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

Percentage Accurate: 88.0% → 99.8%

Time: 6.2s

Alternatives: 10

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: 88.0% 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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y + x}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-271}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ y x) (- 1.0 (/ y z)))))
   (if (<= t_0 -2e-271) t_0 (if (<= t_0 0.0) (* (- -1.0 (/ x y)) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y + x) / (1.0 - (y / z));
	double tmp;
	if (t_0 <= -2e-271) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (-1.0 - (x / 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) / (1.0d0 - (y / z))
    if (t_0 <= (-2d-271)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = ((-1.0d0) - (x / 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) / (1.0 - (y / z));
	double tmp;
	if (t_0 <= -2e-271) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (-1.0 - (x / y)) * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y + x) / (1.0 - (y / z))
	tmp = 0
	if t_0 <= -2e-271:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = (-1.0 - (x / y)) * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y + x) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (t_0 <= -2e-271)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(-1.0 - Float64(x / y)) * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y + x) / (1.0 - (y / z));
	tmp = 0.0;
	if (t_0 <= -2e-271)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = (-1.0 - (x / y)) * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y + x), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e-271], t$95$0, If[LessEqual[t$95$0, 0.0], N[(N[(-1.0 - N[(x / y), $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))) < -1.99999999999999993e-271 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 -1.99999999999999993e-271 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 6.6%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-sub0 N/A

         \[\leadsto \color{blue}{\left(0 - \frac{x + y}{y}\right)} \cdot z \]

      7. +-commutative N/A

         \[\leadsto \left(0 - \frac{\color{blue}{y + x}}{y}\right) \cdot z \]

      8. div-add N/A

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y}{y} + \frac{x}{y}\right)}\right) \cdot z \]

      9. *-inverses N/A

         \[\leadsto \left(0 - \left(\color{blue}{1} + \frac{x}{y}\right)\right) \cdot z \]

      10. associate--r+ N/A

          \[\leadsto \color{blue}{\left(\left(0 - 1\right) - \frac{x}{y}\right)} \cdot z \]

      11. metadata-eval N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y + x}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-271}:\\ \;\;\;\;\frac{y + x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;\frac{y + x}{1 - \frac{y}{z}} \leq 0:\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 65.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -\mathsf{fma}\left(\frac{z}{y}, z, z\right)\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+86}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-79}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{-x}{y} \cdot z\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+107}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fma (/ z y) z z))))
   (if (<= y -1.55e+86)
     t_0
     (if (<= y 1.45e-79)
       (+ y x)
       (if (<= y 5.2e-14)
         (* (/ (- x) y) z)
         (if (<= y 2.2e+107) (+ y x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -fma((z / y), z, z);
	double tmp;
	if (y <= -1.55e+86) {
		tmp = t_0;
	} else if (y <= 1.45e-79) {
		tmp = y + x;
	} else if (y <= 5.2e-14) {
		tmp = (-x / y) * z;
	} else if (y <= 2.2e+107) {
		tmp = y + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(-fma(Float64(z / y), z, z))
	tmp = 0.0
	if (y <= -1.55e+86)
		tmp = t_0;
	elseif (y <= 1.45e-79)
		tmp = Float64(y + x);
	elseif (y <= 5.2e-14)
		tmp = Float64(Float64(Float64(-x) / y) * z);
	elseif (y <= 2.2e+107)
		tmp = Float64(y + x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = (-N[(N[(z / y), $MachinePrecision] * z + z), $MachinePrecision])}, If[LessEqual[y, -1.55e+86], t$95$0, If[LessEqual[y, 1.45e-79], N[(y + x), $MachinePrecision], If[LessEqual[y, 5.2e-14], N[(N[((-x) / y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[y, 2.2e+107], N[(y + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5500000000000001e86 or 2.2e107 < y

   1. Initial program 70.4%

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

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

      2. unsub-neg N/A

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

      3. associate--l- N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. div-add N/A

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

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

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

      8. unsub-neg N/A

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

      9. mul-1-neg N/A

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

      10. distribute-neg-out N/A

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

      11. lower-neg.f64 N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 76.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 70.0%

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

   if -1.5500000000000001e86 < y < 1.45e-79 or 5.19999999999999993e-14 < y < 2.2e107

