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

Percentage Accurate: 88.7% → 99.8%

Time: 8.8s

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

real(8) function code(x, y, z)
    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: 88.7% 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

real(8) function code(x, y, z)
    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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-284}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\frac{-1}{\frac{y}{z \cdot \left(x + z\right)}} - z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (<= t_0 -5e-284)
     t_0
     (if (<= t_0 0.0) (- (/ -1.0 (/ y (* z (+ x z)))) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if (t_0 <= -5e-284) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (-1.0 / (y / (z * (x + z)))) - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if (t_0 <= (-5d-284)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = ((-1.0d0) / (y / (z * (x + z)))) - 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 = (x + y) / (1.0 - (y / z));
	double tmp;
	if (t_0 <= -5e-284) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (-1.0 / (y / (z * (x + z)))) - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if t_0 <= -5e-284:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = (-1.0 / (y / (z * (x + z)))) - z
	else:
		tmp = t_0
	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-284)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(-1.0 / Float64(y / Float64(z * Float64(x + z)))) - z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if (t_0 <= -5e-284)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = (-1.0 / (y / (z * (x + z)))) - z;
	else
		tmp = t_0;
	end
	tmp_2 = 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[LessEqual[t$95$0, -5e-284], t$95$0, If[LessEqual[t$95$0, 0.0], N[(N[(-1.0 / N[(y / N[(z * N[(x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -4.99999999999999973e-284 or -0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.8%

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

   if -4.99999999999999973e-284 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 6.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

      5. distribute-frac-neg N/A

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

      6. mul-1-neg N/A

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

      7. div-sub N/A

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

      8. lower--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. cancel-sign-sub-inv N/A

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

      13. metadata-eval N/A

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

      14. *-lft-identity N/A

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

      15. +-commutative N/A

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

      16. unpow2 N/A

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

      17. distribute-rgt-out N/A

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

      18. lower-*.f64 N/A

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

      19. lower-+.f64 99.9

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

   5. Applied rewrites 99.9%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 99.9

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

   7. Applied rewrites 99.9%

      \[\leadsto \left(-z\right) - \color{blue}{\frac{1}{\frac{y}{z \cdot \left(z + x\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-284}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;\frac{x + y}{1 - \frac{y}{z}} \leq 0:\\ \;\;\;\;\frac{-1}{\frac{y}{z \cdot \left(x + z\right)}} - z\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-284}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(x \cdot z, \frac{-1}{y}, -z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (<= t_0 -5e-284)
     t_0
     (if (<= t_0 0.0) (fma (* x z) (/ -1.0 y) (- z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if (t_0 <= -5e-284) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = fma((x * z), (-1.0 / y), -z);
	} else {
		tmp = t_0;
	}
	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-284)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = fma(Float64(x * z), Float64(-1.0 / y), Float64(-z));
	else
		tmp = t_0;
	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[LessEqual[t$95$0, -5e-284], t$95$0, If[LessEqual[t$95$0, 0.0], N[(N[(x * z), $MachinePrecision] * N[(-1.0 / y), $MachinePrecision] + (-z)), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -4.99999999999999973e-284 or -0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.8%

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

   if -4.99999999999999973e-284 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 6.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. distribute-neg-frac N/A

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

      5. +-commutative N/A

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

      6. distribute-neg-in N/A

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

      7. neg-mul-1 N/A

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

      8. unsub-neg N/A

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

      9. div-sub N/A

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

      10. associate-*l/ N/A

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

      11. metadata-eval N/A

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

      12. distribute-neg-frac N/A

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

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

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

      14. lft-mult-inverse N/A

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

      15. metadata-eval N/A

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

      16. distribute-lft-out-- N/A

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

      17. *-commutative N/A

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

      18. associate-/l* N/A

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

      19. *-commutative N/A

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

      20. unsub-neg N/A

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

      21. mul-1-neg N/A

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

      22. distribute-neg-out N/A

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

      23. lower-neg.f64 N/A

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

   5. Applied rewrites 99.8%

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

      1. lift-/.f64 N/A

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

      2. distribute-neg-in N/A

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

      3. lift-neg.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. distribute-neg-frac2 N/A

