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

Percentage Accurate: 88.4% → 99.6%

Time: 8.2s

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: 88.4% 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: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-289}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 10^{-269}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (<= t_0 -2e-289) t_0 (if (<= t_0 1e-269) (* z (- -1.0 (/ x 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 <= -2e-289) {
		tmp = t_0;
	} else if (t_0 <= 1e-269) {
		tmp = z * (-1.0 - (x / 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 <= (-2d-289)) then
        tmp = t_0
    else if (t_0 <= 1d-269) then
        tmp = z * ((-1.0d0) - (x / 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 <= -2e-289) {
		tmp = t_0;
	} else if (t_0 <= 1e-269) {
		tmp = z * (-1.0 - (x / 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 <= -2e-289:
		tmp = t_0
	elif t_0 <= 1e-269:
		tmp = z * (-1.0 - (x / 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 <= -2e-289)
		tmp = t_0;
	elseif (t_0 <= 1e-269)
		tmp = Float64(z * Float64(-1.0 - Float64(x / 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 <= -2e-289)
		tmp = t_0;
	elseif (t_0 <= 1e-269)
		tmp = z * (-1.0 - (x / 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, -2e-289], t$95$0, If[LessEqual[t$95$0, 1e-269], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $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))) < -2e-289 or 9.9999999999999996e-270 < (/.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 -2e-289 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 9.9999999999999996e-270

   1. Initial program 15.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 100.0

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

   5. Simplified 100.0%

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

Alternative 2: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+87}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-290}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))))
   (if (<= y -1.75e+87)
     t_0
     (if (<= y -1.75e-290)
       (+ x y)
       (if (<= y 6.2e-57) (/ 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 <= -1.75e+87) {
		tmp = t_0;
	} else if (y <= -1.75e-290) {
		tmp = x + y;
	} else if (y <= 6.2e-57) {
		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 <= (-1.75d+87)) then
        tmp = t_0
    else if (y <= (-1.75d-290)) then
        tmp = x + y
    else if (y <= 6.2d-57) 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 <= -1.75e+87) {
		tmp = t_0;
	} else if (y <= -1.75e-290) {
		tmp = x + y;
	} else if (y <= 6.2e-57) {
		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 <= -1.75e+87:
		tmp = t_0
	elif y <= -1.75e-290:
		tmp = x + y
	elif y <= 6.2e-57:
		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 <= -1.75e+87)
		tmp = t_0;
	elseif (y <= -1.75e-290)
		tmp = Float64(x + y);
	elseif (y <= 6.2e-57)
		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 <= -1.75e+87)
		tmp = t_0;
	elseif (y <= -1.75e-290)
		tmp = x + y;
	elseif (y <= 6.2e-57)
		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, -1.75e+87], t$95$0, If[LessEqual[y, -1.75e-290], N[(x + y), $MachinePrecision], If[LessEqual[y, 6.2e-57], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.74999999999999993e87 or 6.19999999999999952e-57 < y

