4e+266], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$1, N[(N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 4.0000000000000001e266

   1. Initial program 74.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      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 95.2

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

   3. Applied rewrites 95.2%

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

   if 4.0000000000000001e266 < (/.f64 (*.f64 z z) (*.f64 t t)) < +inf.0

   1. Initial program 76.9%

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

   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. pow2 N/A

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

      3. times-frac N/A

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

      4. pow2 N/A

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

      5. lower-pow.f64 N/A

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

      6. lower-/.f64 93.3

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

   4. Applied rewrites 93.3%

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

      1. lift-pow.f64 N/A

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

      2. pow2 N/A

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

      3. lift-*.f64 93.3

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

   6. Applied rewrites 93.3%

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

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

   1. Initial program 0.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 79.4

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

   3. Applied rewrites 79.4%

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

Alternative 4: 84.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ t_2 := \frac{z}{t} \cdot \frac{z}{t}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-194}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1 + \left(-z\right) \cdot \frac{-z}{t \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))) (t_2 (* (/ z t) (/ z t))))
   (if (<= t_1 2e-194)
     t_2
     (if (<= t_1 INFINITY) (+ t_1 (* (- z) (/ (- z) (* t t)))) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double t_2 = (z / t) * (z / t);
	double tmp;
	if (t_1 <= 2e-194) {
		tmp = t_2;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1 + (-z * (-z / (t * t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double t_2 = (z / t) * (z / t);
	double tmp;
	if (t_1 <= 2e-194) {
		tmp = t_2;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1 + (-z * (-z / (t * t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * x) / (y * y)
	t_2 = (z / t) * (z / t)
	tmp = 0
	if t_1 <= 2e-194:
		tmp = t_2
	elif t_1 <= math.inf:
		tmp = t_1 + (-z * (-z / (t * t)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) / Float64(y * y))
	t_2 = Float64(Float64(z / t) * Float64(z / t))
	tmp = 0.0
	if (t_1 <= 2e-194)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = Float64(t_1 + Float64(Float64(-z) * Float64(Float64(-z) / Float64(t * t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * x) / (y * y);
	t_2 = (z / t) * (z / t);
	tmp = 0.0;
	if (t_1 <= 2e-194)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = t_1 + (-z * (-z / (t * t)));
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e-194], t$95$2, If[LessEqual[t$95$1, Infinity], N[(t$95$1 + N[((-z) * N[((-z) / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 2.00000000000000004e-194 or +inf.0 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 54.1%

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

   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. pow2 N/A

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

      3. times-frac N/A

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

      4. pow2 N/A

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

      5. lower-pow.f64 N/A

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

      6. lower-/.f64 82.6

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

   4. Applied rewrites 82.6%

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

      1. lift-pow.f64 N/A

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

      2. pow2 N/A

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

      3. lift-*.f64 82.6

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

   6. Applied rewrites 82.6%

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

   if 2.00000000000000004e-194 < (/.f64 (*.f64 x x) (*.f64 y y)) < +inf.0

   1. Initial program 78.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. sqr-neg-rev N/A

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

      5. pow2 N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. pow2 N/A

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

      12. lift-*.f64 87.0

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

   3. Applied rewrites 87.0%

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

Alternative 5: 78.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ t_2 := \frac{z}{t} \cdot \frac{z}{t}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+130}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\frac{\left(x \cdot x\right) \cdot t}{y}}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))) (t_2 (* (/ z t) (/ z t))))
   (if (<= t_1 2e+130)
     t_2
     (if (<= t_1 INFINITY) (/ (/ (* (* x x) t) y) (* t y)) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double t_2 = (z / t) * (z / t);
	double tmp;
	if (t_1 <= 2e+130) {
		tmp = t_2;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (((x * x) * t) / y) / (t * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double t_2 = (z / t) * (z / t);
	double tmp;
	if (t_1 <= 2e+130) {
		tmp = t_2;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (((x * x) * t) / y) / (t * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * x) / (y * y)
	t_2 = (z / t) * (z / t)
	tmp = 0
	if t_1 <= 2e+130:
		tmp = t_2
	elif t_1 <= math.inf:
		tmp = (((x * x) * t) / y) / (t * y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) / Float64(y * y))
	t_2 = Float64(Float64(z / t) * Float64(z / t))
	tmp = 0.0
	if (t_1 <= 2e+130)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(Float64(Float64(x * x) * t) / y) / Float64(t * y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * x) / (y * y);
	t_2 = (z / t) * (z / t);
	tmp = 0.0;
	if (t_1 <= 2e+130)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = (((x * x) * t) / y) / (t * y);
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+130], t$95$2, If[LessEqual[t$95$1, Infinity], N[(N[(N[(N[(x * x), $MachinePrecision] * t), $MachinePrecision] / y), $MachinePrecision] / N[(t * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 2.0000000000000001e130 or +inf.0 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 59.3%

