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

Percentage Accurate: 87.6% → 99.6%

Time: 8.4s

Alternatives: 12

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: 87.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{-272} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-y\right) - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -4e-272) (not (<= t_0 0.0))) t_0 (* z (/ (- (- y) x) y)))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -4e-272) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * ((-y - 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) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-4d-272)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = z * ((-y - x) / y)
    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 <= -4e-272) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * ((-y - x) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -4e-272) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = z * ((-y - x) / y)
	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 <= -4e-272) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(Float64(Float64(-y) - x) / y));
	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 <= -4e-272) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = z * ((-y - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -4e-272], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(z * N[(N[((-y) - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -3.99999999999999972e-272 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 -3.99999999999999972e-272 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 9.6%

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

   3. Taylor expanded in z around 0 98.5%

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

      1. mul-1-neg 98.5%

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

      2. associate-/l* 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. distribute-neg-frac2 100.0%

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

      5. +-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -4 \cdot 10^{-272} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-y\right) - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 64.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+191}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+165}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+82}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -0.0076:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+114}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e+191)
   (- z)
   (if (<= y -5.5e+165)
     (* z (/ x (- y)))
     (if (<= y -1.3e+82)
       (- z)
       (if (<= y -0.0076)
         (+ x y)
         (if (<= y -7e-58)
           (* x (/ z (- y)))
           (if (<= y 1.55e+114) (+ x y) (- z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+191) {
		tmp = -z;
	} else if (y <= -5.5e+165) {
		tmp = z * (x / -y);
	} else if (y <= -1.3e+82) {
		tmp = -z;
	} else if (y <= -0.0076) {
		tmp = x + y;
	} else if (y <= -7e-58) {
		tmp = x * (z / -y);
	} else if (y <= 1.55e+114) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2d+191)) then
        tmp = -z
    else if (y <= (-5.5d+165)) then
        tmp = z * (x / -y)
    else if (y <= (-1.3d+82)) then
        tmp = -z
    else if (y <= (-0.0076d0)) then
        tmp = x + y
    else if (y <= (-7d-58)) then
        tmp = x * (z / -y)
    else if (y <= 1.55d+114) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+191) {
		tmp = -z;
	} else if (y <= -5.5e+165) {
		tmp = z * (x / -y);
	} else if (y <= -1.3e+82) {
		tmp = -z;
	} else if (y <= -0.0076) {
		tmp = x + y;
	} else if (y <= -7e-58) {
		tmp = x * (z / -y);
	} else if (y <= 1.55e+114) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e+191:
		tmp = -z
	elif y <= -5.5e+165:
		tmp = z * (x / -y)
	elif y <= -1.3e+82:
		tmp = -z
	elif y <= -0.0076:
		tmp = x + y
	elif y <= -7e-58:
		tmp = x * (z / -y)
	elif y <= 1.55e+114:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e+191)
		tmp = Float64(-z);
	elseif (y <= -5.5e+165)
		tmp = Float64(z * Float64(x / Float64(-y)));
	elseif (y <= -1.3e+82)
		tmp = Float64(-z);
	elseif (y <= -0.0076)
		tmp = Float64(x + y);
	elseif (y <= -7e-58)
		tmp = Float64(x * Float64(z / Float64(-y)));
	elseif (y <= 1.55e+114)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2e+191)
		tmp = -z;
	elseif (y <= -5.5e+165)
		tmp = z * (x / -y);
	elseif (y <= -1.3e+82)
		tmp = -z;
	elseif (y <= -0.0076)
		tmp = x + y;
	elseif (y <= -7e-58)
		tmp = x * (z / -y);
	elseif (y <= 1.55e+114)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e+191], (-z), If[LessEqual[y, -5.5e+165], N[(z * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.3e+82], (-z), If[LessEqual[y, -0.0076], N[(x + y), $MachinePrecision], If[LessEqual[y, -7e-58], N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+114], N[(x + y), $MachinePrecision], (-z)]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.00000000000000015e191 or -5.4999999999999998e165 < y < -1.2999999999999999e82 or 1.55e114 < y