   1. Initial program 99.3%

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

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

      2. unsub-neg N/A

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

      3. associate--l- N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. div-add N/A

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

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

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

      8. unsub-neg N/A

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

      9. mul-1-neg N/A

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

      10. distribute-neg-out N/A

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

      11. lower-neg.f64 N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 27.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 14.0%

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

   9. Taylor expanded in x around inf

      \[\leadsto -\frac{x \cdot z}{y} \]
   10. Step-by-step derivation

   11. Applied rewrites 15.9%

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

   12. Taylor expanded in z around inf

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

       1. lower-+.f64 72.8

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

   14. Applied rewrites 72.8%

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

   if 1.45e-79 < y < 5.19999999999999993e-14

   1. Initial program 99.7%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-sub0 N/A

         \[\leadsto \color{blue}{\left(0 - \frac{x + y}{y}\right)} \cdot z \]

      7. +-commutative N/A

         \[\leadsto \left(0 - \frac{\color{blue}{y + x}}{y}\right) \cdot z \]

      8. div-add N/A

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y}{y} + \frac{x}{y}\right)}\right) \cdot z \]

      9. *-inverses N/A

         \[\leadsto \left(0 - \left(\color{blue}{1} + \frac{x}{y}\right)\right) \cdot z \]

      10. associate--r+ N/A

          \[\leadsto \color{blue}{\left(\left(0 - 1\right) - \frac{x}{y}\right)} \cdot z \]

      11. metadata-eval N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 77.4

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

   5. Applied rewrites 77.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 76.5%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+86}:\\ \;\;\;\;-\mathsf{fma}\left(\frac{z}{y}, z, z\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-79}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{-x}{y} \cdot z\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+107}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;-\mathsf{fma}\left(\frac{z}{y}, z, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+86}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-79}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{-x}{y} \cdot z\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+107}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.55e+86)
   (- z)
   (if (<= y 1.45e-79)
     (+ y x)
     (if (<= y 5.2e-14)
       (* (/ (- x) y) z)
       (if (<= y 2.2e+107) (+ y x) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.55e+86) {
		tmp = -z;
	} else if (y <= 1.45e-79) {
		tmp = y + x;
	} else if (y <= 5.2e-14) {
		tmp = (-x / y) * z;
	} else if (y <= 2.2e+107) {
		tmp = y + x;
	} 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 <= (-1.55d+86)) then
        tmp = -z
    else if (y <= 1.45d-79) then
        tmp = y + x
    else if (y <= 5.2d-14) then
        tmp = (-x / y) * z
    else if (y <= 2.2d+107) then
        tmp = y + x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.55e+86) {
		tmp = -z;
	} else if (y <= 1.45e-79) {
		tmp = y + x;
	} else if (y <= 5.2e-14) {
		tmp = (-x / y) * z;
	} else if (y <= 2.2e+107) {
		tmp = y + x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.55e+86:
		tmp = -z
	elif y <= 1.45e-79:
		tmp = y + x
	elif y <= 5.2e-14:
		tmp = (-x / y) * z
	elif y <= 2.2e+107:
		tmp = y + x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.55e+86)
		tmp = Float64(-z);
	elseif (y <= 1.45e-79)
		tmp = Float64(y + x);
	elseif (y <= 5.2e-14)
		tmp = Float64(Float64(Float64(-x) / y) * z);
	elseif (y <= 2.2e+107)
		tmp = Float64(y + x);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.55e+86)
		tmp = -z;
	elseif (y <= 1.45e-79)
		tmp = y + x;
	elseif (y <= 5.2e-14)
		tmp = (-x / y) * z;
	elseif (y <= 2.2e+107)
		tmp = y + x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.55e+86], (-z), If[LessEqual[y, 1.45e-79], N[(y + x), $MachinePrecision], If[LessEqual[y, 5.2e-14], N[(N[((-x) / y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[y, 2.2e+107], N[(y + x), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5500000000000001e86 or 2.2e107 < y

   1. Initial program 70.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 69.8

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

   5. Applied rewrites 69.8%

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

   if -1.5500000000000001e86 < y < 1.45e-79 or 5.19999999999999993e-14 < y < 2.2e107

   1. Initial program 99.3%

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

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

      2. unsub-neg N/A

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

      3. associate--l- N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. div-add N/A

