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

Percentage Accurate: 87.9% → 99.8%

Time: 8.3s

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: 87.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-302}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\frac{0 - z \cdot \left(x + y\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (<= t_0 -5e-302)
     t_0
     (if (<= t_0 0.0) (/ (- 0.0 (* z (+ x y))) y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if (t_0 <= -5e-302) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (0.0 - (z * (x + y))) / y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if (t_0 <= (-5d-302)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = (0.0d0 - (z * (x + y))) / y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if (t_0 <= -5e-302) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (0.0 - (z * (x + y))) / y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if t_0 <= -5e-302:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = (0.0 - (z * (x + y))) / y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (t_0 <= -5e-302)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(0.0 - Float64(z * Float64(x + y))) / y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if (t_0 <= -5e-302)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = (0.0 - (z * (x + y))) / y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e-302], t$95$0, If[LessEqual[t$95$0, 0.0], N[(N[(0.0 - N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $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))) < -5.00000000000000033e-302 or 0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.9%

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

   if -5.00000000000000033e-302 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 0.0

   1. Initial program 6.1%

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

   3. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot \left(z \cdot \left(x + y\right)\right)\right), \color{blue}{y}\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(z \cdot \left(x + y\right)\right)\right), y\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(x + y\right)\right)\right)\right), y\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot \left(-1 \cdot \left(x + y\right)\right)\right), y\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(x + y\right)\right)\right), y\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(x + y\right)\right)\right)\right), y\right) \]

      8. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(0 - \left(x + y\right)\right)\right), y\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(0, \left(x + y\right)\right)\right), y\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(0, \left(y + x\right)\right)\right), y\right) \]

      11. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(y, x\right)\right)\right), y\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{z \cdot \left(0 - \left(y + x\right)\right)}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-302}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;\frac{x + y}{1 - \frac{y}{z}} \leq 0:\\ \;\;\;\;\frac{0 - z \cdot \left(x + y\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ t_1 := 1 - \frac{y}{z}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{-54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-296}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{1}{t\_1}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+44}:\\ \;\;\;\;\frac{y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))) (t_1 (- 1.0 (/ y z))))
   (if (<= y -4.6e-54)
     t_0
     (if (<= y -2e-296)
       (+ x y)
       (if (<= y 8.2e-38)
         (* x (/ 1.0 t_1))
         (if (<= y 2.75e+44) (/ y t_1) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double t_1 = 1.0 - (y / z);
	double tmp;
	if (y <= -4.6e-54) {
		tmp = t_0;
	} else if (y <= -2e-296) {
		tmp = x + y;
	} else if (y <= 8.2e-38) {
		tmp = x * (1.0 / t_1);
	} else if (y <= 2.75e+44) {
		tmp = y / t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = z * ((-1.0d0) - (x / y))
    t_1 = 1.0d0 - (y / z)
    if (y <= (-4.6d-54)) then
        tmp = t_0
    else if (y <= (-2d-296)) then
        tmp = x + y
    else if (y <= 8.2d-38) then
        tmp = x * (1.0d0 / t_1)
    else if (y <= 2.75d+44) then
        tmp = y / t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double t_1 = 1.0 - (y / z);
	double tmp;
	if (y <= -4.6e-54) {
		tmp = t_0;
	} else if (y <= -2e-296) {
		tmp = x + y;
	} else if (y <= 8.2e-38) {
		tmp = x * (1.0 / t_1);
	} else if (y <= 2.75e+44) {
		tmp = y / t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	t_1 = 1.0 - (y / z)
	tmp = 0
	if y <= -4.6e-54:
		tmp = t_0
	elif y <= -2e-296:
		tmp = x + y
	elif y <= 8.2e-38:
		tmp = x * (1.0 / t_1)
	elif y <= 2.75e+44:
		tmp = y / t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-1.0 - Float64(x / y)))
	t_1 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if (y <= -4.6e-54)
		tmp = t_0;
	elseif (y <= -2e-296)
		tmp = Float64(x + y);
	elseif (y <= 8.2e-38)
		tmp = Float64(x * Float64(1.0 / t_1));
	elseif (y <= 2.75e+44)
		tmp = Float64(y / t_1);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-1.0 - (x / y));
	t_1 = 1.0 - (y / z);
	tmp = 0.0;
	if (y <= -4.6e-54)
		tmp = t_0;
	elseif (y <= -2e-296)
		tmp = x + y;
	elseif (y <= 8.2e-38)
		tmp = x * (1.0 / t_1);
	elseif (y <= 2.75e+44)
		tmp = y / t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e-54], t$95$0, If[LessEqual[y, -2e-296], N[(x + y), $MachinePrecision], If[LessEqual[y, 8.2e-38], N[(x * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.75e+44], N[(y / t$95$1), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.5999999999999998e-54 or 2.75e44 < y