   1. Initial program 70.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 84.2

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

   5. Simplified 84.2%

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

   if -1.74999999999999993e87 < y < -1.74999999999999991e-290

   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 77.7

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

   5. Simplified 77.7%

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

   if -1.74999999999999991e-290 < y < 6.19999999999999952e-57

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 91.5%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+87}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-290}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+87}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-289}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))))
   (if (<= y -1.7e+87)
     t_0
     (if (<= y -2e-289) (+ x y) (if (<= y 5.6e-57) (* x (/ z (- z y))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -1.7e+87) {
		tmp = t_0;
	} else if (y <= -2e-289) {
		tmp = x + y;
	} else if (y <= 5.6e-57) {
		tmp = x * (z / (z - 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 = z * ((-1.0d0) - (x / y))
    if (y <= (-1.7d+87)) then
        tmp = t_0
    else if (y <= (-2d-289)) then
        tmp = x + y
    else if (y <= 5.6d-57) then
        tmp = x * (z / (z - 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 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -1.7e+87) {
		tmp = t_0;
	} else if (y <= -2e-289) {
		tmp = x + y;
	} else if (y <= 5.6e-57) {
		tmp = x * (z / (z - y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -1.7e+87:
		tmp = t_0
	elif y <= -2e-289:
		tmp = x + y
	elif y <= 5.6e-57:
		tmp = x * (z / (z - y))
	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 <= -1.7e+87)
		tmp = t_0;
	elseif (y <= -2e-289)
		tmp = Float64(x + y);
	elseif (y <= 5.6e-57)
		tmp = Float64(x * Float64(z / Float64(z - y)));
	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 <= -1.7e+87)
		tmp = t_0;
	elseif (y <= -2e-289)
		tmp = x + y;
	elseif (y <= 5.6e-57)
		tmp = x * (z / (z - y));
	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, -1.7e+87], t$95$0, If[LessEqual[y, -2e-289], N[(x + y), $MachinePrecision], If[LessEqual[y, 5.6e-57], N[(x * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7000000000000001e87 or 5.5999999999999999e-57 < y

   1. Initial program 70.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 84.2

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

   5. Simplified 84.2%

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

   if -1.7000000000000001e87 < y < -2e-289

   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 77.7

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

   5. Simplified 77.7%

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

   if -2e-289 < y < 5.5999999999999999e-57

   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. *-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 75.4

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

   5. Simplified 75.4%

      \[\leadsto \color{blue}{\frac{x}{z - y} \cdot z} \]
   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 91.4

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

   7. Applied egg-rr 91.4%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+87}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-289}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+89}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-290}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.6e+89)
   (- 0.0 z)
   (if (<= y -4.8e-290)
     (+ x y)
     (if (<= y 6.5e+24) (* x (/ z (- z y))) (- 0.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.6e+89) {
		tmp = 0.0 - z;
	} else if (y <= -4.8e-290) {
		tmp = x + y;
	} else if (y <= 6.5e+24) {
		tmp = x * (z / (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 <= (-4.6d+89)) then
        tmp = 0.0d0 - z
    else if (y <= (-4.8d-290)) then
        tmp = x + y
    else if (y <= 6.5d+24) then
        tmp = x * (z / (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 <= -4.6e+89) {
		tmp = 0.0 - z;
	} else if (y <= -4.8e-290) {
		tmp = x + y;
	} else if (y <= 6.5e+24) {
		tmp = x * (z / (z - y));
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.6e+89:
		tmp = 0.0 - z
	elif y <= -4.8e-290:
		tmp = x + y
	elif y <= 6.5e+24:
		tmp = x * (z / (z - y))
	else:
		tmp = 0.0 - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.6e+89)
		tmp = Float64(0.0 - z);
	elseif (y <= -4.8e-290)
		tmp = Float64(x + y);
	elseif (y <= 6.5e+24)
		tmp = Float64(x * Float64(z / Float64(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 <= -4.6e+89)
		tmp = 0.0 - z;
	elseif (y <= -4.8e-290)
		tmp = x + y;
	elseif (y <= 6.5e+24)
		tmp = x * (z / (z - y));
	else
		tmp = 0.0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.6e+89], N[(0.0 - z), $MachinePrecision], If[LessEqual[y, -4.8e-290], N[(x + y), $MachinePrecision], If[LessEqual[y, 6.5e+24], N[(x * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.0 - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5999999999999998e89 or 6.4999999999999996e24 < y

   1. Initial program 66.8%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 76.1

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

   5. Simplified 76.1%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 76.1

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

   7. Applied egg-rr 76.1%

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

   if -4.5999999999999998e89 < y < -4.8000000000000001e-290

   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 77.7

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

   5. Simplified 77.7%

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

   if -4.8000000000000001e-290 < y < 6.4999999999999996e24

   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. *-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 71.2

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

   5. Simplified 71.2%

      \[\leadsto \color{blue}{\frac{x}{z - y} \cdot z} \]
   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 84.3

