Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A

Percentage Accurate: 88.5% → 99.8%

Time: 6.8s

Alternatives: 8

Speedup: 0.3×

Specification

Math

\[\begin{array}{l} \\ \frac{x + y}{1 - \frac{y}{z}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (+ x y) (- 1.0 (/ y z))))

C

double code(double x, double y, double z) {
	return (x + y) / (1.0 - (y / z));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) / (1.0d0 - (y / z))
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) / (1.0 - (y / z));
}

Python

def code(x, y, z):
	return (x + y) / (1.0 - (y / z))

Julia

function code(x, y, z)
	return Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) / (1.0 - (y / z));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 88.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{1 - \frac{y}{z}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (+ x y) (- 1.0 (/ y z))))

C

double code(double x, double y, double z) {
	return (x + y) / (1.0 - (y / z));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) / (1.0d0 - (y / z))
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) / (1.0 - (y / z));
}

Python

def code(x, y, z):
	return (x + y) / (1.0 - (y / z))

Julia

function code(x, y, z)
	return Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) / (1.0 - (y / z));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-274} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-\mathsf{fma}\left(z, \frac{x}{y}, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -5e-274) (not (<= t_0 0.0))) t_0 (- (fma z (/ x y) z)))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -5e-274) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -fma(z, (x / y), z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -5e-274) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(-fma(z, Float64(x / y), z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -5e-274], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, (-N[(z * N[(x / y), $MachinePrecision] + z), $MachinePrecision])]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -5e-274 or 0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   if -5e-274 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 0.0

   1. Initial program 9.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}\right) - \frac{{z}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-+r- N/A

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

      2. associate--l+ N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. associate--l- N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

         \[\leadsto -1 \cdot z - \left(\frac{x \cdot z}{y} + \frac{\color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot {z}^{2}}{y}\right) \]

      9. div-add N/A

         \[\leadsto -1 \cdot z - \color{blue}{\frac{x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}}{y}} \]

      10. fp-cancel-sub-sign-inv N/A

          \[\leadsto -1 \cdot z - \frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y} \]

      11. *-lft-identity N/A

          \[\leadsto -1 \cdot z - \color{blue}{1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      12. metadata-eval N/A

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

      13. fp-cancel-sign-sub-inv N/A

          \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      14. distribute-lft-out N/A

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

      15. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(z + \frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)\right)} \]

      16. lower-neg.f64 N/A

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

   5. Applied rewrites 89.3%

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

   7. Applied rewrites 100.0%

      \[\leadsto -\mathsf{fma}\left(z, \frac{z + x}{y}, z\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto -\mathsf{fma}\left(z, \frac{x}{y}, z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-274} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-\mathsf{fma}\left(z, \frac{x}{y}, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4000:\\ \;\;\;\;-\mathsf{fma}\left(z, \frac{x}{y}, z\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+17}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;-\mathsf{fma}\left(\frac{z}{y}, x + z, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4000.0)
   (- (fma z (/ x y) z))
   (if (<= y 2.25e+17) (+ y x) (- (fma (/ z y) (+ x z) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4000.0) {
		tmp = -fma(z, (x / y), z);
	} else if (y <= 2.25e+17) {
		tmp = y + x;
	} else {
		tmp = -fma((z / y), (x + z), z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4000.0)
		tmp = Float64(-fma(z, Float64(x / y), z));
	elseif (y <= 2.25e+17)
		tmp = Float64(y + x);
	else
		tmp = Float64(-fma(Float64(z / y), Float64(x + z), z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4000.0], (-N[(z * N[(x / y), $MachinePrecision] + z), $MachinePrecision]), If[LessEqual[y, 2.25e+17], N[(y + x), $MachinePrecision], (-N[(N[(z / y), $MachinePrecision] * N[(x + z), $MachinePrecision] + z), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if y < -4e3

   1. Initial program 76.1%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}\right) - \frac{{z}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-+r- N/A

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

      2. associate--l+ N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. associate--l- N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

         \[\leadsto -1 \cdot z - \left(\frac{x \cdot z}{y} + \frac{\color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot {z}^{2}}{y}\right) \]