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

   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. pow2 N/A

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

      3. times-frac N/A

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

      4. pow2 N/A

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

      5. lower-pow.f64 N/A

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

      6. lower-/.f64 76.8

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

   4. Applied rewrites 76.8%

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

      1. lift-pow.f64 N/A

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

      2. pow2 N/A

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

      3. lift-*.f64 76.8

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

   6. Applied rewrites 76.8%

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

   if 2.0000000000000001e130 < (/.f64 (*.f64 x x) (*.f64 y y)) < +inf.0

   1. Initial program 78.3%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. 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. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. sqr-neg-rev N/A

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

      9. pow2 N/A

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

      10. associate-/l* N/A

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

      11. pow2 N/A

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

      12. pow2 N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. pow2 N/A

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

      18. lift-*.f64 N/A

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

      19. pow2 N/A

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

      20. pow2 N/A

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

      21. times-frac N/A

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

      22. pow2 N/A

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

      23. lower-pow.f64 N/A

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

      24. lower-/.f64 93.6

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

   3. Applied rewrites 93.6%

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

   5. Applied rewrites 89.4%

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

   6. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. pow2 N/A

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

      5. lower-*.f64 81.1

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

   8. Applied rewrites 81.1%

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

Alternative 6: 77.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{y \cdot y}\\ t_2 := \frac{z}{t} \cdot \frac{z}{t}\\ \mathbf{if}\;t\_1 \leq 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\left(x \cdot x\right) \cdot t}{t \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x x) (* y y))) (t_2 (* (/ z t) (/ z t))))
   (if (<= t_1 1e+48)
     t_2
     (if (<= t_1 INFINITY) (/ (* (* x x) t) (* t (* y y))) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double t_2 = (z / t) * (z / t);
	double tmp;
	if (t_1 <= 1e+48) {
		tmp = t_2;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = ((x * x) * t) / (t * (y * y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * x) / (y * y);
	double t_2 = (z / t) * (z / t);
	double tmp;
	if (t_1 <= 1e+48) {
		tmp = t_2;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = ((x * x) * t) / (t * (y * y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * x) / (y * y)
	t_2 = (z / t) * (z / t)
	tmp = 0
	if t_1 <= 1e+48:
		tmp = t_2
	elif t_1 <= math.inf:
		tmp = ((x * x) * t) / (t * (y * y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) / Float64(y * y))
	t_2 = Float64(Float64(z / t) * Float64(z / t))
	tmp = 0.0
	if (t_1 <= 1e+48)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(Float64(x * x) * t) / Float64(t * Float64(y * y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * x) / (y * y);
	t_2 = (z / t) * (z / t);
	tmp = 0.0;
	if (t_1 <= 1e+48)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = ((x * x) * t) / (t * (y * y));
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+48], t$95$2, If[LessEqual[t$95$1, Infinity], N[(N[(N[(x * x), $MachinePrecision] * t), $MachinePrecision] / N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x x) (*.f64 y y)) < 1.00000000000000004e48 or +inf.0 < (/.f64 (*.f64 x x) (*.f64 y y))

   1. Initial program 58.3%

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

   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. pow2 N/A

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

      3. times-frac N/A

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

      4. pow2 N/A

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

      5. lower-pow.f64 N/A

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

      6. lower-/.f64 78.5

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

   4. Applied rewrites 78.5%

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

      1. lift-pow.f64 N/A

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

      2. pow2 N/A

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

      3. lift-*.f64 78.5

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

   6. Applied rewrites 78.5%

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

   if 1.00000000000000004e48 < (/.f64 (*.f64 x x) (*.f64 y y)) < +inf.0

   1. Initial program 78.4%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. 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. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. sqr-neg-rev N/A

