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

Percentage Accurate: 88.6% → 98.7%

Time: 8.0s

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: 88.6% 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: 98.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-292} \lor \neg \left(t\_0 \leq 2 \cdot 10^{-214}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-z\right) \cdot x}{y} - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -5e-292) (not (<= t_0 2e-214)))
     t_0
     (- (/ (* (- z) x) y) z))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -5e-292) || !(t_0 <= 2e-214)) {
		tmp = t_0;
	} else {
		tmp = ((-z * x) / y) - 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) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-5d-292)) .or. (.not. (t_0 <= 2d-214))) then
        tmp = t_0
    else
        tmp = ((-z * x) / y) - z
    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-292) || !(t_0 <= 2e-214)) {
		tmp = t_0;
	} else {
		tmp = ((-z * x) / y) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -5e-292) or not (t_0 <= 2e-214):
		tmp = t_0
	else:
		tmp = ((-z * x) / y) - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -5e-292) || !(t_0 <= 2e-214))
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(Float64(-z) * x) / y) - z);
	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-292) || ~((t_0 <= 2e-214)))
		tmp = t_0;
	else
		tmp = ((-z * x) / y) - z;
	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[Or[LessEqual[t$95$0, -5e-292], N[Not[LessEqual[t$95$0, 2e-214]], $MachinePrecision]], t$95$0, N[(N[(N[((-z) * x), $MachinePrecision] / y), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -4.99999999999999981e-292 or 1.99999999999999983e-214 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.9%

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

   if -4.99999999999999981e-292 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 1.99999999999999983e-214

   1. Initial program 23.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. flip-+ N/A

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

      4. associate-/l/ N/A

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

      5. difference-of-squares N/A

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

      6. lift-+.f64 N/A

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

      7. associate-/l* N/A

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

      8. lower-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower--.f64 23.2

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

   4. Applied rewrites 23.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. *-inverses N/A

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

      5. lift-/.f64 23.3

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

   6. Applied rewrites 23.3%

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

   7. Taylor expanded in y around inf

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate--l- N/A

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

      7. div-add N/A

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

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

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

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

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

      12. +-commutative N/A

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

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

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

   9. Applied rewrites 100.0%

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

   10. Taylor expanded in x around inf

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

   12. Applied rewrites 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-292} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 2 \cdot 10^{-214}\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-z\right) \cdot x}{y} - z\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-34} \lor \neg \left(y \leq 2.25 \cdot 10^{-5}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y + x, \frac{y}{z}, y\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.4e-34) (not (<= y 2.25e-5)))
   (* z (- -1.0 (/ x y)))
   (+ (fma (+ y x) (/ y z) y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.4e-34) || !(y <= 2.25e-5)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = fma((y + x), (y / z), y) + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.4e-34) || !(y <= 2.25e-5))
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	else
		tmp = Float64(fma(Float64(y + x), Float64(y / z), y) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.4e-34], N[Not[LessEqual[y, 2.25e-5]], $MachinePrecision]], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y + x), $MachinePrecision] * N[(y / z), $MachinePrecision] + y), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.39999999999999998e-34 or 2.25000000000000014e-5 < y

   1. Initial program 81.8%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. div-add N/A

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

      5. distribute-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. *-inverses N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. *-commutative N/A

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

      11. mul-1-neg N/A

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

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

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

      13. associate-/l* N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

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

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. *-commutative N/A

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

      21. *-commutative N/A

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

      22. associate-/l* N/A

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

   5. Applied rewrites 74.0%

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

   if -1.39999999999999998e-34 < y < 2.25000000000000014e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 79.0

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

   5. Applied rewrites 79.0%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-34} \lor \neg \left(y \leq 2.25 \cdot 10^{-5}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y + x, \frac{y}{z}, y\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-34} \lor \neg \left(y \leq 2.25 \cdot 10^{-5}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) \cdot \left(\frac{y}{z} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.4e-34) (not (<= y 2.25e-5)))
   (* z (- -1.0 (/ x y)))
   (* (+ y x) (+ (/ y z) 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.4e-34) || !(y <= 2.25e-5)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = (y + x) * ((y / z) + 1.0);
	}
	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) :: tmp
    if ((y <= (-1.4d-34)) .or. (.not. (y <= 2.25d-5))) then
        tmp = z * ((-1.0d0) - (x / y))
    else
        tmp = (y + x) * ((y / z) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.4e-34) || !(y <= 2.25e-5)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = (y + x) * ((y / z) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.4e-34) or not (y <= 2.25e-5):
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = (y + x) * ((y / z) + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.4e-34) || !(y <= 2.25e-5))
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	else
		tmp = Float64(Float64(y + x) * Float64(Float64(y / z) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.4e-34) || ~((y <= 2.25e-5)))
		tmp = z * (-1.0 - (x / y));
	else
		tmp = (y + x) * ((y / z) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.4e-34], N[Not[LessEqual[y, 2.25e-5]], $MachinePrecision]], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + x), $MachinePrecision] * N[(N[(y / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.39999999999999998e-34 or 2.25000000000000014e-5 < y