      9. div-add N/A

         \[\leadsto -1 \cdot z - \color{blue}{\frac{x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}}{y}} \]

      10. fp-cancel-sub-sign-inv N/A

          \[\leadsto -1 \cdot z - \frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y} \]

      11. *-lft-identity N/A

          \[\leadsto -1 \cdot z - \color{blue}{1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      12. metadata-eval N/A

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

      13. fp-cancel-sign-sub-inv N/A

          \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      14. distribute-lft-out N/A

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

      15. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(z + \frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)\right)} \]

      16. lower-neg.f64 N/A

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

   5. Applied rewrites 75.0%

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

   7. Applied rewrites 79.9%

      \[\leadsto -\mathsf{fma}\left(z, \frac{z + x}{y}, z\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto -\mathsf{fma}\left(z, \frac{x}{y}, z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 80.1%

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

   if -4e3 < y < 2.25e17

   1. Initial program 100.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}\right) - \frac{{z}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-+r- N/A

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

      2. associate--l+ N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. associate--l- N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

         \[\leadsto -1 \cdot z - \left(\frac{x \cdot z}{y} + \frac{\color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot {z}^{2}}{y}\right) \]

      9. div-add N/A

         \[\leadsto -1 \cdot z - \color{blue}{\frac{x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}}{y}} \]

      10. fp-cancel-sub-sign-inv N/A

          \[\leadsto -1 \cdot z - \frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y} \]

      11. *-lft-identity N/A

          \[\leadsto -1 \cdot z - \color{blue}{1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      12. metadata-eval N/A

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

      13. fp-cancel-sign-sub-inv N/A

          \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      14. distribute-lft-out N/A

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

      15. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(z + \frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)\right)} \]

      16. lower-neg.f64 N/A

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

   5. Applied rewrites 21.1%

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

   7. Applied rewrites 17.5%

      \[\leadsto -\mathsf{fma}\left(z, \frac{z + x}{y}, z\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto -\mathsf{fma}\left(z, \frac{x}{y}, z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 18.1%

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

   11. Taylor expanded in z around inf

       \[\leadsto \color{blue}{x + y} \]
   12. Step-by-step derivation

       1. +-commutative N/A

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

       2. lower-+.f64 80.3

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

   13. Applied rewrites 80.3%

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

   if 2.25e17 < y

   1. Initial program 72.1%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}\right) - \frac{{z}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-+r- N/A

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

      2. associate--l+ N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. associate--l- N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

         \[\leadsto -1 \cdot z - \left(\frac{x \cdot z}{y} + \frac{\color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot {z}^{2}}{y}\right) \]

      9. div-add N/A

         \[\leadsto -1 \cdot z - \color{blue}{\frac{x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}}{y}} \]

      10. fp-cancel-sub-sign-inv N/A

          \[\leadsto -1 \cdot z - \frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y} \]

      11. *-lft-identity N/A

          \[\leadsto -1 \cdot z - \color{blue}{1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      12. metadata-eval N/A

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

      13. fp-cancel-sign-sub-inv N/A

          \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      14. distribute-lft-out N/A

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

      15. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(z + \frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)\right)} \]

      16. lower-neg.f64 N/A

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

   5. Applied rewrites 86.7%

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

Alternative 3: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4000:\\ \;\;\;\;-\mathsf{fma}\left(z, \frac{x}{y}, z\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+17}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;-\mathsf{fma}\left(z, \frac{z + x}{y}, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4000.0)
   (- (fma z (/ x y) z))
   (if (<= y 2.25e+17) (+ y x) (- (fma z (/ (+ z x) y) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4000.0) {
		tmp = -fma(z, (x / y), z);
	} else if (y <= 2.25e+17) {
		tmp = y + x;
	} else {
		tmp = -fma(z, ((z + x) / y), z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4000.0)
		tmp = Float64(-fma(z, Float64(x / y), z));
	elseif (y <= 2.25e+17)
		tmp = Float64(y + x);
	else
		tmp = Float64(-fma(z, Float64(Float64(z + x) / y), z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4000.0], (-N[(z * N[(x / y), $MachinePrecision] + z), $MachinePrecision]), If[LessEqual[y, 2.25e+17], N[(y + x), $MachinePrecision], (-N[(z * N[(N[(z + x), $MachinePrecision] / y), $MachinePrecision] + z), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if y < -4e3