   1. Initial program 70.7%

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

   3. Taylor expanded in y around inf 78.3%

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

      1. mul-1-neg 78.3%

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

   5. Simplified 78.3%

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

   if -2.00000000000000015e191 < y < -5.4999999999999998e165

   1. Initial program 68.4%

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

      1. clear-num 68.3%

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

      2. inv-pow 68.3%

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

   4. Applied egg-rr 68.3%

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

      1. unpow-1 68.3%

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

      2. div-inv 68.4%

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

      3. associate-/r* 68.6%

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

      4. frac-2neg 68.6%

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

      5. metadata-eval 68.6%

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

      6. div-inv 68.4%

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

      7. cancel-sign-sub-inv 68.4%

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

      8. div-inv 68.6%

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

      9. distribute-neg-in 68.6%

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

      10. metadata-eval 68.6%

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

      11. distribute-frac-neg2 68.6%

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

      12. frac-2neg 68.6%

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

      13. +-commutative 68.6%

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

   6. Applied egg-rr 68.6%

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

   7. Taylor expanded in y around inf 57.2%

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

      1. associate-*r/ 57.2%

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

      2. mul-1-neg 57.2%

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

   9. Simplified 57.2%

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

   10. Taylor expanded in y around 0 57.6%

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

       1. mul-1-neg 57.6%

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

       2. *-commutative 57.6%

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

       3. associate-*r/ 78.8%

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

       4. distribute-lft-neg-in 78.8%

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

   12. Simplified 78.8%

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

   if -1.2999999999999999e82 < y < -0.00759999999999999998 or -6.9999999999999998e-58 < y < 1.55e114

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf 72.5%

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

      1. +-commutative 72.5%

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

   5. Simplified 72.5%

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

   if -0.00759999999999999998 < y < -6.9999999999999998e-58

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 84.9%

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

      1. mul-1-neg 84.9%

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

      2. *-commutative 84.9%

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

      3. associate-/l* 84.7%

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

      4. distribute-rgt-neg-in 84.7%

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

      5. +-commutative 84.7%

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

      6. distribute-neg-frac2 84.7%

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

   5. Simplified 84.7%

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

   6. Taylor expanded in y around 0 70.1%

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

      1. mul-1-neg 70.1%

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

      2. associate-*r/ 69.9%

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

      3. distribute-rgt-neg-in 69.9%

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

      4. mul-1-neg 69.9%

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

      5. associate-*r/ 69.9%

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

      6. neg-mul-1 69.9%

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

   8. Simplified 69.9%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+191}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+165}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+82}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -0.0076:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+114}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+191}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+165}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+82}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -0.047:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{-61}:\\ \;\;\;\;\frac{x \cdot z}{-y}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+119}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e+191)
   (- z)
   (if (<= y -9e+165)
     (* z (/ x (- y)))
     (if (<= y -1.7e+82)
       (- z)
       (if (<= y -0.047)
         (+ x y)
         (if (<= y -1.32e-61)
           (/ (* x z) (- y))
           (if (<= y 1.55e+119) (+ x y) (- z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+191) {
		tmp = -z;
	} else if (y <= -9e+165) {
		tmp = z * (x / -y);
	} else if (y <= -1.7e+82) {
		tmp = -z;
	} else if (y <= -0.047) {
		tmp = x + y;
	} else if (y <= -1.32e-61) {
		tmp = (x * z) / -y;
	} else if (y <= 1.55e+119) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2d+191)) then
        tmp = -z
    else if (y <= (-9d+165)) then
        tmp = z * (x / -y)
    else if (y <= (-1.7d+82)) then
        tmp = -z
    else if (y <= (-0.047d0)) then
        tmp = x + y
    else if (y <= (-1.32d-61)) then
        tmp = (x * z) / -y
    else if (y <= 1.55d+119) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+191) {
		tmp = -z;
	} else if (y <= -9e+165) {
		tmp = z * (x / -y);
	} else if (y <= -1.7e+82) {
		tmp = -z;
	} else if (y <= -0.047) {
		tmp = x + y;
	} else if (y <= -1.32e-61) {
		tmp = (x * z) / -y;
	} else if (y <= 1.55e+119) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e+191:
		tmp = -z
	elif y <= -9e+165:
		tmp = z * (x / -y)
	elif y <= -1.7e+82:
		tmp = -z
	elif y <= -0.047:
		tmp = x + y
	elif y <= -1.32e-61:
		tmp = (x * z) / -y
	elif y <= 1.55e+119:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e+191)
		tmp = Float64(-z);
	elseif (y <= -9e+165)
		tmp = Float64(z * Float64(x / Float64(-y)));
	elseif (y <= -1.7e+82)
		tmp = Float64(-z);
	elseif (y <= -0.047)
		tmp = Float64(x + y);
	elseif (y <= -1.32e-61)
		tmp = Float64(Float64(x * z) / Float64(-y));
	elseif (y <= 1.55e+119)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2e+191)
		tmp = -z;
	elseif (y <= -9e+165)
		tmp = z * (x / -y);
	elseif (y <= -1.7e+82)
		tmp = -z;
	elseif (y <= -0.047)
		tmp = x + y;
	elseif (y <= -1.32e-61)
		tmp = (x * z) / -y;
	elseif (y <= 1.55e+119)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e+191], (-z), If[LessEqual[y, -9e+165], N[(z * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e+82], (-z), If[LessEqual[y, -0.047], N[(x + y), $MachinePrecision], If[LessEqual[y, -1.32e-61], N[(N[(x * z), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[y, 1.55e+119], N[(x + y), $MachinePrecision], (-z)]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.00000000000000015e191 or -8.9999999999999993e165 < y < -1.69999999999999997e82 or 1.54999999999999998e119 < y