   1. Initial program 81.8%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. div-add N/A

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

      5. distribute-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. *-inverses N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. *-commutative N/A

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

      11. mul-1-neg N/A

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

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

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

      13. associate-/l* N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

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

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. *-commutative N/A

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

      21. *-commutative N/A

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

      22. associate-/l* N/A

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

   5. Applied rewrites 74.0%

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

   if -1.39999999999999998e-34 < y < 2.25000000000000014e-5

   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. lift-+.f64 N/A

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

      3. flip-+ N/A

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

      4. associate-/l/ N/A

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

      5. difference-of-squares N/A

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

      6. lift-+.f64 N/A

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

      7. associate-/l* N/A

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

      8. lower-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower--.f64 97.3

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

   4. Applied rewrites 97.3%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 79.0

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

   7. Applied rewrites 79.0%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-34} \lor \neg \left(y \leq 2.25 \cdot 10^{-5}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) \cdot \left(\frac{y}{z} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-34} \lor \neg \left(y \leq 2.25 \cdot 10^{-5}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{z}, y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.4e-34) (not (<= y 2.25e-5)))
   (* z (- -1.0 (/ x y)))
   (fma x (/ y z) (+ y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.4e-34) || !(y <= 2.25e-5)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = fma(x, (y / z), (y + x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.4e-34) || !(y <= 2.25e-5))
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	else
		tmp = fma(x, Float64(y / z), Float64(y + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.4e-34], N[Not[LessEqual[y, 2.25e-5]], $MachinePrecision]], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision] + N[(y + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.39999999999999998e-34 or 2.25000000000000014e-5 < y

   1. Initial program 81.8%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. div-add N/A

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

      5. distribute-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. *-inverses N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. *-commutative N/A

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

      11. mul-1-neg N/A

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

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

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

      13. associate-/l* N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

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

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. *-commutative N/A

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

      21. *-commutative N/A

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

      22. associate-/l* N/A

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

   5. Applied rewrites 74.0%

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

   if -1.39999999999999998e-34 < y < 2.25000000000000014e-5

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

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. associate-+l+ N/A

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

      6. lower-+.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. metadata-eval N/A

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

      9. *-lft-identity N/A

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

      10. lower-/.f64 74.7

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

   5. Applied rewrites 74.7%

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

   7. Applied rewrites 78.9%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-34} \lor \neg \left(y \leq 2.25 \cdot 10^{-5}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{z}, y + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-34} \lor \neg \left(y \leq 230\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) \cdot 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.7e-34) (not (<= y 230.0)))
   (* z (- -1.0 (/ x y)))
   (* (+ y x) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.7e-34) || !(y <= 230.0)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = (y + x) * 1.0;
	}
	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) :: tmp
    if ((y <= (-1.7d-34)) .or. (.not. (y <= 230.0d0))) then
        tmp = z * ((-1.0d0) - (x / y))
    else
        tmp = (y + x) * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.7e-34) || !(y <= 230.0)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = (y + x) * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.7e-34) or not (y <= 230.0):
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = (y + x) * 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.7e-34) || !(y <= 230.0))
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	else
		tmp = Float64(Float64(y + x) * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.7e-34) || ~((y <= 230.0)))
		tmp = z * (-1.0 - (x / y));
	else
		tmp = (y + x) * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.7e-34], N[Not[LessEqual[y, 230.0]], $MachinePrecision]], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + x), $MachinePrecision] * 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7e-34 or 230 < y

   1. Initial program 81.5%

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

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

      5. distribute-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. *-inverses N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. *-commutative N/A