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

      9. pow2 N/A

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

      10. associate-/l* N/A

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

      11. pow2 N/A

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

      12. pow2 N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. pow2 N/A

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

      18. lift-*.f64 N/A

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

      19. pow2 N/A

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

      20. pow2 N/A

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

      21. times-frac N/A

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

      22. pow2 N/A

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

      23. lower-pow.f64 N/A

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

      24. lower-/.f64 94.0

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

   3. Applied rewrites 94.0%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. pow2 N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*r/ N/A

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

      9. lift-*.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. associate-*r/ N/A

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

      12. lift-neg.f64 N/A

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

      13. lift-neg.f64 N/A

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

      14. sqr-neg-rev N/A

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

      15. pow2 N/A

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

      16. frac-add N/A

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

   5. Applied rewrites 70.5%

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

   6. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{t \cdot {x}^{2}}}{t \cdot \left(y \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. pow2 N/A

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

      4. lift-*.f64 75.4

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

   8. Applied rewrites 75.4%

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

Alternative 7: 93.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{+266}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-x, \frac{-x}{y \cdot y}, \frac{\frac{z}{t} \cdot z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 4e+266)
     (+ (* (/ x y) (/ x y)) t_1)
     (fma (- x) (/ (- x) (* y y)) (/ (* (/ z t) z) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 4e+266) {
		tmp = ((x / y) * (x / y)) + t_1;
	} else {
		tmp = fma(-x, (-x / (y * y)), (((z / t) * z) / t));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * z) / Float64(t * t))
	tmp = 0.0
	if (t_1 <= 4e+266)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + t_1);
	else
		tmp = fma(Float64(-x), Float64(Float64(-x) / Float64(y * y)), Float64(Float64(Float64(z / t) * z) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e+266], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[((-x) * N[((-x) / N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z / t), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 4.0000000000000001e266

   1. Initial program 74.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      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 95.2

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

   3. Applied rewrites 95.2%

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

   if 4.0000000000000001e266 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 58.0%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. 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. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. sqr-neg-rev N/A

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

      9. pow2 N/A

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

      10. associate-/l* N/A

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

      11. pow2 N/A

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

      12. pow2 N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. pow2 N/A

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

      18. lift-*.f64 N/A

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

      19. pow2 N/A

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

      20. pow2 N/A

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

      21. times-frac N/A

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

      22. pow2 N/A

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

      23. lower-pow.f64 N/A

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

      24. lower-/.f64 95.1

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

   3. Applied rewrites 95.1%

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

      1. lift-pow.f64 N/A

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

      2. pow2 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. frac-times N/A

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

      6. pow2 N/A

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

      7. pow2 N/A

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

      8. pow2 N/A

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

      9. associate-/r* N/A

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

      10. lower-/.f64 N/A

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

      11. pow2 N/A

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

      12. associate-*l/ N/A

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

      13. lift-/.f64 N/A

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

      14. lower-*.f64 90.7

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

   5. Applied rewrites 90.7%

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

Alternative 8: 89.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{+266}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 4e+266) (+ (* (/ x y) (/ x y)) t_1) (* (/ z t) (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 4e+266) {
		tmp = ((x / y) * (x / y)) + t_1;
	} else {
		tmp = (z / t) * (z / t);
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (z * z) / (t * t)
    if (t_1 <= 4d+266) then
        tmp = ((x / y) * (x / y)) + t_1
    else
        tmp = (z / t) * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 4e+266) {
		tmp = ((x / y) * (x / y)) + t_1;
	} else {
		tmp = (z / t) * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * z) / (t * t)
	tmp = 0
	if t_1 <= 4e+266:
		tmp = ((x / y) * (x / y)) + t_1
	else:
		tmp = (z / t) * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * z) / Float64(t * t))
	tmp = 0.0
	if (t_1 <= 4e+266)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + t_1);
	else
		tmp = Float64(Float64(z / t) * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * z) / (t * t);
	tmp = 0.0;
	if (t_1 <= 4e+266)
		tmp = ((x / y) * (x / y)) + t_1;
	else
		tmp = (z / t) * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e+266], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 4.0000000000000001e266