   1. Initial program 70.7%

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

   3. Taylor expanded in y around inf 78.3%

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

      1. mul-1-neg 78.3%

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

   5. Simplified 78.3%

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

   if -2.00000000000000015e191 < y < -8.9999999999999993e165

   1. Initial program 68.4%

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

      1. clear-num 68.3%

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

      2. inv-pow 68.3%

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

   4. Applied egg-rr 68.3%

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

      1. unpow-1 68.3%

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

      2. div-inv 68.4%

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

      3. associate-/r* 68.6%

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

      4. frac-2neg 68.6%

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

      5. metadata-eval 68.6%

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

      6. div-inv 68.4%

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

      7. cancel-sign-sub-inv 68.4%

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

      8. div-inv 68.6%

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

      9. distribute-neg-in 68.6%

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

      10. metadata-eval 68.6%

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

      11. distribute-frac-neg2 68.6%

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

      12. frac-2neg 68.6%

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

      13. +-commutative 68.6%

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

   6. Applied egg-rr 68.6%

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

   7. Taylor expanded in y around inf 57.2%

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

      1. associate-*r/ 57.2%

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

      2. mul-1-neg 57.2%

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

   9. Simplified 57.2%

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

   10. Taylor expanded in y around 0 57.6%

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

       1. mul-1-neg 57.6%

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

       2. *-commutative 57.6%

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

       3. associate-*r/ 78.8%

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

       4. distribute-lft-neg-in 78.8%

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

   12. Simplified 78.8%

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

   if -1.69999999999999997e82 < y < -0.047 or -1.32000000000000002e-61 < y < 1.54999999999999998e119

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf 72.5%

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

      1. +-commutative 72.5%

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

   5. Simplified 72.5%

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

   if -0.047 < y < -1.32000000000000002e-61

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 84.9%

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

      1. mul-1-neg 84.9%

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

      2. *-commutative 84.9%

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

      3. associate-/l* 84.7%

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

      4. distribute-rgt-neg-in 84.7%

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

      5. +-commutative 84.7%

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

      6. distribute-neg-frac2 84.7%

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

   5. Simplified 84.7%

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

   6. Taylor expanded in y around 0 70.1%

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

      1. associate-*r/ 70.1%

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

      2. mul-1-neg 70.1%

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

   8. Simplified 70.1%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+191}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+165}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+82}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -0.047:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{-61}:\\ \;\;\;\;\frac{x \cdot z}{-y}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+119}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - \frac{y}{z}}\\ t_1 := \frac{z}{\frac{y}{\left(-y\right) - x}}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -230000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-106}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-276}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+42}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 (/ y z)))) (t_1 (/ z (/ y (- (- y) x)))))
   (if (<= y -1.3e+82)
     t_1
     (if (<= y -230000000.0)
       (+ x y)
       (if (<= y -4e-106)
         t_0
         (if (<= y -1e-276) (+ x y) (if (<= y 3.4e+42) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double t_1 = z / (y / (-y - x));
	double tmp;
	if (y <= -1.3e+82) {
		tmp = t_1;
	} else if (y <= -230000000.0) {
		tmp = x + y;
	} else if (y <= -4e-106) {
		tmp = t_0;
	} else if (y <= -1e-276) {
		tmp = x + y;
	} else if (y <= 3.4e+42) {
		tmp = 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 = x / (1.0d0 - (y / z))
    t_1 = z / (y / (-y - x))
    if (y <= (-1.3d+82)) then
        tmp = t_1
    else if (y <= (-230000000.0d0)) then
        tmp = x + y
    else if (y <= (-4d-106)) then
        tmp = t_0
    else if (y <= (-1d-276)) then
        tmp = x + y
    else if (y <= 3.4d+42) then
        tmp = 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 = x / (1.0 - (y / z));
	double t_1 = z / (y / (-y - x));
	double tmp;
	if (y <= -1.3e+82) {
		tmp = t_1;
	} else if (y <= -230000000.0) {
		tmp = x + y;
	} else if (y <= -4e-106) {
		tmp = t_0;
	} else if (y <= -1e-276) {
		tmp = x + y;
	} else if (y <= 3.4e+42) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (1.0 - (y / z))
	t_1 = z / (y / (-y - x))
	tmp = 0
	if y <= -1.3e+82:
		tmp = t_1
	elif y <= -230000000.0:
		tmp = x + y
	elif y <= -4e-106:
		tmp = t_0
	elif y <= -1e-276:
		tmp = x + y
	elif y <= 3.4e+42:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(1.0 - Float64(y / z)))
	t_1 = Float64(z / Float64(y / Float64(Float64(-y) - x)))
	tmp = 0.0
	if (y <= -1.3e+82)
		tmp = t_1;
	elseif (y <= -230000000.0)
		tmp = Float64(x + y);
	elseif (y <= -4e-106)
		tmp = t_0;
	elseif (y <= -1e-276)
		tmp = Float64(x + y);
	elseif (y <= 3.4e+42)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (1.0 - (y / z));
	t_1 = z / (y / (-y - x));
	tmp = 0.0;
	if (y <= -1.3e+82)
		tmp = t_1;
	elseif (y <= -230000000.0)
		tmp = x + y;
	elseif (y <= -4e-106)
		tmp = t_0;
	elseif (y <= -1e-276)
		tmp = x + y;
	elseif (y <= 3.4e+42)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z / N[(y / N[((-y) - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+82], t$95$1, If[LessEqual[y, -230000000.0], N[(x + y), $MachinePrecision], If[LessEqual[y, -4e-106], t$95$0, If[LessEqual[y, -1e-276], N[(x + y), $MachinePrecision], If[LessEqual[y, 3.4e+42], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2999999999999999e82 or 3.39999999999999975e42 < y

