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

Percentage Accurate: 88.3% → 99.8%

Time: 6.2s

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: 88.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-283) (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 <= -1e-283) || !(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 <= (-1d-283)) .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 <= -1e-283) || !(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 <= -1e-283) 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 <= -1e-283) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(z / Float64(y / Float64(Float64(-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 <= -1e-283) || ~((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, -1e-283], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(z / N[(y / N[((-x) - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.9%

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

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

   1. Initial program 12.4%

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

   3. Taylor expanded in z around 0 94.6%

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

      1. mul-1-neg 94.6%

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

      2. associate-/l* 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. distribute-neg-frac2 99.9%

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

      5. +-commutative 99.9%

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

   5. Simplified 99.9%

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

      1. associate-*r/ 94.6%

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

      2. distribute-frac-neg2 94.6%

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

      3. add-sqr-sqrt 42.3%

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

      4. sqrt-unprod 30.4%

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

      5. sqr-neg 30.4%

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

      6. sqrt-unprod 3.1%

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

      7. add-sqr-sqrt 5.8%

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

      8. associate-*r/ 5.7%

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

      9. clear-num 5.7%

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

      10. un-div-inv 5.7%

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

      11. add-sqr-sqrt 3.0%

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

      12. sqrt-unprod 30.4%

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

      13. sqr-neg 30.4%

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

      14. sqrt-unprod 42.3%

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

      15. add-sqr-sqrt 100.0%

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

      16. +-commutative 100.0%

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

   7. Applied egg-rr 100.0%

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

4. Final simplification 99.9%

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

Alternative 2: 67.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - \frac{y}{z}}\\ \mathbf{if}\;y \leq -4 \cdot 10^{+59}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-107}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+45}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 10^{+66}:\\ \;\;\;\;y \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+103}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 (/ y z)))))
   (if (<= y -4e+59)
     (- z)
     (if (<= y 4.1e-107)
       (+ x y)
       (if (<= y 9.2e+45)
         t_0
         (if (<= y 1e+66)
           (* y (+ 1.0 (/ y z)))
           (if (<= y 2.1e+103) t_0 (- z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -4e+59) {
		tmp = -z;
	} else if (y <= 4.1e-107) {
		tmp = x + y;
	} else if (y <= 9.2e+45) {
		tmp = t_0;
	} else if (y <= 1e+66) {
		tmp = y * (1.0 + (y / z));
	} else if (y <= 2.1e+103) {
		tmp = 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 = x / (1.0d0 - (y / z))
    if (y <= (-4d+59)) then
        tmp = -z
    else if (y <= 4.1d-107) then
        tmp = x + y
    else if (y <= 9.2d+45) then
        tmp = t_0
    else if (y <= 1d+66) then
        tmp = y * (1.0d0 + (y / z))
    else if (y <= 2.1d+103) then
        tmp = 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 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -4e+59) {
		tmp = -z;
	} else if (y <= 4.1e-107) {
		tmp = x + y;
	} else if (y <= 9.2e+45) {
		tmp = t_0;
	} else if (y <= 1e+66) {
		tmp = y * (1.0 + (y / z));
	} else if (y <= 2.1e+103) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (1.0 - (y / z))
	tmp = 0
	if y <= -4e+59:
		tmp = -z
	elif y <= 4.1e-107:
		tmp = x + y
	elif y <= 9.2e+45:
		tmp = t_0
	elif y <= 1e+66:
		tmp = y * (1.0 + (y / z))
	elif y <= 2.1e+103:
		tmp = t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (y <= -4e+59)
		tmp = Float64(-z);
	elseif (y <= 4.1e-107)
		tmp = Float64(x + y);
	elseif (y <= 9.2e+45)
		tmp = t_0;
	elseif (y <= 1e+66)
		tmp = Float64(y * Float64(1.0 + Float64(y / z)));
	elseif (y <= 2.1e+103)
		tmp = t_0;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (1.0 - (y / z));
	tmp = 0.0;
	if (y <= -4e+59)
		tmp = -z;
	elseif (y <= 4.1e-107)
		tmp = x + y;
	elseif (y <= 9.2e+45)
		tmp = t_0;
	elseif (y <= 1e+66)
		tmp = y * (1.0 + (y / z));
	elseif (y <= 2.1e+103)
		tmp = t_0;
	else
		tmp = -z;
	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]}, If[LessEqual[y, -4e+59], (-z), If[LessEqual[y, 4.1e-107], N[(x + y), $MachinePrecision], If[LessEqual[y, 9.2e+45], t$95$0, If[LessEqual[y, 1e+66], N[(y * N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+103], t$95$0, (-z)]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.99999999999999989e59 or 2.1000000000000002e103 < y