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

      7. div-inv N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. frac-2neg N/A

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

      11. metadata-eval N/A

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

      12. remove-double-neg N/A

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

      13. lower-/.f64 99.9

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

   7. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot x, \frac{-1}{y}, -z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-284}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;\frac{x + y}{1 - \frac{y}{z}} \leq 0:\\ \;\;\;\;\mathsf{fma}\left(x \cdot z, \frac{-1}{y}, -z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -\mathsf{fma}\left(z, \frac{x}{y}, z\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{-12}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-142}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\frac{-1}{z}, y, 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fma z (/ x y) z))))
   (if (<= y -1.45e-12)
     t_0
     (if (<= y 1.9e-142)
       (+ x y)
       (if (<= y 2.4e-67) (/ x (fma (/ -1.0 z) y 1.0)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -fma(z, (x / y), z);
	double tmp;
	if (y <= -1.45e-12) {
		tmp = t_0;
	} else if (y <= 1.9e-142) {
		tmp = x + y;
	} else if (y <= 2.4e-67) {
		tmp = x / fma((-1.0 / z), y, 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(-fma(z, Float64(x / y), z))
	tmp = 0.0
	if (y <= -1.45e-12)
		tmp = t_0;
	elseif (y <= 1.9e-142)
		tmp = Float64(x + y);
	elseif (y <= 2.4e-67)
		tmp = Float64(x / fma(Float64(-1.0 / z), y, 1.0));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = (-N[(z * N[(x / y), $MachinePrecision] + z), $MachinePrecision])}, If[LessEqual[y, -1.45e-12], t$95$0, If[LessEqual[y, 1.9e-142], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.4e-67], N[(x / N[(N[(-1.0 / z), $MachinePrecision] * y + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4500000000000001e-12 or 2.4e-67 < y

   1. Initial program 73.1%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. distribute-neg-frac N/A

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

      5. +-commutative N/A

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

      6. distribute-neg-in N/A

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

      7. neg-mul-1 N/A

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

      8. unsub-neg N/A

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

      9. div-sub N/A

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

      10. associate-*l/ N/A

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

      11. metadata-eval N/A

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

      12. distribute-neg-frac N/A

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

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

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

      14. lft-mult-inverse N/A

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

      15. metadata-eval N/A

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

      16. distribute-lft-out-- N/A

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

      17. *-commutative N/A

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

      18. associate-/l* N/A

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

      19. *-commutative N/A

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

      20. unsub-neg N/A

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

      21. mul-1-neg N/A

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

      22. distribute-neg-out N/A

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

      23. lower-neg.f64 N/A

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

   5. Applied rewrites 80.6%

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

   if -1.4500000000000001e-12 < y < 1.89999999999999986e-142

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 82.4

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

   5. Applied rewrites 82.4%

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

   if 1.89999999999999986e-142 < y < 2.4e-67

   1. Initial program 99.7%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. div-inv N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{1 + -1 \cdot \frac{y}{z}}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 77.8

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

   7. Applied rewrites 77.8%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. div-inv N/A

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

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

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

      7. lift-neg.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 77.9

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

   9. Applied rewrites 77.9%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(-y, \frac{1}{z}, 1\right)}} \]
   10. Step-by-step derivation

       1. lift-neg.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. lift-neg.f64 N/A