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

      11. mul-1-neg N/A

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

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

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

      13. associate-/l* N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

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

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. *-commutative N/A

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

      21. *-commutative N/A

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

      22. associate-/l* N/A

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

   5. Applied rewrites 74.4%

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

   if -1.7e-34 < y < 230

   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. lift-+.f64 N/A

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

      3. flip-+ N/A

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

      4. associate-/l/ N/A

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

      5. difference-of-squares N/A

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

      6. lift-+.f64 N/A

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

      7. associate-/l* N/A

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

      8. lower-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower--.f64 96.5

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

   4. Applied rewrites 96.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. *-inverses N/A

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

      5. lift-/.f64 99.9

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 77.7%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-34} \lor \neg \left(y \leq 230\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) \cdot 1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-34} \lor \neg \left(y \leq 230\right):\\ \;\;\;\;-\mathsf{fma}\left(\frac{z}{y}, x, z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) \cdot 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.7e-34) (not (<= y 230.0)))
   (- (fma (/ z y) x z))
   (* (+ y x) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.7e-34) || !(y <= 230.0)) {
		tmp = -fma((z / y), x, z);
	} else {
		tmp = (y + x) * 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.7e-34) || !(y <= 230.0))
		tmp = Float64(-fma(Float64(z / y), x, z));
	else
		tmp = Float64(Float64(y + x) * 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.7e-34], N[Not[LessEqual[y, 230.0]], $MachinePrecision]], (-N[(N[(z / y), $MachinePrecision] * x + z), $MachinePrecision]), N[(N[(y + x), $MachinePrecision] * 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7e-34 or 230 < y

   1. Initial program 81.5%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

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

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   5. Applied rewrites 71.9%

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

   6. Taylor expanded in y around 0

      \[\leadsto \left(-x\right) \cdot -1 \]
   7. Step-by-step derivation

   8. Applied rewrites 11.3%

      \[\leadsto \left(-x\right) \cdot -1 \]

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 72.4%

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

   if -1.7e-34 < y < 230

   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. lift-+.f64 N/A

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

      3. flip-+ N/A

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

      4. associate-/l/ N/A

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

      5. difference-of-squares N/A

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

      6. lift-+.f64 N/A

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

      7. associate-/l* N/A

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

      8. lower-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower--.f64 96.5

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

   4. Applied rewrites 96.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. *-inverses N/A

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

      5. lift-/.f64 99.9

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 77.7%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-34} \lor \neg \left(y \leq 230\right):\\ \;\;\;\;-\mathsf{fma}\left(\frac{z}{y}, x, z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) \cdot 1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+24}:\\ \;\;\;\;-\mathsf{fma}\left(\frac{z}{y}, z, z\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+108}:\\ \;\;\;\;\left(y + x\right) \cdot 1\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.6e+24)
   (- (fma (/ z y) z z))
   (if (<= y 3.2e+108) (* (+ y x) 1.0) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.6e+24) {
		tmp = -fma((z / y), z, z);
	} else if (y <= 3.2e+108) {
		tmp = (y + x) * 1.0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.6e+24)
		tmp = Float64(-fma(Float64(z / y), z, z));
	elseif (y <= 3.2e+108)
		tmp = Float64(Float64(y + x) * 1.0);
	else
		tmp = Float64(-z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.6e+24], (-N[(N[(z / y), $MachinePrecision] * z + z), $MachinePrecision]), If[LessEqual[y, 3.2e+108], N[(N[(y + x), $MachinePrecision] * 1.0), $MachinePrecision], (-z)]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5999999999999998e24