   1. Initial program 74.1%

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

      1. clear-num 73.8%

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

      2. inv-pow 73.8%

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

   4. Applied egg-rr 73.8%

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

      1. unpow-1 73.8%

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

      2. div-inv 73.7%

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

      3. associate-/r* 73.7%

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

      4. frac-2neg 73.7%

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

      5. metadata-eval 73.7%

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

      6. div-inv 73.6%

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

      7. cancel-sign-sub-inv 73.6%

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

      8. div-inv 73.7%

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

      9. distribute-neg-in 73.7%

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

      10. metadata-eval 73.7%

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

      11. distribute-frac-neg2 73.7%

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

      12. frac-2neg 73.7%

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

      13. +-commutative 73.7%

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

   6. Applied egg-rr 73.7%

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

   7. Taylor expanded in y around inf 59.6%

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

      1. associate-*r/ 59.6%

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

      2. mul-1-neg 59.6%

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

   9. Simplified 59.6%

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

       1. associate-/l/ 84.3%

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

       2. distribute-frac-neg 84.3%

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

       3. associate-*l/ 84.5%

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

       4. *-un-lft-identity 84.5%

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

   11. Applied egg-rr 84.5%

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

   if -1.2999999999999999e82 < y < -2.3e8 or -3.99999999999999976e-106 < y < -1e-276

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf 89.7%

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

      1. +-commutative 89.7%

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

   5. Simplified 89.7%

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

   if -2.3e8 < y < -3.99999999999999976e-106 or -1e-276 < y < 3.39999999999999975e42

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 78.2%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+82}:\\ \;\;\;\;\frac{z}{\frac{y}{\left(-y\right) - x}}\\ \mathbf{elif}\;y \leq -230000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-276}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{\left(-y\right) - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - \frac{y}{z}}\\ t_1 := \frac{z}{\frac{y}{\left(-y\right) - x}}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -128000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-102}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-272}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+41}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 (/ y z)))) (t_1 (/ z (/ y (- (- y) x)))))
   (if (<= y -1.3e+82)
     t_1
     (if (<= y -128000000.0)
       (+ x y)
       (if (<= y -1.15e-102)
         t_0
         (if (<= y -4e-272)
           (* (+ x y) (+ 1.0 (/ y z)))
           (if (<= y 1.55e+41) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double t_1 = z / (y / (-y - x));
	double tmp;
	if (y <= -1.3e+82) {
		tmp = t_1;
	} else if (y <= -128000000.0) {
		tmp = x + y;
	} else if (y <= -1.15e-102) {
		tmp = t_0;
	} else if (y <= -4e-272) {
		tmp = (x + y) * (1.0 + (y / z));
	} else if (y <= 1.55e+41) {
		tmp = 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 = x / (1.0d0 - (y / z))
    t_1 = z / (y / (-y - x))
    if (y <= (-1.3d+82)) then
        tmp = t_1
    else if (y <= (-128000000.0d0)) then
        tmp = x + y
    else if (y <= (-1.15d-102)) then
        tmp = t_0
    else if (y <= (-4d-272)) then
        tmp = (x + y) * (1.0d0 + (y / z))
    else if (y <= 1.55d+41) then
        tmp = 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 = x / (1.0 - (y / z));
	double t_1 = z / (y / (-y - x));
	double tmp;
	if (y <= -1.3e+82) {
		tmp = t_1;
	} else if (y <= -128000000.0) {
		tmp = x + y;
	} else if (y <= -1.15e-102) {
		tmp = t_0;
	} else if (y <= -4e-272) {
		tmp = (x + y) * (1.0 + (y / z));
	} else if (y <= 1.55e+41) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (1.0 - (y / z))
	t_1 = z / (y / (-y - x))
	tmp = 0
	if y <= -1.3e+82:
		tmp = t_1
	elif y <= -128000000.0:
		tmp = x + y
	elif y <= -1.15e-102:
		tmp = t_0
	elif y <= -4e-272:
		tmp = (x + y) * (1.0 + (y / z))
	elif y <= 1.55e+41:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(1.0 - Float64(y / z)))
	t_1 = Float64(z / Float64(y / Float64(Float64(-y) - x)))
	tmp = 0.0
	if (y <= -1.3e+82)
		tmp = t_1;
	elseif (y <= -128000000.0)
		tmp = Float64(x + y);
	elseif (y <= -1.15e-102)
		tmp = t_0;
	elseif (y <= -4e-272)
		tmp = Float64(Float64(x + y) * Float64(1.0 + Float64(y / z)));
	elseif (y <= 1.55e+41)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (1.0 - (y / z));
	t_1 = z / (y / (-y - x));
	tmp = 0.0;
	if (y <= -1.3e+82)
		tmp = t_1;
	elseif (y <= -128000000.0)
		tmp = x + y;
	elseif (y <= -1.15e-102)
		tmp = t_0;
	elseif (y <= -4e-272)
		tmp = (x + y) * (1.0 + (y / z));
	elseif (y <= 1.55e+41)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z / N[(y / N[((-y) - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+82], t$95$1, If[LessEqual[y, -128000000.0], N[(x + y), $MachinePrecision], If[LessEqual[y, -1.15e-102], t$95$0, If[LessEqual[y, -4e-272], N[(N[(x + y), $MachinePrecision] * N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+41], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.2999999999999999e82 or 1.55e41 < y

