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

Percentage Accurate: 88.3% → 99.8%

Time: 8.7s

Alternatives: 8

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.3% 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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-283}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\frac{z \cdot \left(x + z\right)}{0 - y} - z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (<= t_0 -1e-283)
     t_0
     (if (<= t_0 0.0) (- (/ (* z (+ x z)) (- 0.0 y)) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if (t_0 <= -1e-283) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = ((z * (x + z)) / (0.0 - 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 = (x + y) / (1.0d0 - (y / z))
    if (t_0 <= (-1d-283)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = ((z * (x + z)) / (0.0d0 - 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 = (x + y) / (1.0 - (y / z));
	double tmp;
	if (t_0 <= -1e-283) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = ((z * (x + z)) / (0.0 - y)) - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if t_0 <= -1e-283:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = ((z * (x + z)) / (0.0 - y)) - z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (t_0 <= -1e-283)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(Float64(z * Float64(x + z)) / Float64(0.0 - y)) - z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if (t_0 <= -1e-283)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = ((z * (x + z)) / (0.0 - y)) - z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-283], t$95$0, If[LessEqual[t$95$0, 0.0], N[(N[(N[(z * N[(x + z), $MachinePrecision]), $MachinePrecision] / N[(0.0 - y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -9.99999999999999947e-284 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 -9.99999999999999947e-284 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 8.2%

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

   3. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

      5. distribute-frac-neg N/A

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

      6. mul-1-neg N/A

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

      7. div-sub N/A

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

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

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

      9. mul-1-neg N/A

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

      10. neg-sub0 N/A

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

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

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

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

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

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

          \[\leadsto \left(0 - z\right) - \frac{\color{blue}{x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}}}{y} \]

      14. metadata-eval N/A

          \[\leadsto \left(0 - z\right) - \frac{x \cdot z + \color{blue}{1} \cdot {z}^{2}}{y} \]

      15. *-lft-identity N/A

          \[\leadsto \left(0 - z\right) - \frac{x \cdot z + \color{blue}{{z}^{2}}}{y} \]

      16. +-commutative N/A

          \[\leadsto \left(0 - z\right) - \frac{\color{blue}{{z}^{2} + x \cdot z}}{y} \]

      17. unpow2 N/A

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

      18. distribute-rgt-out N/A

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

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

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

      20. +-lowering-+.f64 100.0

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

   5. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-283}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;\frac{x + y}{1 - \frac{y}{z}} \leq 0:\\ \;\;\;\;\frac{z \cdot \left(x + z\right)}{0 - y} - z\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 71.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+63}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-156}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-56}:\\ \;\;\;\;\frac{z \cdot \left(x + z\right)}{0 - y} - z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.5e+63)
   (+ x y)
   (if (<= z -4.7e-156)
     (* x (/ z (- z y)))
     (if (<= z 2.8e-56) (- (/ (* z (+ x z)) (- 0.0 y)) z) (+ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.5e+63) {
		tmp = x + y;
	} else if (z <= -4.7e-156) {
		tmp = x * (z / (z - y));
	} else if (z <= 2.8e-56) {
		tmp = ((z * (x + z)) / (0.0 - y)) - z;
	} 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 <= (-3.5d+63)) then
        tmp = x + y
    else if (z <= (-4.7d-156)) then
        tmp = x * (z / (z - y))
    else if (z <= 2.8d-56) then
        tmp = ((z * (x + z)) / (0.0d0 - y)) - z
    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 <= -3.5e+63) {
		tmp = x + y;
	} else if (z <= -4.7e-156) {
		tmp = x * (z / (z - y));
	} else if (z <= 2.8e-56) {
		tmp = ((z * (x + z)) / (0.0 - y)) - z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.5e+63:
		tmp = x + y
	elif z <= -4.7e-156:
		tmp = x * (z / (z - y))
	elif z <= 2.8e-56:
		tmp = ((z * (x + z)) / (0.0 - y)) - z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.5e+63)
		tmp = Float64(x + y);
	elseif (z <= -4.7e-156)
		tmp = Float64(x * Float64(z / Float64(z - y)));
	elseif (z <= 2.8e-56)
		tmp = Float64(Float64(Float64(z * Float64(x + z)) / Float64(0.0 - y)) - z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.5e+63)
		tmp = x + y;
	elseif (z <= -4.7e-156)
		tmp = x * (z / (z - y));
	elseif (z <= 2.8e-56)
		tmp = ((z * (x + z)) / (0.0 - y)) - z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.5e+63], N[(x + y), $MachinePrecision], If[LessEqual[z, -4.7e-156], N[(x * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-56], N[(N[(N[(z * N[(x + z), $MachinePrecision]), $MachinePrecision] / N[(0.0 - y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.50000000000000029e63 or 2.79999999999999993e-56 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 85.8