   1. Initial program 76.1%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}\right) - \frac{{z}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-+r- N/A

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

      2. associate--l+ N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. associate--l- N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

         \[\leadsto -1 \cdot z - \left(\frac{x \cdot z}{y} + \frac{\color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot {z}^{2}}{y}\right) \]

      9. div-add N/A

         \[\leadsto -1 \cdot z - \color{blue}{\frac{x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}}{y}} \]

      10. fp-cancel-sub-sign-inv N/A

          \[\leadsto -1 \cdot z - \frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y} \]

      11. *-lft-identity N/A

          \[\leadsto -1 \cdot z - \color{blue}{1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      12. metadata-eval N/A

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

      13. fp-cancel-sign-sub-inv N/A

          \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      14. distribute-lft-out N/A

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

      15. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(z + \frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)\right)} \]

      16. lower-neg.f64 N/A

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

   5. Applied rewrites 75.0%

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

   7. Applied rewrites 79.9%

      \[\leadsto -\mathsf{fma}\left(z, \frac{z + x}{y}, z\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto -\mathsf{fma}\left(z, \frac{x}{y}, z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 80.1%

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

   if -4e3 < y < 2.25e17

   1. Initial program 100.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}\right) - \frac{{z}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-+r- N/A

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

      2. associate--l+ N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. associate--l- N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

         \[\leadsto -1 \cdot z - \left(\frac{x \cdot z}{y} + \frac{\color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot {z}^{2}}{y}\right) \]

      9. div-add N/A

         \[\leadsto -1 \cdot z - \color{blue}{\frac{x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}}{y}} \]

      10. fp-cancel-sub-sign-inv N/A

          \[\leadsto -1 \cdot z - \frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y} \]

      11. *-lft-identity N/A

          \[\leadsto -1 \cdot z - \color{blue}{1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      12. metadata-eval N/A

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

      13. fp-cancel-sign-sub-inv N/A

          \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      14. distribute-lft-out N/A

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

      15. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(z + \frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)\right)} \]

      16. lower-neg.f64 N/A

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

   5. Applied rewrites 21.1%

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

   7. Applied rewrites 17.5%

      \[\leadsto -\mathsf{fma}\left(z, \frac{z + x}{y}, z\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto -\mathsf{fma}\left(z, \frac{x}{y}, z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 18.1%

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

   11. Taylor expanded in z around inf

       \[\leadsto \color{blue}{x + y} \]
   12. Step-by-step derivation

       1. +-commutative N/A

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

       2. lower-+.f64 80.3

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

   13. Applied rewrites 80.3%

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

   if 2.25e17 < y

   1. Initial program 72.1%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}\right) - \frac{{z}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-+r- N/A

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

      2. associate--l+ N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. associate--l- N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

         \[\leadsto -1 \cdot z - \left(\frac{x \cdot z}{y} + \frac{\color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot {z}^{2}}{y}\right) \]

      9. div-add N/A

         \[\leadsto -1 \cdot z - \color{blue}{\frac{x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}}{y}} \]

      10. fp-cancel-sub-sign-inv N/A

          \[\leadsto -1 \cdot z - \frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y} \]

      11. *-lft-identity N/A

          \[\leadsto -1 \cdot z - \color{blue}{1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      12. metadata-eval N/A

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

      13. fp-cancel-sign-sub-inv N/A

          \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      14. distribute-lft-out N/A

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

      15. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(z + \frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)\right)} \]