   1. Initial program 75.6%

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

      5. distribute-frac-neg N/A

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

      6. mul-1-neg N/A

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

      7. div-sub N/A

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

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), \left(\frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y}\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(0 - z\right), \left(\frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(x \cdot z - -1 \cdot {z}^{2}\right), \color{blue}{y}\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}\right), y\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(x \cdot z + 1 \cdot {z}^{2}\right), y\right)\right) \]

      15. *-lft-identity N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(x \cdot z + {z}^{2}\right), y\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left({z}^{2} + x \cdot z\right), y\right)\right) \]

      17. unpow2 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(z \cdot z + x \cdot z\right), y\right)\right) \]

      18. distribute-rgt-out N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(z \cdot \left(z + x\right)\right), y\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(z + x\right)\right), y\right)\right) \]

      20. +-lowering-+.f64 71.8%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, x\right)\right), y\right)\right) \]

   5. Simplified 71.8%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

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

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(\left(1 + \frac{x}{y}\right)\right)\right)}\right) \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y}\right)\right)}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(-1 + \left(\mathsf{neg}\left(\color{blue}{\frac{x}{y}}\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(-1 - \color{blue}{\frac{x}{y}}\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(-1, \color{blue}{\left(\frac{x}{y}\right)}\right)\right) \]

      8. /-lowering-/.f64 74.4%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(-1, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 74.4%

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

   if -4.5999999999999998e-54 < y < -2e-296

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 82.1%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 82.1%

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

   if -2e-296 < y < 8.1999999999999996e-38

   1. Initial program 99.9%

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

      1. div-inv N/A

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

      2. flip3-- N/A

         \[\leadsto \left(x + y\right) \cdot \frac{1}{\frac{{1}^{3} - {\left(\frac{y}{z}\right)}^{3}}{\color{blue}{1 \cdot 1 + \left(\frac{y}{z} \cdot \frac{y}{z} + 1 \cdot \frac{y}{z}\right)}}} \]

      3. clear-num N/A

         \[\leadsto \left(x + y\right) \cdot \frac{1 \cdot 1 + \left(\frac{y}{z} \cdot \frac{y}{z} + 1 \cdot \frac{y}{z}\right)}{\color{blue}{{1}^{3} - {\left(\frac{y}{z}\right)}^{3}}} \]

      4. *-commutative N/A

         \[\leadsto \frac{1 \cdot 1 + \left(\frac{y}{z} \cdot \frac{y}{z} + 1 \cdot \frac{y}{z}\right)}{{1}^{3} - {\left(\frac{y}{z}\right)}^{3}} \cdot \color{blue}{\left(x + y\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1 \cdot 1 + \left(\frac{y}{z} \cdot \frac{y}{z} + 1 \cdot \frac{y}{z}\right)}{{1}^{3} - {\left(\frac{y}{z}\right)}^{3}}\right), \color{blue}{\left(x + y\right)}\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{{1}^{3} - {\left(\frac{y}{z}\right)}^{3}}{1 \cdot 1 + \left(\frac{y}{z} \cdot \frac{y}{z} + 1 \cdot \frac{y}{z}\right)}}\right), \left(\color{blue}{x} + y\right)\right) \]

      7. flip3-- N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{1 - \frac{y}{z}}\right), \left(x + y\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(1 - \frac{y}{z}\right)\right), \left(\color{blue}{x} + y\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \left(\frac{y}{z}\right)\right)\right), \left(x + y\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, z\right)\right)\right), \left(x + y\right)\right) \]

      11. +-lowering-+.f64 99.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, z\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right) \]

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, z\right)\right)\right), \color{blue}{x}\right) \]
   6. Step-by-step derivation