   1. Initial program 74.1%

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

      1. clear-num 73.8%

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

      2. inv-pow 73.8%

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

   4. Applied egg-rr 73.8%

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

      1. unpow-1 73.8%

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

      2. div-inv 73.7%

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

      3. associate-/r* 73.7%

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

      4. frac-2neg 73.7%

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

      5. metadata-eval 73.7%

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

      6. div-inv 73.6%

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

      7. cancel-sign-sub-inv 73.6%

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

      8. div-inv 73.7%

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

      9. distribute-neg-in 73.7%

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

      10. metadata-eval 73.7%

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

      11. distribute-frac-neg2 73.7%

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

      12. frac-2neg 73.7%

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

      13. +-commutative 73.7%

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

   6. Applied egg-rr 73.7%

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

   7. Taylor expanded in y around inf 59.6%

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

      1. associate-*r/ 59.6%

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

      2. mul-1-neg 59.6%

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

   9. Simplified 59.6%

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

       1. associate-/l/ 84.3%

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

       2. distribute-frac-neg 84.3%

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

       3. associate-*l/ 84.5%

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

       4. *-un-lft-identity 84.5%

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

   11. Applied egg-rr 84.5%

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

   if -1.2999999999999999e82 < y < -1.28e8

   1. Initial program 91.4%

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

   3. Taylor expanded in z around inf 74.3%

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

      1. +-commutative 74.3%

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

   5. Simplified 74.3%

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

   if -1.28e8 < y < -1.14999999999999993e-102 or -3.99999999999999972e-272 < y < 1.55e41

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 78.2%

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

   if -1.14999999999999993e-102 < y < -3.99999999999999972e-272

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 93.6%

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

      1. associate-+r+ 93.6%

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

      2. *-rgt-identity 93.6%

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

      3. *-commutative 93.6%

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

      4. associate-/l* 93.6%

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

      5. distribute-lft-in 93.5%

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

      6. +-commutative 93.5%

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

   5. Simplified 93.5%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+82}:\\ \;\;\;\;\frac{z}{\frac{y}{\left(-y\right) - x}}\\ \mathbf{elif}\;y \leq -128000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-102}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-272}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{\left(-y\right) - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+191}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+165}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+82}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -120000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e+191)
   (- z)
   (if (<= y -9e+165)
     (* z (/ x (- y)))
     (if (<= y -1.7e+82)
       (- z)
       (if (<= y -120000000.0)
         (+ x y)
         (if (<= y 9e+125) (/ x (- 1.0 (/ y z))) (- z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+191) {
		tmp = -z;
	} else if (y <= -9e+165) {
		tmp = z * (x / -y);
	} else if (y <= -1.7e+82) {
		tmp = -z;
	} else if (y <= -120000000.0) {
		tmp = x + y;
	} else if (y <= 9e+125) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2d+191)) then
        tmp = -z
    else if (y <= (-9d+165)) then
        tmp = z * (x / -y)
    else if (y <= (-1.7d+82)) then
        tmp = -z
    else if (y <= (-120000000.0d0)) then
        tmp = x + y
    else if (y <= 9d+125) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+191) {
		tmp = -z;
	} else if (y <= -9e+165) {
		tmp = z * (x / -y);
	} else if (y <= -1.7e+82) {
		tmp = -z;
	} else if (y <= -120000000.0) {
		tmp = x + y;
	} else if (y <= 9e+125) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e+191:
		tmp = -z
	elif y <= -9e+165:
		tmp = z * (x / -y)
	elif y <= -1.7e+82:
		tmp = -z
	elif y <= -120000000.0:
		tmp = x + y
	elif y <= 9e+125:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e+191)
		tmp = Float64(-z);
	elseif (y <= -9e+165)
		tmp = Float64(z * Float64(x / Float64(-y)));
	elseif (y <= -1.7e+82)
		tmp = Float64(-z);
	elseif (y <= -120000000.0)
		tmp = Float64(x + y);
	elseif (y <= 9e+125)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2e+191)
		tmp = -z;
	elseif (y <= -9e+165)
		tmp = z * (x / -y);
	elseif (y <= -1.7e+82)
		tmp = -z;
	elseif (y <= -120000000.0)
		tmp = x + y;
	elseif (y <= 9e+125)
		tmp = x / (1.0 - (y / z));
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e+191], (-z), If[LessEqual[y, -9e+165], N[(z * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e+82], (-z), If[LessEqual[y, -120000000.0], N[(x + y), $MachinePrecision], If[LessEqual[y, 9e+125], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-z)]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.00000000000000015e191 or -8.9999999999999993e165 < y < -1.69999999999999997e82 or 9.0000000000000001e125 < y