      16. lower-neg.f64 N/A

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

   5. Applied rewrites 86.7%

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

   7. Applied rewrites 86.6%

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

Alternative 4: 74.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4000 \lor \neg \left(y \leq 2.25 \cdot 10^{+17}\right):\\ \;\;\;\;-\mathsf{fma}\left(z, \frac{x}{y}, z\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4000.0) (not (<= y 2.25e+17))) (- (fma z (/ x y) z)) (+ y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4000.0) || !(y <= 2.25e+17)) {
		tmp = -fma(z, (x / y), z);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4000.0) || !(y <= 2.25e+17))
		tmp = Float64(-fma(z, Float64(x / y), z));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4000.0], N[Not[LessEqual[y, 2.25e+17]], $MachinePrecision]], (-N[(z * N[(x / y), $MachinePrecision] + z), $MachinePrecision]), N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4e3 or 2.25e17 < y

   1. Initial program 74.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}\right) - \frac{{z}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-+r- N/A

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

      2. associate--l+ N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. associate--l- N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

         \[\leadsto -1 \cdot z - \left(\frac{x \cdot z}{y} + \frac{\color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot {z}^{2}}{y}\right) \]

      9. div-add N/A

         \[\leadsto -1 \cdot z - \color{blue}{\frac{x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}}{y}} \]

      10. fp-cancel-sub-sign-inv N/A

          \[\leadsto -1 \cdot z - \frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y} \]

      11. *-lft-identity N/A

          \[\leadsto -1 \cdot z - \color{blue}{1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      12. metadata-eval N/A

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

      13. fp-cancel-sign-sub-inv N/A

          \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      14. distribute-lft-out N/A

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

      15. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(z + \frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)\right)} \]

      16. lower-neg.f64 N/A

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

   5. Applied rewrites 79.6%

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

   7. Applied rewrites 82.5%

      \[\leadsto -\mathsf{fma}\left(z, \frac{z + x}{y}, z\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto -\mathsf{fma}\left(z, \frac{x}{y}, z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 82.6%

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

   if -4e3 < y < 2.25e17

   1. Initial program 100.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}\right) - \frac{{z}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-+r- N/A

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

      2. associate--l+ N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. associate--l- N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

         \[\leadsto -1 \cdot z - \left(\frac{x \cdot z}{y} + \frac{\color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot {z}^{2}}{y}\right) \]

      9. div-add N/A

         \[\leadsto -1 \cdot z - \color{blue}{\frac{x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}}{y}} \]

      10. fp-cancel-sub-sign-inv N/A

          \[\leadsto -1 \cdot z - \frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y} \]

      11. *-lft-identity N/A

          \[\leadsto -1 \cdot z - \color{blue}{1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      12. metadata-eval N/A

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

      13. fp-cancel-sign-sub-inv N/A

          \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      14. distribute-lft-out N/A

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

      15. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(z + \frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)\right)} \]

      16. lower-neg.f64 N/A

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

   5. Applied rewrites 21.1%

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

   7. Applied rewrites 17.5%

      \[\leadsto -\mathsf{fma}\left(z, \frac{z + x}{y}, z\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto -\mathsf{fma}\left(z, \frac{x}{y}, z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 18.1%

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

   11. Taylor expanded in z around inf

       \[\leadsto \color{blue}{x + y} \]
   12. Step-by-step derivation

       1. +-commutative N/A

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

       2. lower-+.f64 80.3

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

   13. Applied rewrites 80.3%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4000 \lor \neg \left(y \leq 2.25 \cdot 10^{+17}\right):\\ \;\;\;\;-\mathsf{fma}\left(z, \frac{x}{y}, z\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4000:\\ \;\;\;\;-\mathsf{fma}\left(z, \frac{x}{y}, z\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+17}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4000.0)
   (- (fma z (/ x y) z))
   (if (<= y 2.25e+17) (+ y x) (* z (- -1.0 (/ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4000.0) {
		tmp = -fma(z, (x / y), z);
	} else if (y <= 2.25e+17) {
		tmp = y + x;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4000.0)
		tmp = Float64(-fma(z, Float64(x / y), z));
	elseif (y <= 2.25e+17)
		tmp = Float64(y + x);
	else
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4000.0], (-N[(z * N[(x / y), $MachinePrecision] + z), $MachinePrecision]), If[LessEqual[y, 2.25e+17], N[(y + x), $MachinePrecision], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4e3