   7. Simplified 84.6%

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

   if 8.1999999999999996e-38 < y < 2.75e44

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(1 - \frac{y}{z}\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      3. /-lowering-/.f64 73.2%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 73.2%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{y}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-54}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-296}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{1}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+44}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-296}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+46}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (* z (- -1.0 (/ x y)))))
   (if (<= y -6.5e-55)
     t_1
     (if (<= y -2e-296)
       (+ x y)
       (if (<= y 2.2e-44) (/ x t_0) (if (<= y 3e+46) (/ y t_0) t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -6.5e-55) {
		tmp = t_1;
	} else if (y <= -2e-296) {
		tmp = x + y;
	} else if (y <= 2.2e-44) {
		tmp = x / t_0;
	} else if (y <= 3e+46) {
		tmp = y / t_0;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = z * ((-1.0d0) - (x / y))
    if (y <= (-6.5d-55)) then
        tmp = t_1
    else if (y <= (-2d-296)) then
        tmp = x + y
    else if (y <= 2.2d-44) then
        tmp = x / t_0
    else if (y <= 3d+46) then
        tmp = y / t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -6.5e-55) {
		tmp = t_1;
	} else if (y <= -2e-296) {
		tmp = x + y;
	} else if (y <= 2.2e-44) {
		tmp = x / t_0;
	} else if (y <= 3e+46) {
		tmp = y / t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -6.5e-55:
		tmp = t_1
	elif y <= -2e-296:
		tmp = x + y
	elif y <= 2.2e-44:
		tmp = x / t_0
	elif y <= 3e+46:
		tmp = y / t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(z * Float64(-1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -6.5e-55)
		tmp = t_1;
	elseif (y <= -2e-296)
		tmp = Float64(x + y);
	elseif (y <= 2.2e-44)
		tmp = Float64(x / t_0);
	elseif (y <= 3e+46)
		tmp = Float64(y / t_0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = z * (-1.0 - (x / y));
	tmp = 0.0;
	if (y <= -6.5e-55)
		tmp = t_1;
	elseif (y <= -2e-296)
		tmp = x + y;
	elseif (y <= 2.2e-44)
		tmp = x / t_0;
	elseif (y <= 3e+46)
		tmp = y / t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e-55], t$95$1, If[LessEqual[y, -2e-296], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.2e-44], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 3e+46], N[(y / t$95$0), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.50000000000000006e-55 or 3.00000000000000023e46 < y

   1. Initial program 75.6%

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

      5. distribute-frac-neg N/A

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

      6. mul-1-neg N/A

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

      7. div-sub N/A

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

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), \left(\frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y}\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(0 - z\right), \left(\frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(x \cdot z - -1 \cdot {z}^{2}\right), \color{blue}{y}\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}\right), y\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(x \cdot z + 1 \cdot {z}^{2}\right), y\right)\right) \]

      15. *-lft-identity N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(x \cdot z + {z}^{2}\right), y\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left({z}^{2} + x \cdot z\right), y\right)\right) \]

      17. unpow2 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(z \cdot z + x \cdot z\right), y\right)\right) \]

      18. distribute-rgt-out N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(z \cdot \left(z + x\right)\right), y\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(z + x\right)\right), y\right)\right) \]

      20. +-lowering-+.f64 71.8%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, x\right)\right), y\right)\right) \]

   5. Simplified 71.8%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

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

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(\left(1 + \frac{x}{y}\right)\right)\right)}\right) \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y}\right)\right)}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(-1 + \left(\mathsf{neg}\left(\color{blue}{\frac{x}{y}}\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(-1 - \color{blue}{\frac{x}{y}}\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(-1, \color{blue}{\left(\frac{x}{y}\right)}\right)\right) \]

      8. /-lowering-/.f64 74.4%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(-1, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 74.4%

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

   if -6.50000000000000006e-55 < y < -2e-296

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 82.1%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 82.1%

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

   if -2e-296 < y < 2.20000000000000012e-44

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 - \frac{y}{z}\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      3. /-lowering-/.f64 84.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 84.6%