   1. Initial program 69.9%

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

   3. Taylor expanded in y around inf 79.1%

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

      1. mul-1-neg 79.1%

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

   5. Simplified 79.1%

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

   if -2.00000000000000015e191 < y < -8.9999999999999993e165

   1. Initial program 68.4%

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

      1. clear-num 68.3%

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

      2. inv-pow 68.3%

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

   4. Applied egg-rr 68.3%

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

      1. unpow-1 68.3%

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

      2. div-inv 68.4%

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

      3. associate-/r* 68.6%

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

      4. frac-2neg 68.6%

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

      5. metadata-eval 68.6%

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

      6. div-inv 68.4%

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

      7. cancel-sign-sub-inv 68.4%

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

      8. div-inv 68.6%

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

      9. distribute-neg-in 68.6%

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

      10. metadata-eval 68.6%

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

      11. distribute-frac-neg2 68.6%

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

      12. frac-2neg 68.6%

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

      13. +-commutative 68.6%

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

   6. Applied egg-rr 68.6%

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

   7. Taylor expanded in y around inf 57.2%

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

      1. associate-*r/ 57.2%

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

      2. mul-1-neg 57.2%

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

   9. Simplified 57.2%

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

   10. Taylor expanded in y around 0 57.6%

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

       1. mul-1-neg 57.6%

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

       2. *-commutative 57.6%

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

       3. associate-*r/ 78.8%

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

       4. distribute-lft-neg-in 78.8%

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

   12. Simplified 78.8%

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

   if -1.69999999999999997e82 < y < -1.2e8

   1. Initial program 91.4%

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

   3. Taylor expanded in z around inf 74.3%

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

      1. +-commutative 74.3%

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

   5. Simplified 74.3%

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

   if -1.2e8 < y < 9.0000000000000001e125

   1. Initial program 99.4%

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

   3. Taylor expanded in x around inf 77.3%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+191}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+165}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+82}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -120000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;y \leq -2 \cdot 10^{+191}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+165}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+127}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -128000000:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (<= y -2e+191)
     (- z)
     (if (<= y -9e+165)
       (* z (/ x (- y)))
       (if (<= y -1.5e+127)
         (- z)
         (if (<= y -128000000.0)
           (/ y t_0)
           (if (<= y 3.8e+125) (/ x t_0) (- z))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -2e+191) {
		tmp = -z;
	} else if (y <= -9e+165) {
		tmp = z * (x / -y);
	} else if (y <= -1.5e+127) {
		tmp = -z;
	} else if (y <= -128000000.0) {
		tmp = y / t_0;
	} else if (y <= 3.8e+125) {
		tmp = x / t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    if (y <= (-2d+191)) then
        tmp = -z
    else if (y <= (-9d+165)) then
        tmp = z * (x / -y)
    else if (y <= (-1.5d+127)) then
        tmp = -z
    else if (y <= (-128000000.0d0)) then
        tmp = y / t_0
    else if (y <= 3.8d+125) then
        tmp = x / t_0
    else
        tmp = -z
    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 tmp;
	if (y <= -2e+191) {
		tmp = -z;
	} else if (y <= -9e+165) {
		tmp = z * (x / -y);
	} else if (y <= -1.5e+127) {
		tmp = -z;
	} else if (y <= -128000000.0) {
		tmp = y / t_0;
	} else if (y <= 3.8e+125) {
		tmp = x / t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if y <= -2e+191:
		tmp = -z
	elif y <= -9e+165:
		tmp = z * (x / -y)
	elif y <= -1.5e+127:
		tmp = -z
	elif y <= -128000000.0:
		tmp = y / t_0
	elif y <= 3.8e+125:
		tmp = x / t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if (y <= -2e+191)
		tmp = Float64(-z);
	elseif (y <= -9e+165)
		tmp = Float64(z * Float64(x / Float64(-y)));
	elseif (y <= -1.5e+127)
		tmp = Float64(-z);
	elseif (y <= -128000000.0)
		tmp = Float64(y / t_0);
	elseif (y <= 3.8e+125)
		tmp = Float64(x / t_0);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	tmp = 0.0;
	if (y <= -2e+191)
		tmp = -z;
	elseif (y <= -9e+165)
		tmp = z * (x / -y);
	elseif (y <= -1.5e+127)
		tmp = -z;
	elseif (y <= -128000000.0)
		tmp = y / t_0;
	elseif (y <= 3.8e+125)
		tmp = x / t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+191], (-z), If[LessEqual[y, -9e+165], N[(z * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.5e+127], (-z), If[LessEqual[y, -128000000.0], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, 3.8e+125], N[(x / t$95$0), $MachinePrecision], (-z)]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.00000000000000015e191 or -8.9999999999999993e165 < y < -1.5000000000000001e127 or 3.80000000000000002e125 < y