   1. Initial program 76.1%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}\right) - \frac{{z}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-+r- N/A

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

      2. associate--l+ N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. associate--l- N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

         \[\leadsto -1 \cdot z - \left(\frac{x \cdot z}{y} + \frac{\color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot {z}^{2}}{y}\right) \]

      9. div-add N/A

         \[\leadsto -1 \cdot z - \color{blue}{\frac{x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}}{y}} \]

      10. fp-cancel-sub-sign-inv N/A

          \[\leadsto -1 \cdot z - \frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y} \]

      11. *-lft-identity N/A

          \[\leadsto -1 \cdot z - \color{blue}{1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      12. metadata-eval N/A

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

      13. fp-cancel-sign-sub-inv N/A

          \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      14. distribute-lft-out N/A

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

      15. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(z + \frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)\right)} \]

      16. lower-neg.f64 N/A

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

   5. Applied rewrites 75.0%

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

   7. Applied rewrites 79.9%

      \[\leadsto -\mathsf{fma}\left(z, \frac{z + x}{y}, z\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto -\mathsf{fma}\left(z, \frac{x}{y}, z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 80.1%

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

   if -4e3 < y < 2.25e17

   1. Initial program 100.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}\right) - \frac{{z}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-+r- N/A

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

      2. associate--l+ N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. associate--l- N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

         \[\leadsto -1 \cdot z - \left(\frac{x \cdot z}{y} + \frac{\color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot {z}^{2}}{y}\right) \]

      9. div-add N/A

         \[\leadsto -1 \cdot z - \color{blue}{\frac{x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}}{y}} \]

      10. fp-cancel-sub-sign-inv N/A

          \[\leadsto -1 \cdot z - \frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y} \]

      11. *-lft-identity N/A

          \[\leadsto -1 \cdot z - \color{blue}{1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      12. metadata-eval N/A

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

      13. fp-cancel-sign-sub-inv N/A

          \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      14. distribute-lft-out N/A

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

      15. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(z + \frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)\right)} \]

      16. lower-neg.f64 N/A

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

   5. Applied rewrites 21.1%

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

   7. Applied rewrites 17.5%

      \[\leadsto -\mathsf{fma}\left(z, \frac{z + x}{y}, z\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto -\mathsf{fma}\left(z, \frac{x}{y}, z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 18.1%

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

   11. Taylor expanded in z around inf

       \[\leadsto \color{blue}{x + y} \]
   12. Step-by-step derivation

       1. +-commutative N/A

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

       2. lower-+.f64 80.3

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

   13. Applied rewrites 80.3%

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

   if 2.25e17 < y

   1. Initial program 72.1%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(x + y\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. div-add N/A

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

      5. distribute-neg-in N/A

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

      6. mul-1-neg N/A

         \[\leadsto z \cdot \left(\color{blue}{-1 \cdot \frac{x}{y}} + \left(\mathsf{neg}\left(\frac{y}{y}\right)\right)\right) \]

      7. *-inverses N/A

         \[\leadsto z \cdot \left(-1 \cdot \frac{x}{y} + \left(\mathsf{neg}\left(\color{blue}{1}\right)\right)\right) \]

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. *-commutative N/A

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

      11. mul-1-neg N/A

          \[\leadsto z \cdot \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y}\right)\right)} + -1 \cdot z \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z \cdot \frac{x}{y}\right)\right)} + -1 \cdot z \]

      13. associate-/l* N/A

          \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\frac{z \cdot x}{y}}\right)\right) + -1 \cdot z \]

      14. *-commutative N/A

          \[\leadsto \left(\mathsf{neg}\left(\frac{\color{blue}{x \cdot z}}{y}\right)\right) + -1 \cdot z \]