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

   if 2.20000000000000012e-44 < y < 3.00000000000000023e46

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(1 - \frac{y}{z}\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      3. /-lowering-/.f64 73.2%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 73.2%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{y}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-55}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-296}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+46}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-296}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))))
   (if (<= y -1.15e-53)
     t_0
     (if (<= y -2.9e-296)
       (+ x y)
       (if (<= y 2.6e-38) (/ x (- 1.0 (/ y z))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -1.15e-53) {
		tmp = t_0;
	} else if (y <= -2.9e-296) {
		tmp = x + y;
	} else if (y <= 2.6e-38) {
		tmp = x / (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 = z * ((-1.0d0) - (x / y))
    if (y <= (-1.15d-53)) then
        tmp = t_0
    else if (y <= (-2.9d-296)) then
        tmp = x + y
    else if (y <= 2.6d-38) then
        tmp = x / (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 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -1.15e-53) {
		tmp = t_0;
	} else if (y <= -2.9e-296) {
		tmp = x + y;
	} else if (y <= 2.6e-38) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -1.15e-53:
		tmp = t_0
	elif y <= -2.9e-296:
		tmp = x + y
	elif y <= 2.6e-38:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -1.15e-53)
		tmp = t_0;
	elseif (y <= -2.9e-296)
		tmp = Float64(x + y);
	elseif (y <= 2.6e-38)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-1.0 - (x / y));
	tmp = 0.0;
	if (y <= -1.15e-53)
		tmp = t_0;
	elseif (y <= -2.9e-296)
		tmp = x + y;
	elseif (y <= 2.6e-38)
		tmp = x / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e-53], t$95$0, If[LessEqual[y, -2.9e-296], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.6e-38], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1500000000000001e-53 or 2.60000000000000011e-38 < y

   1. Initial program 78.7%

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

      5. distribute-frac-neg N/A

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

      6. mul-1-neg N/A

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

      7. div-sub N/A

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

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), \left(\frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y}\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(0 - z\right), \left(\frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(x \cdot z - -1 \cdot {z}^{2}\right), \color{blue}{y}\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}\right), y\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(x \cdot z + 1 \cdot {z}^{2}\right), y\right)\right) \]

      15. *-lft-identity N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(x \cdot z + {z}^{2}\right), y\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left({z}^{2} + x \cdot z\right), y\right)\right) \]

      17. unpow2 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(z \cdot z + x \cdot z\right), y\right)\right) \]

      18. distribute-rgt-out N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(z \cdot \left(z + x\right)\right), y\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(z + x\right)\right), y\right)\right) \]

      20. +-lowering-+.f64 68.4%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, x\right)\right), y\right)\right) \]

   5. Simplified 68.4%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

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

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(\left(1 + \frac{x}{y}\right)\right)\right)}\right) \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y}\right)\right)}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(-1 + \left(\mathsf{neg}\left(\color{blue}{\frac{x}{y}}\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(-1 - \color{blue}{\frac{x}{y}}\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(-1, \color{blue}{\left(\frac{x}{y}\right)}\right)\right) \]

      8. /-lowering-/.f64 70.8%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(-1, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 70.8%

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

   if -1.1500000000000001e-53 < y < -2.89999999999999983e-296

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 82.1%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 82.1%

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

   if -2.89999999999999983e-296 < y < 2.60000000000000011e-38

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 - \frac{y}{z}\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      3. /-lowering-/.f64 84.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 84.6%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-296}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+81}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+32}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+78}:\\ \;\;\;\;\frac{x \cdot \left(0 - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.2e+81)
   (- 0.0 z)
   (if (<= y 6e+32)
     (+ x y)
     (if (<= y 2.6e+78) (/ (* x (- 0.0 z)) y) (- 0.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.2e+81) {
		tmp = 0.0 - z;
	} else if (y <= 6e+32) {
		tmp = x + y;
	} else if (y <= 2.6e+78) {
		tmp = (x * (0.0 - z)) / y;
	} else {
		tmp = 0.0 - 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 <= (-9.2d+81)) then
        tmp = 0.0d0 - z
    else if (y <= 6d+32) then
        tmp = x + y
    else if (y <= 2.6d+78) then
        tmp = (x * (0.0d0 - z)) / y
    else
        tmp = 0.0d0 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.2e+81) {
		tmp = 0.0 - z;
	} else if (y <= 6e+32) {
		tmp = x + y;
	} else if (y <= 2.6e+78) {
		tmp = (x * (0.0 - z)) / y;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.2e+81:
		tmp = 0.0 - z
	elif y <= 6e+32:
		tmp = x + y
	elif y <= 2.6e+78:
		tmp = (x * (0.0 - z)) / y
	else:
		tmp = 0.0 - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.2e+81)
		tmp = Float64(0.0 - z);
	elseif (y <= 6e+32)
		tmp = Float64(x + y);
	elseif (y <= 2.6e+78)
		tmp = Float64(Float64(x * Float64(0.0 - z)) / y);
	else
		tmp = Float64(0.0 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.2e+81)
		tmp = 0.0 - z;
	elseif (y <= 6e+32)
		tmp = x + y;
	elseif (y <= 2.6e+78)
		tmp = (x * (0.0 - z)) / y;
	else
		tmp = 0.0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.2e+81], N[(0.0 - z), $MachinePrecision], If[LessEqual[y, 6e+32], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.6e+78], N[(N[(x * N[(0.0 - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(0.0 - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.1999999999999995e81 or 2.6e78 < y