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

   5. Simplified 85.8%

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

   if -3.50000000000000029e63 < z < -4.70000000000000046e-156

   1. Initial program 93.4%

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

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

      2. div-sub N/A

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

      3. associate-/r/ N/A

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

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

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

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

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

      6. --lowering--.f64 61.2

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

   5. Simplified 61.2%

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

      1. associate-*l/ N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 65.4

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

   7. Applied egg-rr 65.4%

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

   if -4.70000000000000046e-156 < z < 2.79999999999999993e-56

   1. Initial program 66.9%

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

      5. distribute-frac-neg N/A

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

      6. mul-1-neg N/A

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

      7. div-sub N/A

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

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

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

      9. mul-1-neg N/A

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

      10. neg-sub0 N/A

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

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

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

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

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

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

          \[\leadsto \left(0 - z\right) - \frac{\color{blue}{x \cdot z + \left(\mathsf{neg}\left(-1\right)\right) \cdot {z}^{2}}}{y} \]

      14. metadata-eval N/A

          \[\leadsto \left(0 - z\right) - \frac{x \cdot z + \color{blue}{1} \cdot {z}^{2}}{y} \]

      15. *-lft-identity N/A

          \[\leadsto \left(0 - z\right) - \frac{x \cdot z + \color{blue}{{z}^{2}}}{y} \]

      16. +-commutative N/A

          \[\leadsto \left(0 - z\right) - \frac{\color{blue}{{z}^{2} + x \cdot z}}{y} \]

      17. unpow2 N/A

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

      18. distribute-rgt-out N/A

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

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

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

      20. +-lowering-+.f64 82.5

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

   5. Simplified 82.5%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+63}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-156}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-56}:\\ \;\;\;\;\frac{z \cdot \left(x + z\right)}{0 - y} - z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;z \leq 10^{-51}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.55e+67)
   (+ x y)
   (if (<= z -3.1e-158)
     (* x (/ z (- z y)))
     (if (<= z 1e-51) (* z (- -1.0 (/ x y))) (+ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e+67) {
		tmp = x + y;
	} else if (z <= -3.1e-158) {
		tmp = x * (z / (z - y));
	} else if (z <= 1e-51) {
		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 <= (-1.55d+67)) then
        tmp = x + y
    else if (z <= (-3.1d-158)) then
        tmp = x * (z / (z - y))
    else if (z <= 1d-51) 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 <= -1.55e+67) {
		tmp = x + y;
	} else if (z <= -3.1e-158) {
		tmp = x * (z / (z - y));
	} else if (z <= 1e-51) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.55e+67:
		tmp = x + y
	elif z <= -3.1e-158:
		tmp = x * (z / (z - y))
	elif z <= 1e-51:
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.55e+67)
		tmp = Float64(x + y);
	elseif (z <= -3.1e-158)
		tmp = Float64(x * Float64(z / Float64(z - y)));
	elseif (z <= 1e-51)
		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 <= -1.55e+67)
		tmp = x + y;
	elseif (z <= -3.1e-158)
		tmp = x * (z / (z - y));
	elseif (z <= 1e-51)
		tmp = z * (-1.0 - (x / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.55e+67], N[(x + y), $MachinePrecision], If[LessEqual[z, -3.1e-158], N[(x * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-51], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.54999999999999998e67 or 1e-51 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 85.8