   1. Initial program 74.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      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 95.2

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

   3. Applied rewrites 95.2%

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

   if 4.0000000000000001e266 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 58.0%

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

   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. pow2 N/A

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

      3. times-frac N/A

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

      4. pow2 N/A

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

      5. lower-pow.f64 N/A

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

      6. lower-/.f64 83.2

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

   4. Applied rewrites 83.2%

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

      1. lift-pow.f64 N/A

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

      2. pow2 N/A

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

      3. lift-*.f64 83.2

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

   6. Applied rewrites 83.2%

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

Alternative 9: 81.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{+266}:\\ \;\;\;\;\frac{x}{y \cdot y} \cdot x + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z z) (* t t))))
   (if (<= t_1 4e+266) (+ (* (/ x (* y y)) x) t_1) (* (/ z t) (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 4e+266) {
		tmp = ((x / (y * y)) * x) + t_1;
	} else {
		tmp = (z / t) * (z / t);
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (z * z) / (t * t)
    if (t_1 <= 4d+266) then
        tmp = ((x / (y * y)) * x) + t_1
    else
        tmp = (z / t) * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 4e+266) {
		tmp = ((x / (y * y)) * x) + t_1;
	} else {
		tmp = (z / t) * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * z) / (t * t)
	tmp = 0
	if t_1 <= 4e+266:
		tmp = ((x / (y * y)) * x) + t_1
	else:
		tmp = (z / t) * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * z) / Float64(t * t))
	tmp = 0.0
	if (t_1 <= 4e+266)
		tmp = Float64(Float64(Float64(x / Float64(y * y)) * x) + t_1);
	else
		tmp = Float64(Float64(z / t) * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * z) / (t * t);
	tmp = 0.0;
	if (t_1 <= 4e+266)
		tmp = ((x / (y * y)) * x) + t_1;
	else
		tmp = (z / t) * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e+266], N[(N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 4.0000000000000001e266

   1. Initial program 74.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. pow2 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. pow2 N/A

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

      9. associate-/r* N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 91.0

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

   3. Applied rewrites 91.0%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l/ N/A

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

      4. pow2 N/A

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

      5. lower-/.f64 N/A

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

      6. pow2 N/A

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

      7. lift-*.f64 80.6

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

   5. Applied rewrites 80.6%

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

   if 4.0000000000000001e266 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 58.0%

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

   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. pow2 N/A

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

      3. times-frac N/A

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

      4. pow2 N/A

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

      5. lower-pow.f64 N/A

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

      6. lower-/.f64 83.2

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

   4. Applied rewrites 83.2%

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

      1. lift-pow.f64 N/A

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

      2. pow2 N/A

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

      3. lift-*.f64 83.2

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

   6. Applied rewrites 83.2%

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

Alternative 10: 59.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 8.2 \cdot 10^{+227}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(z \cdot \frac{-1}{t \cdot t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* x x) 8.2e+227)
   (* (/ z t) (/ z t))
   (* (- z) (* z (/ -1.0 (* t t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 8.2e+227) {
		tmp = (z / t) * (z / t);
	} else {
		tmp = -z * (z * (-1.0 / (t * t)));
	}
	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 * x) <= 8.2d+227) then
        tmp = (z / t) * (z / t)
    else
        tmp = -z * (z * ((-1.0d0) / (t * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 8.2e+227) {
		tmp = (z / t) * (z / t);
	} else {
		tmp = -z * (z * (-1.0 / (t * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x * x) <= 8.2e+227:
		tmp = (z / t) * (z / t)
	else:
		tmp = -z * (z * (-1.0 / (t * t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x * x) <= 8.2e+227)
		tmp = Float64(Float64(z / t) * Float64(z / t));
	else
		tmp = Float64(Float64(-z) * Float64(z * Float64(-1.0 / Float64(t * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x * x) <= 8.2e+227)
		tmp = (z / t) * (z / t);
	else
		tmp = -z * (z * (-1.0 / (t * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x * x), $MachinePrecision], 8.2e+227], N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], N[((-z) * N[(z * N[(-1.0 / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 8.19999999999999992e227