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. fp-cancel-sign-sub-inv N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. *-commutative N/A

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

      21. *-commutative N/A

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

      22. associate-/l* N/A

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

   5. Applied rewrites 86.5%

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

Alternative 6: 67.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+68}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+18}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;-\mathsf{fma}\left(\frac{z}{y}, z, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.25e+68) (- z) (if (<= y 8.2e+18) (+ y x) (- (fma (/ z y) z z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.25e+68) {
		tmp = -z;
	} else if (y <= 8.2e+18) {
		tmp = y + x;
	} else {
		tmp = -fma((z / y), z, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.25e+68)
		tmp = Float64(-z);
	elseif (y <= 8.2e+18)
		tmp = Float64(y + x);
	else
		tmp = Float64(-fma(Float64(z / y), z, z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.25e+68], (-z), If[LessEqual[y, 8.2e+18], N[(y + x), $MachinePrecision], (-N[(N[(z / y), $MachinePrecision] * z + z), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2500000000000001e68

   1. Initial program 69.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 69.0

         \[\leadsto \color{blue}{-z} \]

   5. Applied rewrites 69.0%

      \[\leadsto \color{blue}{-z} \]

   if -1.2500000000000001e68 < y < 8.2e18

   1. Initial program 99.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}\right) - \frac{{z}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-+r- N/A

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

      2. associate--l+ N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. associate--l- N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

         \[\leadsto -1 \cdot z - \left(\frac{x \cdot z}{y} + \frac{\color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot {z}^{2}}{y}\right) \]

      9. div-add N/A

         \[\leadsto -1 \cdot z - \color{blue}{\frac{x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}}{y}} \]

      10. fp-cancel-sub-sign-inv N/A

          \[\leadsto -1 \cdot z - \frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y} \]

      11. *-lft-identity N/A

          \[\leadsto -1 \cdot z - \color{blue}{1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      12. metadata-eval N/A

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

      13. fp-cancel-sign-sub-inv N/A

          \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      14. distribute-lft-out N/A

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

      15. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(z + \frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)\right)} \]

      16. lower-neg.f64 N/A

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

   5. Applied rewrites 24.7%

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

   7. Applied rewrites 21.6%

      \[\leadsto -\mathsf{fma}\left(z, \frac{z + x}{y}, z\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto -\mathsf{fma}\left(z, \frac{x}{y}, z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 22.2%

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

   11. Taylor expanded in z around inf

       \[\leadsto \color{blue}{x + y} \]
   12. Step-by-step derivation

       1. +-commutative N/A

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

       2. lower-+.f64 75.9

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

   13. Applied rewrites 75.9%

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

   if 8.2e18 < y

   1. Initial program 72.1%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}\right) - \frac{{z}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-+r- N/A

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

      2. associate--l+ N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. associate--l- N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

         \[\leadsto -1 \cdot z - \left(\frac{x \cdot z}{y} + \frac{\color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot {z}^{2}}{y}\right) \]

      9. div-add N/A

         \[\leadsto -1 \cdot z - \color{blue}{\frac{x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}}{y}} \]

      10. fp-cancel-sub-sign-inv N/A

          \[\leadsto -1 \cdot z - \frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y} \]

      11. *-lft-identity N/A

          \[\leadsto -1 \cdot z - \color{blue}{1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      12. metadata-eval N/A

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

      13. fp-cancel-sign-sub-inv N/A

          \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      14. distribute-lft-out N/A

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

      15. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(z + \frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)\right)} \]

      16. lower-neg.f64 N/A

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

   5. Applied rewrites 86.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto -\left(z + \frac{{z}^{2}}{y}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 75.4%