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

   5. Simplified 85.8%

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

   if -1.54999999999999998e67 < z < -3.10000000000000018e-158

   1. Initial program 93.5%

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

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

      2. div-sub N/A

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

      3. associate-/r/ N/A

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

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

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

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

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

      6. --lowering--.f64 60.0

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

   5. Simplified 60.0%

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

      1. associate-*l/ N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 66.2

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

   7. Applied egg-rr 66.2%

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

   if -3.10000000000000018e-158 < z < 1e-51

   1. Initial program 66.6%

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

   3. Taylor expanded in z around 0

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

      1. 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. mul-1-neg N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. distribute-lft-in N/A

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

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

      11. div-sub N/A

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

      12. associate-*l/ N/A

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

      13. metadata-eval N/A

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

      14. distribute-neg-frac N/A

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

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

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

      16. lft-mult-inverse N/A

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

      17. metadata-eval N/A

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

      18. --lowering--.f64 N/A

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

      19. /-lowering-/.f64 79.1

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

   5. Simplified 79.1%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;z \leq 10^{-51}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+185}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-222}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+96}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.32e+185)
   (- 0.0 z)
   (if (<= y 1.18e-222)
     (* x (/ z (- z y)))
     (if (<= y 1.2e+96) (+ x y) (- 0.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.32e+185) {
		tmp = 0.0 - z;
	} else if (y <= 1.18e-222) {
		tmp = x * (z / (z - y));
	} else if (y <= 1.2e+96) {
		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 <= (-1.32d+185)) then
        tmp = 0.0d0 - z
    else if (y <= 1.18d-222) then
        tmp = x * (z / (z - y))
    else if (y <= 1.2d+96) 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 <= -1.32e+185) {
		tmp = 0.0 - z;
	} else if (y <= 1.18e-222) {
		tmp = x * (z / (z - y));
	} else if (y <= 1.2e+96) {
		tmp = x + y;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.32e+185:
		tmp = 0.0 - z
	elif y <= 1.18e-222:
		tmp = x * (z / (z - y))
	elif y <= 1.2e+96:
		tmp = x + y
	else:
		tmp = 0.0 - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.32e+185)
		tmp = Float64(0.0 - z);
	elseif (y <= 1.18e-222)
		tmp = Float64(x * Float64(z / Float64(z - y)));
	elseif (y <= 1.2e+96)
		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 <= -1.32e+185)
		tmp = 0.0 - z;
	elseif (y <= 1.18e-222)
		tmp = x * (z / (z - y));
	elseif (y <= 1.2e+96)
		tmp = x + y;
	else
		tmp = 0.0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.32e+185], N[(0.0 - z), $MachinePrecision], If[LessEqual[y, 1.18e-222], N[(x * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+96], N[(x + y), $MachinePrecision], N[(0.0 - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3199999999999999e185 or 1.19999999999999996e96 < y