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

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

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

      8. unsub-neg N/A

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

      9. mul-1-neg N/A

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

      10. distribute-neg-out N/A

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

      11. lower-neg.f64 N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 27.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 14.0%

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

   9. Taylor expanded in x around inf

      \[\leadsto -\frac{x \cdot z}{y} \]
   10. Step-by-step derivation

   11. Applied rewrites 15.9%

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

   12. Taylor expanded in z around inf

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

       1. lower-+.f64 72.8

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

   14. Applied rewrites 72.8%

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

   if 1.45e-79 < y < 5.19999999999999993e-14

   1. Initial program 99.7%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-sub0 N/A

         \[\leadsto \color{blue}{\left(0 - \frac{x + y}{y}\right)} \cdot z \]

      7. +-commutative N/A

         \[\leadsto \left(0 - \frac{\color{blue}{y + x}}{y}\right) \cdot z \]

      8. div-add N/A

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y}{y} + \frac{x}{y}\right)}\right) \cdot z \]

      9. *-inverses N/A

         \[\leadsto \left(0 - \left(\color{blue}{1} + \frac{x}{y}\right)\right) \cdot z \]

      10. associate--r+ N/A

          \[\leadsto \color{blue}{\left(\left(0 - 1\right) - \frac{x}{y}\right)} \cdot z \]

      11. metadata-eval N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 77.4

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

   5. Applied rewrites 77.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 76.5%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+86}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-79}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{-x}{y} \cdot z\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+107}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+86}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-79}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{-z}{y} \cdot x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+107}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.55e+86)
   (- z)
   (if (<= y 1.45e-79)
     (+ y x)
     (if (<= y 5.2e-14)
       (* (/ (- z) y) x)
       (if (<= y 2.2e+107) (+ y x) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.55e+86) {
		tmp = -z;
	} else if (y <= 1.45e-79) {
		tmp = y + x;
	} else if (y <= 5.2e-14) {
		tmp = (-z / y) * x;
	} else if (y <= 2.2e+107) {
		tmp = y + x;
	} 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 <= (-1.55d+86)) then
        tmp = -z
    else if (y <= 1.45d-79) then
        tmp = y + x
    else if (y <= 5.2d-14) then
        tmp = (-z / y) * x
    else if (y <= 2.2d+107) then
        tmp = y + x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.55e+86) {
		tmp = -z;
	} else if (y <= 1.45e-79) {
		tmp = y + x;
	} else if (y <= 5.2e-14) {
		tmp = (-z / y) * x;
	} else if (y <= 2.2e+107) {
		tmp = y + x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.55e+86:
		tmp = -z
	elif y <= 1.45e-79:
		tmp = y + x
	elif y <= 5.2e-14:
		tmp = (-z / y) * x
	elif y <= 2.2e+107:
		tmp = y + x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.55e+86)
		tmp = Float64(-z);
	elseif (y <= 1.45e-79)
		tmp = Float64(y + x);
	elseif (y <= 5.2e-14)
		tmp = Float64(Float64(Float64(-z) / y) * x);
	elseif (y <= 2.2e+107)
		tmp = Float64(y + x);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.55e+86)
		tmp = -z;
	elseif (y <= 1.45e-79)
		tmp = y + x;
	elseif (y <= 5.2e-14)
		tmp = (-z / y) * x;
	elseif (y <= 2.2e+107)
		tmp = y + x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.55e+86], (-z), If[LessEqual[y, 1.45e-79], N[(y + x), $MachinePrecision], If[LessEqual[y, 5.2e-14], N[(N[((-z) / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 2.2e+107], N[(y + x), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5500000000000001e86 or 2.2e107 < y

   1. Initial program 70.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 69.8

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

   5. Applied rewrites 69.8%

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

   if -1.5500000000000001e86 < y < 1.45e-79 or 5.19999999999999993e-14 < y < 2.2e107

   1. Initial program 99.3%

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

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

      2. unsub-neg N/A

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

      3. associate--l- N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. div-add N/A

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

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

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

      8. unsub-neg N/A

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

      9. mul-1-neg N/A

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

      10. distribute-neg-out N/A

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

      11. lower-neg.f64 N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 27.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 14.0%