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

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

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

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

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

       6. neg-mul-1 N/A

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

       7. lift-/.f64 N/A

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

       8. div-inv N/A

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

       9. *-commutative N/A

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

       10. lower-fma.f64 N/A

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

       11. lower-/.f64 77.9

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

   11. Applied rewrites 77.9%

       \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(\frac{-1}{z}, y, 1\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-12}:\\ \;\;\;\;-\mathsf{fma}\left(z, \frac{x}{y}, z\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-142}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\frac{-1}{z}, y, 1\right)}\\ \mathbf{else}:\\ \;\;\;\;-\mathsf{fma}\left(z, \frac{x}{y}, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -\mathsf{fma}\left(z, \frac{x}{y}, z\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{-12}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-142}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fma z (/ x y) z))))
   (if (<= y -1.45e-12)
     t_0
     (if (<= y 1.9e-142)
       (+ x y)
       (if (<= y 2.4e-67) (/ x (- 1.0 (/ y z))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -fma(z, (x / y), z);
	double tmp;
	if (y <= -1.45e-12) {
		tmp = t_0;
	} else if (y <= 1.9e-142) {
		tmp = x + y;
	} else if (y <= 2.4e-67) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(-fma(z, Float64(x / y), z))
	tmp = 0.0
	if (y <= -1.45e-12)
		tmp = t_0;
	elseif (y <= 1.9e-142)
		tmp = Float64(x + y);
	elseif (y <= 2.4e-67)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = (-N[(z * N[(x / y), $MachinePrecision] + z), $MachinePrecision])}, If[LessEqual[y, -1.45e-12], t$95$0, If[LessEqual[y, 1.9e-142], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.4e-67], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4500000000000001e-12 or 2.4e-67 < y

   1. Initial program 73.1%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. distribute-neg-frac N/A

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

      5. +-commutative N/A

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

      6. distribute-neg-in N/A

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

      7. neg-mul-1 N/A

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

      8. unsub-neg N/A

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

      9. div-sub N/A

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

      10. associate-*l/ N/A

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

      11. metadata-eval N/A

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

      12. distribute-neg-frac N/A

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

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

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

      14. lft-mult-inverse N/A

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

      15. metadata-eval N/A

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

      16. distribute-lft-out-- N/A

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

      17. *-commutative N/A

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

      18. associate-/l* N/A

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

      19. *-commutative N/A

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

      20. unsub-neg N/A

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

      21. mul-1-neg N/A

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

      22. distribute-neg-out N/A

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

      23. lower-neg.f64 N/A

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

   5. Applied rewrites 80.6%

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

   if -1.4500000000000001e-12 < y < 1.89999999999999986e-142

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 82.4

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

   5. Applied rewrites 82.4%

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

   if 1.89999999999999986e-142 < y < 2.4e-67

   1. Initial program 99.7%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. div-inv N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{1 + -1 \cdot \frac{y}{z}}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 77.8

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

   7. Applied rewrites 77.8%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-12}:\\ \;\;\;\;-\mathsf{fma}\left(z, \frac{x}{y}, z\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-142}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-\mathsf{fma}\left(z, \frac{x}{y}, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -\mathsf{fma}\left(z, \frac{x}{y}, z\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{-12}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-101}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fma z (/ x y) z))))
   (if (<= y -1.45e-12) t_0 (if (<= y 5.2e-101) (+ x y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -fma(z, (x / y), z);
	double tmp;
	if (y <= -1.45e-12) {
		tmp = t_0;
	} else if (y <= 5.2e-101) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(-fma(z, Float64(x / y), z))
	tmp = 0.0
	if (y <= -1.45e-12)
		tmp = t_0;
	elseif (y <= 5.2e-101)
		tmp = Float64(x + y);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = (-N[(z * N[(x / y), $MachinePrecision] + z), $MachinePrecision])}, If[LessEqual[y, -1.45e-12], t$95$0, If[LessEqual[y, 5.2e-101], N[(x + y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4500000000000001e-12 or 5.2000000000000002e-101 < y