   1. Initial program 79.6%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. flip-+ N/A

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

      4. associate-/l/ N/A

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

      5. difference-of-squares N/A

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

      6. lift-+.f64 N/A

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

      7. associate-/l* N/A

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

      8. lower-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower--.f64 56.8

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

   4. Applied rewrites 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. *-inverses N/A

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

      5. lift-/.f64 79.5

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

   6. Applied rewrites 79.5%

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

   7. Taylor expanded in y around inf

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate--l- N/A

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

      7. div-add N/A

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

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

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

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

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

      12. +-commutative N/A

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

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

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

   9. Applied rewrites 72.8%

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

   10. Taylor expanded in x around 0

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

   12. Applied rewrites 65.0%

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

   if -6.5999999999999998e24 < y < 3.1999999999999999e108

   1. Initial program 98.7%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. flip-+ N/A

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

      4. associate-/l/ N/A

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

      5. difference-of-squares N/A

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

      6. lift-+.f64 N/A

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

      7. associate-/l* N/A

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

      8. lower-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower--.f64 94.9

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

   4. Applied rewrites 94.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. *-inverses N/A

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

      5. lift-/.f64 98.6

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

   6. Applied rewrites 98.6%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 69.6%

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

   if 3.1999999999999999e108 < y

   1. Initial program 72.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 63.0

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

   5. Applied rewrites 63.0%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+24}:\\ \;\;\;\;-\mathsf{fma}\left(\frac{z}{y}, z, z\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+108}:\\ \;\;\;\;\left(y + x\right) \cdot 1\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+24} \lor \neg \left(y \leq 3.2 \cdot 10^{+108}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) \cdot 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.6e+24) (not (<= y 3.2e+108))) (- z) (* (+ y x) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.6e+24) || !(y <= 3.2e+108)) {
		tmp = -z;
	} else {
		tmp = (y + x) * 1.0;
	}
	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) :: tmp
    if ((y <= (-6.6d+24)) .or. (.not. (y <= 3.2d+108))) then
        tmp = -z
    else
        tmp = (y + x) * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.6e+24) || !(y <= 3.2e+108)) {
		tmp = -z;
	} else {
		tmp = (y + x) * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.6e+24) or not (y <= 3.2e+108):
		tmp = -z
	else:
		tmp = (y + x) * 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.6e+24) || !(y <= 3.2e+108))
		tmp = Float64(-z);
	else
		tmp = Float64(Float64(y + x) * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.6e+24) || ~((y <= 3.2e+108)))
		tmp = -z;
	else
		tmp = (y + x) * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.6e+24], N[Not[LessEqual[y, 3.2e+108]], $MachinePrecision]], (-z), N[(N[(y + x), $MachinePrecision] * 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5999999999999998e24 or 3.1999999999999999e108 < y

   1. Initial program 76.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 63.9

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

   5. Applied rewrites 63.9%

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

   if -6.5999999999999998e24 < y < 3.1999999999999999e108

   1. Initial program 98.7%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. flip-+ N/A

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

      4. associate-/l/ N/A

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

      5. difference-of-squares N/A

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

      6. lift-+.f64 N/A

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

      7. associate-/l* N/A

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

      8. lower-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower--.f64 94.9

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

   4. Applied rewrites 94.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. *-inverses N/A

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

      5. lift-/.f64 98.6

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

   6. Applied rewrites 98.6%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 69.6%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+24} \lor \neg \left(y \leq 3.2 \cdot 10^{+108}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) \cdot 1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{-36} \lor \neg \left(y \leq 7.5 \cdot 10^{-53}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.9e-36) (not (<= y 7.5e-53))) (- z) (* (- x) -1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.9e-36) || !(y <= 7.5e-53)) {
		tmp = -z;
	} else {
		tmp = -x * -1.0;
	}
	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) :: tmp
    if ((y <= (-4.9d-36)) .or. (.not. (y <= 7.5d-53))) then
        tmp = -z
    else
        tmp = -x * (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.9e-36) || !(y <= 7.5e-53)) {
		tmp = -z;
	} else {
		tmp = -x * -1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.9e-36) or not (y <= 7.5e-53):
		tmp = -z
	else:
		tmp = -x * -1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.9e-36) || !(y <= 7.5e-53))
		tmp = Float64(-z);
	else
		tmp = Float64(Float64(-x) * -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.9e-36) || ~((y <= 7.5e-53)))
		tmp = -z;
	else
		tmp = -x * -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.9e-36], N[Not[LessEqual[y, 7.5e-53]], $MachinePrecision]], (-z), N[((-x) * -1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8999999999999997e-36 or 7.5000000000000001e-53 < y

   1. Initial program 83.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 51.7

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

   5. Applied rewrites 51.7%

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

   if -4.8999999999999997e-36 < y < 7.5000000000000001e-53

   1. Initial program 99.9%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

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

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in y around 0

      \[\leadsto \left(-x\right) \cdot -1 \]
   7. Step-by-step derivation

   8. Applied rewrites 70.0%

      \[\leadsto \left(-x\right) \cdot -1 \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{-36} \lor \neg \left(y \leq 7.5 \cdot 10^{-53}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot -1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.1% 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 90.0%

   \[\frac{x + y}{1 - \frac{y}{z}} \]
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 34.4

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

5. Applied rewrites 34.4%

   \[\leadsto \color{blue}{-z} \]
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 2024337 
(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))))