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

   9. Taylor expanded in x around inf

      \[\leadsto -\frac{x \cdot z}{y} \]
   10. Step-by-step derivation

   11. Applied rewrites 15.9%

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

   12. Taylor expanded in z around inf

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

       1. lower-+.f64 72.8

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

   14. Applied rewrites 72.8%

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

   if 1.45e-79 < y < 5.19999999999999993e-14

   1. Initial program 99.7%

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

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

      2. unsub-neg N/A

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

      3. associate--l- N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. div-add N/A

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

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

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

      8. unsub-neg N/A

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

      9. mul-1-neg N/A

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

      10. distribute-neg-out N/A

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

      11. lower-neg.f64 N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 77.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 76.5%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+86}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-79}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{-z}{y} \cdot x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+107}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-43}:\\ \;\;\;\;\left(1 + \frac{y}{z}\right) \cdot \left(y + x\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-5}:\\ \;\;\;\;-\frac{\left(\left(z + x\right) + y\right) \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, x\right) + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.8e-43)
   (* (+ 1.0 (/ y z)) (+ y x))
   (if (<= z 1.02e-5) (- (/ (* (+ (+ z x) y) z) y)) (+ (fma (/ x z) y x) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.8e-43) {
		tmp = (1.0 + (y / z)) * (y + x);
	} else if (z <= 1.02e-5) {
		tmp = -((((z + x) + y) * z) / y);
	} else {
		tmp = fma((x / z), y, x) + y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.8e-43)
		tmp = Float64(Float64(1.0 + Float64(y / z)) * Float64(y + x));
	elseif (z <= 1.02e-5)
		tmp = Float64(-Float64(Float64(Float64(Float64(z + x) + y) * z) / y));
	else
		tmp = Float64(fma(Float64(x / z), y, x) + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.8e-43], N[(N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision] * N[(y + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e-5], (-N[(N[(N[(N[(z + x), $MachinePrecision] + y), $MachinePrecision] * z), $MachinePrecision] / y), $MachinePrecision]), N[(N[(N[(x / z), $MachinePrecision] * y + x), $MachinePrecision] + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7999999999999999e-43

   1. Initial program 99.9%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. inv-pow N/A

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

      6. lower-pow.f64 99.8

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 81.6

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

   7. Applied rewrites 81.6%

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

   if -1.7999999999999999e-43 < z < 1.0200000000000001e-5

   1. Initial program 80.6%

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

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

      2. unsub-neg N/A

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

      3. associate--l- N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. div-add N/A

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

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

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

      8. unsub-neg N/A

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

      9. mul-1-neg N/A

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

      10. distribute-neg-out N/A

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

      11. lower-neg.f64 N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 73.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 42.9%

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

   9. Taylor expanded in x around inf

      \[\leadsto -\frac{x \cdot z}{y} \]
   10. Step-by-step derivation

   11. Applied rewrites 34.4%

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

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 74.7%

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

   if 1.0200000000000001e-5 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. associate-+l+ N/A

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

      6. lower-+.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. remove-double-neg N/A

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

      10. lower-/.f64 78.7

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

   5. Applied rewrites 78.7%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-43}:\\ \;\;\;\;\left(1 + \frac{y}{z}\right) \cdot \left(y + x\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-5}:\\ \;\;\;\;-\frac{\left(\left(z + x\right) + y\right) \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, x\right) + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-43}:\\ \;\;\;\;\left(1 + \frac{y}{z}\right) \cdot \left(y + x\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-5}:\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, x\right) + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.8e-43)
   (* (+ 1.0 (/ y z)) (+ y x))
   (if (<= z 1.02e-5) (* (- -1.0 (/ x y)) z) (+ (fma (/ x z) y x) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.8e-43) {
		tmp = (1.0 + (y / z)) * (y + x);
	} else if (z <= 1.02e-5) {
		tmp = (-1.0 - (x / y)) * z;
	} else {
		tmp = fma((x / z), y, x) + y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.8e-43)
		tmp = Float64(Float64(1.0 + Float64(y / z)) * Float64(y + x));
	elseif (z <= 1.02e-5)
		tmp = Float64(Float64(-1.0 - Float64(x / y)) * z);
	else
		tmp = Float64(fma(Float64(x / z), y, x) + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.8e-43], N[(N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision] * N[(y + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e-5], N[(N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[(N[(x / z), $MachinePrecision] * y + x), $MachinePrecision] + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7999999999999999e-43