   1. Initial program 74.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. distribute-neg-frac N/A

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

      5. +-commutative N/A

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

      6. distribute-neg-in N/A

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

      7. neg-mul-1 N/A

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

      8. unsub-neg N/A

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

      9. div-sub N/A

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

      10. associate-*l/ N/A

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

      11. metadata-eval N/A

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

      12. distribute-neg-frac N/A

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

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

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

      14. lft-mult-inverse N/A

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

      15. metadata-eval N/A

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

      16. distribute-lft-out-- N/A

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

      17. *-commutative N/A

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

      18. associate-/l* N/A

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

      19. *-commutative N/A

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

      20. unsub-neg N/A

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

      21. mul-1-neg N/A

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

      22. distribute-neg-out N/A

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

      23. lower-neg.f64 N/A

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

   5. Applied rewrites 78.9%

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

   if -1.4500000000000001e-12 < y < 5.2000000000000002e-101

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 80.2

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

   5. Applied rewrites 80.2%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-12}:\\ \;\;\;\;-\mathsf{fma}\left(z, \frac{x}{y}, z\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-101}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-\mathsf{fma}\left(z, \frac{x}{y}, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+128}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.5e+128) (- z) (if (<= y 4.5e-5) (+ x y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.5e+128) {
		tmp = -z;
	} else if (y <= 4.5e-5) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.5d+128)) then
        tmp = -z
    else if (y <= 4.5d-5) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.5e+128) {
		tmp = -z;
	} else if (y <= 4.5e-5) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.5e+128:
		tmp = -z
	elif y <= 4.5e-5:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.5e+128)
		tmp = Float64(-z);
	elseif (y <= 4.5e-5)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.5e+128)
		tmp = -z;
	elseif (y <= 4.5e-5)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.5e+128], (-z), If[LessEqual[y, 4.5e-5], N[(x + y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4999999999999999e128 or 4.50000000000000028e-5 < y

   1. Initial program 68.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 67.6

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

   5. Applied rewrites 67.6%

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

   if -1.4999999999999999e128 < y < 4.50000000000000028e-5

   1. Initial program 97.2%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 67.8

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

   5. Applied rewrites 67.8%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+128}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 39.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+150}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+200}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.8e+150) y (if (<= z 2.9e+200) (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.8e+150) {
		tmp = y;
	} else if (z <= 2.9e+200) {
		tmp = -z;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-3.8d+150)) then
        tmp = y
    else if (z <= 2.9d+200) then
        tmp = -z
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.8e+150) {
		tmp = y;
	} else if (z <= 2.9e+200) {
		tmp = -z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.8e+150:
		tmp = y
	elif z <= 2.9e+200:
		tmp = -z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.8e+150)
		tmp = y;
	elseif (z <= 2.9e+200)
		tmp = Float64(-z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.8e+150)
		tmp = y;
	elseif (z <= 2.9e+200)
		tmp = -z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.8e+150], y, If[LessEqual[z, 2.9e+200], (-z), y]]

Derivation

1. Split input into 2 regimes

2. if z < -3.79999999999999989e150 or 2.8999999999999999e200 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-inverses N/A

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

      2. div-sub N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 43.0

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

   5. Applied rewrites 43.0%

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

   6. Taylor expanded in y around 0

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

      1. lower-/.f64 31.4

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

   8. Applied rewrites 31.4%

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

      1. associate-*l/ N/A

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

      2. associate-/l* N/A

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

      3. *-inverses N/A

         \[\leadsto y \cdot \color{blue}{1} \]

      4. *-rgt-identity 40.8

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

   10. Applied rewrites 40.8%

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

   if -3.79999999999999989e150 < z < 2.8999999999999999e200

   1. Initial program 79.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 45.9

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

   5. Applied rewrites 45.9%

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

Alternative 8: 19.1% accurate, 29.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

1. Initial program 84.4%

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

3. Taylor expanded in x around 0

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

   1. *-inverses N/A

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

   2. div-sub N/A

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

   3. associate-/r/ N/A

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

   4. lower-*.f64 N/A

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

   5. lower-/.f64 N/A

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

   6. lower--.f64 49.8

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

5. Applied rewrites 49.8%

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

6. Taylor expanded in y around 0

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

   1. lower-/.f64 13.9

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

8. Applied rewrites 13.9%

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

   1. associate-*l/ N/A

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

   2. associate-/l* N/A

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

   3. *-inverses N/A

      \[\leadsto y \cdot \color{blue}{1} \]

   4. *-rgt-identity 16.1

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

10. Applied rewrites 16.1%

    \[\leadsto \color{blue}{y} \]
11. Add Preprocessing

Developer Target 1: 94.1% 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

real(8) function code(x, y, z)
    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 2024214 
(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))))