   1. Initial program 55.7%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. neg-sub0 N/A

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

      3. --lowering--.f64 70.3

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

   5. Simplified 70.3%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 70.3

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

   7. Applied egg-rr 70.3%

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

   if -1.3199999999999999e185 < y < 1.18000000000000007e-222

   1. Initial program 97.7%

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

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

      2. div-sub N/A

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

      3. associate-/r/ N/A

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

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

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

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

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

      6. --lowering--.f64 67.7

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

   5. Simplified 67.7%

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

      1. associate-*l/ N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 75.4

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

   7. Applied egg-rr 75.4%

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

   if 1.18000000000000007e-222 < y < 1.19999999999999996e96

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 63.5

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

   5. Simplified 63.5%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+185}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-222}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+96}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+72}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+96}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.5e+72) (- 0.0 z) (if (<= y 6.4e+96) (+ x y) (- 0.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.5e+72) {
		tmp = 0.0 - z;
	} else if (y <= 6.4e+96) {
		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 <= (-8.5d+72)) then
        tmp = 0.0d0 - z
    else if (y <= 6.4d+96) 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 <= -8.5e+72) {
		tmp = 0.0 - z;
	} else if (y <= 6.4e+96) {
		tmp = x + y;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.5e+72:
		tmp = 0.0 - z
	elif y <= 6.4e+96:
		tmp = x + y
	else:
		tmp = 0.0 - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.5e+72)
		tmp = Float64(0.0 - z);
	elseif (y <= 6.4e+96)
		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 <= -8.5e+72)
		tmp = 0.0 - z;
	elseif (y <= 6.4e+96)
		tmp = x + y;
	else
		tmp = 0.0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.5e+72], N[(0.0 - z), $MachinePrecision], If[LessEqual[y, 6.4e+96], N[(x + y), $MachinePrecision], N[(0.0 - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5000000000000004e72 or 6.40000000000000013e96 < y

   1. Initial program 61.7%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. neg-sub0 N/A

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

      3. --lowering--.f64 62.1

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

   5. Simplified 62.1%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 62.1

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

   7. Applied egg-rr 62.1%

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

   if -8.5000000000000004e72 < y < 6.40000000000000013e96

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 72.5

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

   5. Simplified 72.5%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+72}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+96}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-19}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.5e-19) (- 0.0 z) (if (<= y 9.6e-48) x (- 0.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.5e-19) {
		tmp = 0.0 - z;
	} else if (y <= 9.6e-48) {
		tmp = x;
	} 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 <= (-9.5d-19)) then
        tmp = 0.0d0 - z
    else if (y <= 9.6d-48) then
        tmp = x
    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 <= -9.5e-19) {
		tmp = 0.0 - z;
	} else if (y <= 9.6e-48) {
		tmp = x;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.5e-19:
		tmp = 0.0 - z
	elif y <= 9.6e-48:
		tmp = x
	else:
		tmp = 0.0 - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.5e-19)
		tmp = Float64(0.0 - z);
	elseif (y <= 9.6e-48)
		tmp = x;
	else
		tmp = Float64(0.0 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.5e-19)
		tmp = 0.0 - z;
	elseif (y <= 9.6e-48)
		tmp = x;
	else
		tmp = 0.0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.5e-19], N[(0.0 - z), $MachinePrecision], If[LessEqual[y, 9.6e-48], x, N[(0.0 - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.4999999999999995e-19 or 9.6e-48 < y

   1. Initial program 73.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. neg-sub0 N/A

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

      3. --lowering--.f64 49.9

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

   5. Simplified 49.9%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 49.9

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

   7. Applied egg-rr 49.9%

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

   if -9.4999999999999995e-19 < y < 9.6e-48

   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 66.5%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-19}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 40.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-199}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-191}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.6e-199) x (if (<= x 1.18e-191) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.6e-199) {
		tmp = x;
	} else if (x <= 1.18e-191) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.6d-199)) then
        tmp = x
    else if (x <= 1.18d-191) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.6e-199) {
		tmp = x;
	} else if (x <= 1.18e-191) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.6e-199:
		tmp = x
	elif x <= 1.18e-191:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.6e-199)
		tmp = x;
	elseif (x <= 1.18e-191)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.6e-199)
		tmp = x;
	elseif (x <= 1.18e-191)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.6e-199], x, If[LessEqual[x, 1.18e-191], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.60000000000000036e-199 or 1.1799999999999999e-191 < x

   1. Initial program 85.7%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 44.1%

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

   if -5.60000000000000036e-199 < x < 1.1799999999999999e-191

   1. Initial program 94.1%

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

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

      2. div-sub N/A

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

      3. associate-/r/ N/A

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

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

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

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

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

      6. --lowering--.f64 71.4

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

   5. Simplified 71.4%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 54.7%

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

Alternative 8: 35.0% accurate, 29.0× 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 87.3%

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

3. Taylor expanded in y around 0

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

5. Simplified 40.2%

   \[\leadsto \color{blue}{x} \]
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 2024196 
(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))))