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

Alternative 7: 67.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+68} \lor \neg \left(y \leq 8 \cdot 10^{+18}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.25e+68) (not (<= y 8e+18))) (- z) (+ y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.25e+68) || !(y <= 8e+18)) {
		tmp = -z;
	} else {
		tmp = y + x;
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.25d+68)) .or. (.not. (y <= 8d+18))) then
        tmp = -z
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.25e+68) || !(y <= 8e+18)) {
		tmp = -z;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.25e+68) or not (y <= 8e+18):
		tmp = -z
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.25e+68) || !(y <= 8e+18))
		tmp = Float64(-z);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.25e+68) || ~((y <= 8e+18)))
		tmp = -z;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.25e+68], N[Not[LessEqual[y, 8e+18]], $MachinePrecision]], (-z), N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2500000000000001e68 or 8e18 < y

   1. Initial program 70.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 71.9

         \[\leadsto \color{blue}{-z} \]

   5. Applied rewrites 71.9%

      \[\leadsto \color{blue}{-z} \]

   if -1.2500000000000001e68 < y < 8e18

   1. Initial program 99.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}\right) - \frac{{z}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-+r- N/A

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

      2. associate--l+ N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. associate--l- N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

         \[\leadsto -1 \cdot z - \left(\frac{x \cdot z}{y} + \frac{\color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot {z}^{2}}{y}\right) \]

      9. div-add N/A

         \[\leadsto -1 \cdot z - \color{blue}{\frac{x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}}{y}} \]

      10. fp-cancel-sub-sign-inv N/A

          \[\leadsto -1 \cdot z - \frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y} \]

      11. *-lft-identity N/A

          \[\leadsto -1 \cdot z - \color{blue}{1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      12. metadata-eval N/A

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

      13. fp-cancel-sign-sub-inv N/A

          \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      14. distribute-lft-out N/A

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

      15. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(z + \frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)\right)} \]

      16. lower-neg.f64 N/A

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

   5. Applied rewrites 24.7%

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

   7. Applied rewrites 21.6%

      \[\leadsto -\mathsf{fma}\left(z, \frac{z + x}{y}, z\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto -\mathsf{fma}\left(z, \frac{x}{y}, z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 22.2%

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

   11. Taylor expanded in z around inf

       \[\leadsto \color{blue}{x + y} \]
   12. Step-by-step derivation

       1. +-commutative N/A

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

       2. lower-+.f64 75.9

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

   13. Applied rewrites 75.9%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+68} \lor \neg \left(y \leq 8 \cdot 10^{+18}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 34.6% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ -z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- z))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = -z
end function

Java

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

Python

def code(x, y, z):
	return -z

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := (-z)

Derivation

1. Initial program 87.1%

   \[\frac{x + y}{1 - \frac{y}{z}} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{-1 \cdot z} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

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

   2. lower-neg.f64 36.7

      \[\leadsto \color{blue}{-z} \]

5. Applied rewrites 36.7%

   \[\leadsto \color{blue}{-z} \]
6. Add Preprocessing

Developer Target 1: 93.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y + x}{-y} \cdot z\\ \mathbf{if}\;y < -3.7429310762689856 \cdot 10^{+171}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y < 3.5534662456086734 \cdot 10^{+168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ (+ y x) (- y)) z)))
   (if (< y -3.7429310762689856e+171)
     t_0
     (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y + x) / -y) * z
    if (y < (-3.7429310762689856d+171)) then
        tmp = t_0
    else if (y < 3.5534662456086734d+168) then
        tmp = (x + y) / (1.0d0 - (y / z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y + x) / -y) * z
	tmp = 0
	if y < -3.7429310762689856e+171:
		tmp = t_0
	elif y < 3.5534662456086734e+168:
		tmp = (x + y) / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y + x) / Float64(-y)) * z)
	tmp = 0.0
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y + x) / -y) * z;
	tmp = 0.0;
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = (x + y) / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y + x), $MachinePrecision] / (-y)), $MachinePrecision] * z), $MachinePrecision]}, If[Less[y, -3.7429310762689856e+171], t$95$0, If[Less[y, 3.5534662456086734e+168], N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024350 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -3742931076268985600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* (/ (+ y x) (- y)) z) (if (< y 3553466245608673400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ x y) (- 1 (/ y z))) (* (/ (+ y x) (- y)) z))))

  (/ (+ x y) (- 1.0 (/ y z))))