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

   7. Applied egg-rr 84.3%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+89}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-290}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+91}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.9e+91) (- 0.0 z) (if (<= y 1.2e+101) (+ x y) (- 0.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.9e+91) {
		tmp = 0.0 - z;
	} else if (y <= 1.2e+101) {
		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 <= (-2.9d+91)) then
        tmp = 0.0d0 - z
    else if (y <= 1.2d+101) 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 <= -2.9e+91) {
		tmp = 0.0 - z;
	} else if (y <= 1.2e+101) {
		tmp = x + y;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.9e+91:
		tmp = 0.0 - z
	elif y <= 1.2e+101:
		tmp = x + y
	else:
		tmp = 0.0 - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.9e+91)
		tmp = Float64(0.0 - z);
	elseif (y <= 1.2e+101)
		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 <= -2.9e+91)
		tmp = 0.0 - z;
	elseif (y <= 1.2e+101)
		tmp = x + y;
	else
		tmp = 0.0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.9e+91], N[(0.0 - z), $MachinePrecision], If[LessEqual[y, 1.2e+101], N[(x + y), $MachinePrecision], N[(0.0 - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.90000000000000014e91 or 1.19999999999999994e101 < y

   1. Initial program 60.7%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 83.8

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

   5. Simplified 83.8%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 83.8

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

   7. Applied egg-rr 83.8%

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

   if -2.90000000000000014e91 < y < 1.19999999999999994e101

   1. Initial program 99.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 71.8

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

   5. Simplified 71.8%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+91}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+51}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.1e+51) (- 0.0 z) (if (<= y 2e-71) x (- 0.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.1e+51) {
		tmp = 0.0 - z;
	} else if (y <= 2e-71) {
		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 <= (-3.1d+51)) then
        tmp = 0.0d0 - z
    else if (y <= 2d-71) 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 <= -3.1e+51) {
		tmp = 0.0 - z;
	} else if (y <= 2e-71) {
		tmp = x;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.1e+51:
		tmp = 0.0 - z
	elif y <= 2e-71:
		tmp = x
	else:
		tmp = 0.0 - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.1e+51)
		tmp = Float64(0.0 - z);
	elseif (y <= 2e-71)
		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 <= -3.1e+51)
		tmp = 0.0 - z;
	elseif (y <= 2e-71)
		tmp = x;
	else
		tmp = 0.0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.1e+51], N[(0.0 - z), $MachinePrecision], If[LessEqual[y, 2e-71], x, N[(0.0 - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.10000000000000011e51 or 1.9999999999999998e-71 < y

   1. Initial program 73.0%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 68.4

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

   5. Simplified 68.4%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 68.4

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

   7. Applied egg-rr 68.4%

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

   if -3.10000000000000011e51 < y < 1.9999999999999998e-71

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 62.9%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+51}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 41.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-130}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-202}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.5e-130) x (if (<= x 1.05e-202) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.5e-130) {
		tmp = x;
	} else if (x <= 1.05e-202) {
		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 <= (-1.5d-130)) then
        tmp = x
    else if (x <= 1.05d-202) 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 <= -1.5e-130) {
		tmp = x;
	} else if (x <= 1.05e-202) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.5e-130:
		tmp = x
	elif x <= 1.05e-202:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.5e-130)
		tmp = x;
	elseif (x <= 1.05e-202)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.5e-130)
		tmp = x;
	elseif (x <= 1.05e-202)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.5e-130], x, If[LessEqual[x, 1.05e-202], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.49999999999999993e-130 or 1.04999999999999993e-202 < x

   1. Initial program 88.2%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 46.5%

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

   if -1.49999999999999993e-130 < x < 1.04999999999999993e-202

   1. Initial program 82.2%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 47.8

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

   5. Simplified 47.8%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 42.3%

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

Alternative 8: 35.5% 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 86.7%

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

3. Taylor expanded in y around 0

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

5. Simplified 37.1%

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

Developer Target 1: 93.9% 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 2024195 
(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))))