   1. Initial program 99.9%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. inv-pow N/A

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

      6. lower-pow.f64 99.8

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 81.6

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

   7. Applied rewrites 81.6%

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

   if -1.7999999999999999e-43 < z < 1.0200000000000001e-5

   1. Initial program 80.6%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-sub0 N/A

         \[\leadsto \color{blue}{\left(0 - \frac{x + y}{y}\right)} \cdot z \]

      7. +-commutative N/A

         \[\leadsto \left(0 - \frac{\color{blue}{y + x}}{y}\right) \cdot z \]

      8. div-add N/A

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y}{y} + \frac{x}{y}\right)}\right) \cdot z \]

      9. *-inverses N/A

         \[\leadsto \left(0 - \left(\color{blue}{1} + \frac{x}{y}\right)\right) \cdot z \]

      10. associate--r+ N/A

          \[\leadsto \color{blue}{\left(\left(0 - 1\right) - \frac{x}{y}\right)} \cdot z \]

      11. metadata-eval N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 73.9

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

   5. Applied rewrites 73.9%

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

   if 1.0200000000000001e-5 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. associate-+l+ N/A

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

      6. lower-+.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. remove-double-neg N/A

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

      10. lower-/.f64 78.7

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

   5. Applied rewrites 78.7%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-43}:\\ \;\;\;\;\left(1 + \frac{y}{z}\right) \cdot \left(y + x\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-5}:\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, x\right) + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\frac{x}{z}, y, x\right) + y\\ \mathbf{if}\;z \leq -2.65 \cdot 10^{-42}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-5}:\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (fma (/ x z) y x) y)))
   (if (<= z -2.65e-42) t_0 (if (<= z 1.02e-5) (* (- -1.0 (/ x y)) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma((x / z), y, x) + y;
	double tmp;
	if (z <= -2.65e-42) {
		tmp = t_0;
	} else if (z <= 1.02e-5) {
		tmp = (-1.0 - (x / y)) * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(fma(Float64(x / z), y, x) + y)
	tmp = 0.0
	if (z <= -2.65e-42)
		tmp = t_0;
	elseif (z <= 1.02e-5)
		tmp = Float64(Float64(-1.0 - Float64(x / y)) * z);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x / z), $MachinePrecision] * y + x), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[z, -2.65e-42], t$95$0, If[LessEqual[z, 1.02e-5], N[(N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.65e-42 or 1.0200000000000001e-5 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. associate-+l+ N/A

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

      6. lower-+.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. remove-double-neg N/A

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

      10. lower-/.f64 79.9

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

   5. Applied rewrites 79.9%

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

   if -2.65e-42 < z < 1.0200000000000001e-5

   1. Initial program 80.6%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-sub0 N/A

         \[\leadsto \color{blue}{\left(0 - \frac{x + y}{y}\right)} \cdot z \]

      7. +-commutative N/A

         \[\leadsto \left(0 - \frac{\color{blue}{y + x}}{y}\right) \cdot z \]

      8. div-add N/A

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y}{y} + \frac{x}{y}\right)}\right) \cdot z \]

      9. *-inverses N/A

         \[\leadsto \left(0 - \left(\color{blue}{1} + \frac{x}{y}\right)\right) \cdot z \]

      10. associate--r+ N/A

          \[\leadsto \color{blue}{\left(\left(0 - 1\right) - \frac{x}{y}\right)} \cdot z \]