   1. Initial program 64.5%

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

   3. Taylor expanded in y around inf 81.7%

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

      1. mul-1-neg 81.7%

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

   5. Simplified 81.7%

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

   if -2.00000000000000015e191 < y < -8.9999999999999993e165

   1. Initial program 68.4%

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

      1. clear-num 68.3%

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

      2. inv-pow 68.3%

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

   4. Applied egg-rr 68.3%

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

      1. unpow-1 68.3%

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

      2. div-inv 68.4%

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

      3. associate-/r* 68.6%

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

      4. frac-2neg 68.6%

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

      5. metadata-eval 68.6%

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

      6. div-inv 68.4%

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

      7. cancel-sign-sub-inv 68.4%

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

      8. div-inv 68.6%

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

      9. distribute-neg-in 68.6%

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

      10. metadata-eval 68.6%

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

      11. distribute-frac-neg2 68.6%

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

      12. frac-2neg 68.6%

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

      13. +-commutative 68.6%

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

   6. Applied egg-rr 68.6%

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

   7. Taylor expanded in y around inf 57.2%

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

      1. associate-*r/ 57.2%

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

      2. mul-1-neg 57.2%

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

   9. Simplified 57.2%

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

   10. Taylor expanded in y around 0 57.6%

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

       1. mul-1-neg 57.6%

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

       2. *-commutative 57.6%

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

       3. associate-*r/ 78.8%

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

       4. distribute-lft-neg-in 78.8%

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

   12. Simplified 78.8%

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

   if -1.5000000000000001e127 < y < -1.28e8

   1. Initial program 95.6%

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

   3. Taylor expanded in x around 0 73.6%

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

   if -1.28e8 < y < 3.80000000000000002e125

   1. Initial program 99.4%

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

   3. Taylor expanded in x around inf 77.3%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+191}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+165}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+127}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -128000000:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+82}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -0.095:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+115}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.65e+82)
   (- z)
   (if (<= y -0.095)
     (+ x y)
     (if (<= y -6.5e-58)
       (* x (/ z (- y)))
       (if (<= y 5.8e+115) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.65e+82) {
		tmp = -z;
	} else if (y <= -0.095) {
		tmp = x + y;
	} else if (y <= -6.5e-58) {
		tmp = x * (z / -y);
	} else if (y <= 5.8e+115) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.65d+82)) then
        tmp = -z
    else if (y <= (-0.095d0)) then
        tmp = x + y
    else if (y <= (-6.5d-58)) then
        tmp = x * (z / -y)
    else if (y <= 5.8d+115) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.65e+82) {
		tmp = -z;
	} else if (y <= -0.095) {
		tmp = x + y;
	} else if (y <= -6.5e-58) {
		tmp = x * (z / -y);
	} else if (y <= 5.8e+115) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.65e+82:
		tmp = -z
	elif y <= -0.095:
		tmp = x + y
	elif y <= -6.5e-58:
		tmp = x * (z / -y)
	elif y <= 5.8e+115:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.65e+82)
		tmp = Float64(-z);
	elseif (y <= -0.095)
		tmp = Float64(x + y);
	elseif (y <= -6.5e-58)
		tmp = Float64(x * Float64(z / Float64(-y)));
	elseif (y <= 5.8e+115)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.65e+82)
		tmp = -z;
	elseif (y <= -0.095)
		tmp = x + y;
	elseif (y <= -6.5e-58)
		tmp = x * (z / -y);
	elseif (y <= 5.8e+115)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.65e+82], (-z), If[LessEqual[y, -0.095], N[(x + y), $MachinePrecision], If[LessEqual[y, -6.5e-58], N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+115], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6499999999999999e82 or 5.80000000000000009e115 < y