   1. Initial program 68.9%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z} \]

      3. --lowering--.f64 64.2%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 64.2%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 64.2%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   7. Applied egg-rr 64.2%

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

   if -9.1999999999999995e81 < y < 6e32

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 68.2%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 68.2%

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

   if 6e32 < y < 2.6e78

   1. Initial program 92.9%

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

      5. distribute-frac-neg N/A

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

      6. mul-1-neg N/A

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

      7. div-sub N/A

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

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), \left(\frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y}\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(0 - z\right), \left(\frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(x \cdot z - -1 \cdot {z}^{2}\right), \color{blue}{y}\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}\right), y\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(x \cdot z + 1 \cdot {z}^{2}\right), y\right)\right) \]

      15. *-lft-identity N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(x \cdot z + {z}^{2}\right), y\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left({z}^{2} + x \cdot z\right), y\right)\right) \]

      17. unpow2 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(z \cdot z + x \cdot z\right), y\right)\right) \]

      18. distribute-rgt-out N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(z \cdot \left(z + x\right)\right), y\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(z + x\right)\right), y\right)\right) \]

      20. +-lowering-+.f64 71.7%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, x\right)\right), y\right)\right) \]

   5. Simplified 71.7%

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

   6. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{\frac{x \cdot z}{y}} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{x \cdot z}{y}\right)}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\frac{z}{y}}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{z}{y}\right)}\right)\right) \]

      6. /-lowering-/.f64 65.0%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 65.0%

      \[\leadsto \color{blue}{0 - x \cdot \frac{z}{y}} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

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

      2. associate-*r/ N/A

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

      3. distribute-neg-frac N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(x \cdot z\right)\right), \color{blue}{y}\right) \]

   10. Applied egg-rr 66.8%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+81}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+32}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+78}:\\ \;\;\;\;\frac{x \cdot \left(0 - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-54}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+83}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8e-54)
   (- 0.0 z)
   (if (<= y 5.8e-30) x (if (<= y 1.4e+83) y (- 0.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e-54) {
		tmp = 0.0 - z;
	} else if (y <= 5.8e-30) {
		tmp = x;
	} else if (y <= 1.4e+83) {
		tmp = y;
	} else {
		tmp = 0.0 - 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 <= (-8d-54)) then
        tmp = 0.0d0 - z
    else if (y <= 5.8d-30) then
        tmp = x
    else if (y <= 1.4d+83) then
        tmp = y
    else
        tmp = 0.0d0 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e-54) {
		tmp = 0.0 - z;
	} else if (y <= 5.8e-30) {
		tmp = x;
	} else if (y <= 1.4e+83) {
		tmp = y;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8e-54:
		tmp = 0.0 - z
	elif y <= 5.8e-30:
		tmp = x
	elif y <= 1.4e+83:
		tmp = y
	else:
		tmp = 0.0 - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8e-54)
		tmp = Float64(0.0 - z);
	elseif (y <= 5.8e-30)
		tmp = x;
	elseif (y <= 1.4e+83)
		tmp = y;
	else
		tmp = Float64(0.0 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8e-54)
		tmp = 0.0 - z;
	elseif (y <= 5.8e-30)
		tmp = x;
	elseif (y <= 1.4e+83)
		tmp = y;
	else
		tmp = 0.0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8e-54], N[(0.0 - z), $MachinePrecision], If[LessEqual[y, 5.8e-30], x, If[LessEqual[y, 1.4e+83], y, N[(0.0 - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.0000000000000002e-54 or 1.4e83 < y

   1. Initial program 74.1%

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

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z} \]

      3. --lowering--.f64 59.1%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 59.1%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 59.1%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   7. Applied egg-rr 59.1%

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

   if -8.0000000000000002e-54 < y < 5.79999999999999978e-30

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 62.1%

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

   if 5.79999999999999978e-30 < y < 1.4e83

   1. Initial program 96.4%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(1 - \frac{y}{z}\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      3. /-lowering-/.f64 55.1%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 55.1%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 41.6%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-54}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+83}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-83}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.1e-38)
   (+ x y)
   (if (<= z 2.6e-83) (* z (- -1.0 (/ x y))) (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.1e-38) {
		tmp = x + y;
	} else if (z <= 2.6e-83) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-4.1d-38)) then
        tmp = x + y
    else if (z <= 2.6d-83) then
        tmp = z * ((-1.0d0) - (x / y))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.1e-38) {
		tmp = x + y;
	} else if (z <= 2.6e-83) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.1e-38:
		tmp = x + y
	elif z <= 2.6e-83:
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.1e-38)
		tmp = Float64(x + y);
	elseif (z <= 2.6e-83)
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.1e-38)
		tmp = x + y;
	elseif (z <= 2.6e-83)
		tmp = z * (-1.0 - (x / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.1e-38], N[(x + y), $MachinePrecision], If[LessEqual[z, 2.6e-83], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.0999999999999998e-38 or 2.60000000000000009e-83 < z