   1. Initial program 68.9%

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

   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. pow2 N/A

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

      3. times-frac N/A

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

      4. pow2 N/A

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

      5. lower-pow.f64 N/A

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

      6. lower-/.f64 68.9

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

   4. Applied rewrites 68.9%

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

      1. lift-pow.f64 N/A

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

      2. pow2 N/A

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

      3. lift-*.f64 68.9

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

   6. Applied rewrites 68.9%

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

   if 8.19999999999999992e227 < (*.f64 x x)

   1. Initial program 61.6%

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

   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. pow2 N/A

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

      3. times-frac N/A

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

      4. pow2 N/A

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

      5. lower-pow.f64 N/A

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

      6. lower-/.f64 37.5

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

   4. Applied rewrites 37.5%

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

      1. lift-pow.f64 N/A

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

      2. pow2 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. frac-times N/A

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

      6. sqr-neg-rev N/A

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

      7. associate-/l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-neg.f64 N/A

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

      12. lift-*.f64 39.0

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

   6. Applied rewrites 39.0%

      \[\leadsto \left(-z\right) \cdot \color{blue}{\frac{-z}{t \cdot t}} \]
   7. Step-by-step derivation

      1. lift-neg.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

      6. pow2 N/A

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

      7. associate-/l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. pow2 N/A

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

      11. lift-*.f64 39.2

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

   8. Applied rewrites 39.2%

      \[\leadsto \left(-z\right) \cdot \left(z \cdot \color{blue}{\frac{-1}{t \cdot t}}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 59.3% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Fortran

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) * (z / t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.7%

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

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. pow2 N/A

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

   3. times-frac N/A

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

   4. pow2 N/A

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

   5. lower-pow.f64 N/A

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

   6. lower-/.f64 59.3

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

4. Applied rewrites 59.3%

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

   1. lift-pow.f64 N/A

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

   2. pow2 N/A

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

   3. lift-*.f64 59.3

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

6. Applied rewrites 59.3%

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

Alternative 12: 52.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \left(-z\right) \cdot \frac{-z}{t \cdot t} \end{array} \]

FPCore

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

C

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

Fortran

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 * (-z / (t * t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[((-z) * N[((-z) / N[(t * t), $MachinePrecision]), $MachinePrecision]), $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 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. pow2 N/A

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

   3. times-frac N/A

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

   4. pow2 N/A

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

   5. lower-pow.f64 N/A

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

   6. lower-/.f64 59.3

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

4. Applied rewrites 59.3%

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

   1. lift-pow.f64 N/A

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

   2. pow2 N/A

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

   3. lift-/.f64 N/A

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

   4. lift-/.f64 N/A

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

   5. frac-times N/A

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

   6. sqr-neg-rev N/A

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

   7. associate-/l* N/A

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

   8. lower-*.f64 N/A

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

   9. lower-neg.f64 N/A

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

   10. lower-/.f64 N/A

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

   11. lower-neg.f64 N/A

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

   12. lift-*.f64 52.6

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

6. Applied rewrites 52.6%

   \[\leadsto \left(-z\right) \cdot \color{blue}{\frac{-z}{t \cdot t}} \]
7. Add Preprocessing

Alternative 13: 48.9% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

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 * z) / (t * t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.7%

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

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. pow2 N/A

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

   3. times-frac N/A

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

   4. pow2 N/A

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

   5. lower-pow.f64 N/A

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

   6. lower-/.f64 59.3

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

4. Applied rewrites 59.3%

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

   1. lift-pow.f64 N/A

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

   2. pow2 N/A

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

   3. lift-/.f64 N/A

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

   4. lift-/.f64 N/A

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

   5. frac-times N/A

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

   6. lift-/.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. lift-*.f64 48.9

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

6. Applied rewrites 48.9%

   \[\leadsto \frac{z \cdot z}{\color{blue}{t \cdot t}} \]
7. 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 2025095 
(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))))