      11. metadata-eval N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 73.9

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

   5. Applied rewrites 73.9%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-42}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, x\right) + y\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-5}:\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, x\right) + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-43}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-5}:\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.8e-43)
   (+ y x)
   (if (<= z 1.02e-5) (* (- -1.0 (/ x y)) z) (+ y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.8e-43) {
		tmp = y + x;
	} else if (z <= 1.02e-5) {
		tmp = (-1.0 - (x / y)) * z;
	} else {
		tmp = y + x;
	}
	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 <= (-1.8d-43)) then
        tmp = y + x
    else if (z <= 1.02d-5) then
        tmp = ((-1.0d0) - (x / y)) * 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 (z <= -1.8e-43) {
		tmp = y + x;
	} else if (z <= 1.02e-5) {
		tmp = (-1.0 - (x / y)) * z;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.8e-43:
		tmp = y + x
	elif z <= 1.02e-5:
		tmp = (-1.0 - (x / y)) * z
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.8e-43)
		tmp = Float64(y + x);
	elseif (z <= 1.02e-5)
		tmp = Float64(Float64(-1.0 - Float64(x / y)) * z);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.8e-43)
		tmp = y + x;
	elseif (z <= 1.02e-5)
		tmp = (-1.0 - (x / y)) * z;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.8e-43], N[(y + x), $MachinePrecision], If[LessEqual[z, 1.02e-5], N[(N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7999999999999999e-43 or 1.0200000000000001e-5 < z

   1. Initial program 99.9%

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

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

      2. unsub-neg N/A

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

      3. associate--l- N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. div-add N/A

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

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

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

      8. unsub-neg N/A

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

      9. mul-1-neg N/A

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

      10. distribute-neg-out N/A

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

      11. lower-neg.f64 N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 19.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 17.9%

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

   9. Taylor expanded in x around inf

      \[\leadsto -\frac{x \cdot z}{y} \]
   10. Step-by-step derivation

   11. Applied rewrites 4.2%

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

   12. Taylor expanded in z around inf

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

       1. lower-+.f64 79.4

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

   14. Applied rewrites 79.4%

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

   if -1.7999999999999999e-43 < z < 1.0200000000000001e-5

   1. Initial program 80.6%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-sub0 N/A

         \[\leadsto \color{blue}{\left(0 - \frac{x + y}{y}\right)} \cdot z \]

      7. +-commutative N/A

         \[\leadsto \left(0 - \frac{\color{blue}{y + x}}{y}\right) \cdot z \]

      8. div-add N/A

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y}{y} + \frac{x}{y}\right)}\right) \cdot z \]

      9. *-inverses N/A

         \[\leadsto \left(0 - \left(\color{blue}{1} + \frac{x}{y}\right)\right) \cdot z \]

      10. associate--r+ N/A

          \[\leadsto \color{blue}{\left(\left(0 - 1\right) - \frac{x}{y}\right)} \cdot z \]

      11. metadata-eval N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 73.9

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

   5. Applied rewrites 73.9%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-43}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-5}:\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+86}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+107}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.55e+86) (- z) (if (<= y 2.2e+107) (+ y x) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.55e+86) {
		tmp = -z;
	} else if (y <= 2.2e+107) {
		tmp = y + x;
	} 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 <= (-1.55d+86)) then
        tmp = -z
    else if (y <= 2.2d+107) then
        tmp = y + x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.55e+86) {
		tmp = -z;
	} else if (y <= 2.2e+107) {
		tmp = y + x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.55e+86:
		tmp = -z
	elif y <= 2.2e+107:
		tmp = y + x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.55e+86)
		tmp = Float64(-z);
	elseif (y <= 2.2e+107)
		tmp = Float64(y + x);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.55e+86)
		tmp = -z;
	elseif (y <= 2.2e+107)
		tmp = y + x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.55e+86], (-z), If[LessEqual[y, 2.2e+107], N[(y + x), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5500000000000001e86 or 2.2e107 < y

   1. Initial program 70.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 69.8

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

   5. Applied rewrites 69.8%

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

   if -1.5500000000000001e86 < y < 2.2e107

   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. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. associate--l- N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. div-add N/A

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

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

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

      8. unsub-neg N/A

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

      9. mul-1-neg N/A

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

      10. distribute-neg-out N/A

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

      11. lower-neg.f64 N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 31.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 13.1%

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

   9. Taylor expanded in x around inf

      \[\leadsto -\frac{x \cdot z}{y} \]
   10. Step-by-step derivation

   11. Applied rewrites 20.9%

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

   12. Taylor expanded in z around inf

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

       1. lower-+.f64 68.7

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

   14. Applied rewrites 68.7%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+86}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+107}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 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

real(8) function code(x, y, z)
    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 91.1%

   \[\frac{x + y}{1 - \frac{y}{z}} \]
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 29.7

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

5. Applied rewrites 29.7%

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

Developer Target 1: 93.7% 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 2024298 
(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))))