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 73.9%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 73.9%

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

   if -4.0999999999999998e-38 < z < 2.60000000000000009e-83

   1. Initial program 74.1%

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

   3. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

      5. distribute-frac-neg N/A

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

      6. mul-1-neg N/A

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

      7. div-sub N/A

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

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), \left(\frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y}\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(0 - z\right), \left(\frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\frac{\color{blue}{x \cdot z - -1 \cdot {z}^{2}}}{y}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(x \cdot z - -1 \cdot {z}^{2}\right), \color{blue}{y}\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}\right), y\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(x \cdot z + 1 \cdot {z}^{2}\right), y\right)\right) \]

      15. *-lft-identity N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(x \cdot z + {z}^{2}\right), y\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left({z}^{2} + x \cdot z\right), y\right)\right) \]

      17. unpow2 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(z \cdot z + x \cdot z\right), y\right)\right) \]

      18. distribute-rgt-out N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\left(z \cdot \left(z + x\right)\right), y\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(z + x\right)\right), y\right)\right) \]

      20. +-lowering-+.f64 77.6%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, x\right)\right), y\right)\right) \]

   5. Simplified 77.6%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

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

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(\left(1 + \frac{x}{y}\right)\right)\right)}\right) \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y}\right)\right)}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(-1 + \left(\mathsf{neg}\left(\color{blue}{\frac{x}{y}}\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(-1 - \color{blue}{\frac{x}{y}}\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(-1, \color{blue}{\left(\frac{x}{y}\right)}\right)\right) \]

      8. /-lowering-/.f64 74.1%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(-1, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 74.1%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-83}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+83}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+84}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.3e+83) (- 0.0 z) (if (<= y 1.35e+84) (+ x y) (- 0.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.3e+83) {
		tmp = 0.0 - z;
	} else if (y <= 1.35e+84) {
		tmp = x + y;
	} else {
		tmp = 0.0 - 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 <= (-1.3d+83)) then
        tmp = 0.0d0 - z
    else if (y <= 1.35d+84) then
        tmp = x + y
    else
        tmp = 0.0d0 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.3e+83) {
		tmp = 0.0 - z;
	} else if (y <= 1.35e+84) {
		tmp = x + y;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.3e+83:
		tmp = 0.0 - z
	elif y <= 1.35e+84:
		tmp = x + y
	else:
		tmp = 0.0 - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.3e+83)
		tmp = Float64(0.0 - z);
	elseif (y <= 1.35e+84)
		tmp = Float64(x + y);
	else
		tmp = Float64(0.0 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.3e+83)
		tmp = 0.0 - z;
	elseif (y <= 1.35e+84)
		tmp = x + y;
	else
		tmp = 0.0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.3e+83], N[(0.0 - z), $MachinePrecision], If[LessEqual[y, 1.35e+84], N[(x + y), $MachinePrecision], N[(0.0 - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3000000000000001e83 or 1.35e84 < y

   1. Initial program 68.6%

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

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z} \]

      3. --lowering--.f64 64.9%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 64.9%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 64.9%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   7. Applied egg-rr 64.9%

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

   if -1.3000000000000001e83 < y < 1.35e84

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 65.2%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 65.2%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+83}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+84}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.1 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 2.1e-24) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.1e-24) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 2.1d-24) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.1e-24) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.1e-24:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.1e-24)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.1e-24)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.1e-24], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 2.0999999999999999e-24

   1. Initial program 92.2%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 44.6%

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

   if 2.0999999999999999e-24 < y

   1. Initial program 78.1%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(1 - \frac{y}{z}\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      3. /-lowering-/.f64 61.3%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 61.3%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 29.8%

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

Alternative 10: 35.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 88.1%

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

3. Taylor expanded in y around 0

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

5. Simplified 33.3%

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

Developer Target 1: 93.9% accurate, 0.5× 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 2024161 
(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))))