   1. Initial program 70.5%

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

   3. Taylor expanded in y around inf 71.5%

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

      1. mul-1-neg 71.5%

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

   5. Simplified 71.5%

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

   if -1.6499999999999999e82 < y < -0.095000000000000001 or -6.49999999999999964e-58 < y < 5.80000000000000009e115

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf 72.5%

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

      1. +-commutative 72.5%

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

   5. Simplified 72.5%

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

   if -0.095000000000000001 < y < -6.49999999999999964e-58

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 84.9%

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

      1. mul-1-neg 84.9%

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

      2. *-commutative 84.9%

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

      3. associate-/l* 84.7%

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

      4. distribute-rgt-neg-in 84.7%

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

      5. +-commutative 84.7%

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

      6. distribute-neg-frac2 84.7%

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

   5. Simplified 84.7%

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

   6. Taylor expanded in y around 0 70.1%

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

      1. mul-1-neg 70.1%

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

      2. associate-*r/ 69.9%

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

      3. distribute-rgt-neg-in 69.9%

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

      4. mul-1-neg 69.9%

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

      5. associate-*r/ 69.9%

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

      6. neg-mul-1 69.9%

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

   8. Simplified 69.9%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+82}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -0.095:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+115}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+82} \lor \neg \left(y \leq 1.8 \cdot 10^{+114}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.4e+82) (not (<= y 1.8e+114))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.4e+82) || !(y <= 1.8e+114)) {
		tmp = -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 ((y <= (-1.4d+82)) .or. (.not. (y <= 1.8d+114))) then
        tmp = -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 ((y <= -1.4e+82) || !(y <= 1.8e+114)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.4e+82) or not (y <= 1.8e+114):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.4e+82) || !(y <= 1.8e+114))
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.4e+82) || ~((y <= 1.8e+114)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.4e+82], N[Not[LessEqual[y, 1.8e+114]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e82 or 1.8e114 < y

   1. Initial program 70.5%

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

   3. Taylor expanded in y around inf 71.5%

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

      1. mul-1-neg 71.5%

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

   5. Simplified 71.5%

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

   if -1.4e82 < y < 1.8e114

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf 68.5%

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

      1. +-commutative 68.5%

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

   5. Simplified 68.5%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+82} \lor \neg \left(y \leq 1.8 \cdot 10^{+114}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+82} \lor \neg \left(y \leq 1.6 \cdot 10^{+41}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.3e+82) (not (<= y 1.6e+41))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.3e+82) || !(y <= 1.6e+41)) {
		tmp = -z;
	} 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 ((y <= (-1.3d+82)) .or. (.not. (y <= 1.6d+41))) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.3e+82) || !(y <= 1.6e+41)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.3e+82) or not (y <= 1.6e+41):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.3e+82) || !(y <= 1.6e+41))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.3e+82) || ~((y <= 1.6e+41)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.3e+82], N[Not[LessEqual[y, 1.6e+41]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -1.2999999999999999e82 or 1.60000000000000005e41 < y

   1. Initial program 74.1%

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

   3. Taylor expanded in y around inf 65.8%

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

      1. mul-1-neg 65.8%

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

   5. Simplified 65.8%

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

   if -1.2999999999999999e82 < y < 1.60000000000000005e41

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0 54.8%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+82} \lor \neg \left(y \leq 1.6 \cdot 10^{+41}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 40.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-216}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2e-120) x (if (<= x 8.2e-216) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2e-120) {
		tmp = x;
	} else if (x <= 8.2e-216) {
		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 <= (-2d-120)) then
        tmp = x
    else if (x <= 8.2d-216) 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 <= -2e-120) {
		tmp = x;
	} else if (x <= 8.2e-216) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2e-120:
		tmp = x
	elif x <= 8.2e-216:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2e-120)
		tmp = x;
	elseif (x <= 8.2e-216)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2e-120)
		tmp = x;
	elseif (x <= 8.2e-216)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2e-120], x, If[LessEqual[x, 8.2e-216], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.99999999999999996e-120 or 8.20000000000000047e-216 < x

   1. Initial program 89.4%

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

   3. Taylor expanded in y around 0 43.5%

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

   if -1.99999999999999996e-120 < x < 8.20000000000000047e-216

   1. Initial program 90.4%

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

   3. Taylor expanded in x around 0 75.6%

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

   4. Taylor expanded in y around 0 38.1%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-216}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 34.9% 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 89.6%

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

3. Taylor expanded in y around 0 37.0%

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

4. Final simplification 37.0%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 93.6% 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 2024115 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :alt
  (if (< y -3.7429310762689856e+171) (* (/ (+ y x) (- y)) z) (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) (* (/ (+ y x) (- y)) z)))

  (/ (+ x y) (- 1.0 (/ y z))))