   1. Initial program 68.5%

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

   3. Taylor expanded in y around inf 73.4%

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

      1. mul-1-neg 73.4%

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

   5. Simplified 73.4%

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

   if -3.99999999999999989e59 < y < 4.0999999999999999e-107

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 75.6%

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

      1. +-commutative 75.6%

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

   5. Simplified 75.6%

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

   if 4.0999999999999999e-107 < y < 9.20000000000000049e45 or 9.99999999999999945e65 < y < 2.1000000000000002e103

   1. Initial program 93.6%

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

   3. Taylor expanded in x around inf 72.7%

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

   if 9.20000000000000049e45 < y < 9.99999999999999945e65

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.1%

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

   4. Taylor expanded in y around 0 64.6%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+59}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-107}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 10^{+66}:\\ \;\;\;\;y \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+103}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+63}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-107}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+75}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (<= y -2.8e+63)
     (- z)
     (if (<= y 3.6e-107)
       (+ x y)
       (if (<= y 2.15e+38) (/ x t_0) (if (<= y 4.8e+75) (/ y t_0) (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -2.8e+63) {
		tmp = -z;
	} else if (y <= 3.6e-107) {
		tmp = x + y;
	} else if (y <= 2.15e+38) {
		tmp = x / t_0;
	} else if (y <= 4.8e+75) {
		tmp = y / 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 <= (-2.8d+63)) then
        tmp = -z
    else if (y <= 3.6d-107) then
        tmp = x + y
    else if (y <= 2.15d+38) then
        tmp = x / t_0
    else if (y <= 4.8d+75) then
        tmp = y / 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 <= -2.8e+63) {
		tmp = -z;
	} else if (y <= 3.6e-107) {
		tmp = x + y;
	} else if (y <= 2.15e+38) {
		tmp = x / t_0;
	} else if (y <= 4.8e+75) {
		tmp = y / t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if y <= -2.8e+63:
		tmp = -z
	elif y <= 3.6e-107:
		tmp = x + y
	elif y <= 2.15e+38:
		tmp = x / t_0
	elif y <= 4.8e+75:
		tmp = y / 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 <= -2.8e+63)
		tmp = Float64(-z);
	elseif (y <= 3.6e-107)
		tmp = Float64(x + y);
	elseif (y <= 2.15e+38)
		tmp = Float64(x / t_0);
	elseif (y <= 4.8e+75)
		tmp = Float64(y / 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 <= -2.8e+63)
		tmp = -z;
	elseif (y <= 3.6e-107)
		tmp = x + y;
	elseif (y <= 2.15e+38)
		tmp = x / t_0;
	elseif (y <= 4.8e+75)
		tmp = y / 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, -2.8e+63], (-z), If[LessEqual[y, 3.6e-107], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.15e+38], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 4.8e+75], N[(y / t$95$0), $MachinePrecision], (-z)]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.79999999999999987e63 or 4.8e75 < y

   1. Initial program 69.6%

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

   3. Taylor expanded in y around inf 71.1%

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

      1. mul-1-neg 71.1%

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

   5. Simplified 71.1%

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

   if -2.79999999999999987e63 < y < 3.59999999999999976e-107

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 75.6%

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

      1. +-commutative 75.6%

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

   5. Simplified 75.6%

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

   if 3.59999999999999976e-107 < y < 2.1499999999999998e38

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf 74.9%

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

   if 2.1499999999999998e38 < y < 4.8e75

   1. Initial program 88.7%

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

   3. Taylor expanded in x around 0 86.2%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+63}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-107}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+75}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{\frac{y}{\left(-x\right) - y}}\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+41}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-107}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ z (/ y (- (- x) y)))))
   (if (<= y -6.2e+41)
     t_0
     (if (<= y 3.9e-107)
       (* (+ x y) (+ 1.0 (/ y z)))
       (if (<= y 2.5e+27) (/ x (- 1.0 (/ y z))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z / (y / (-x - y));
	double tmp;
	if (y <= -6.2e+41) {
		tmp = t_0;
	} else if (y <= 3.9e-107) {
		tmp = (x + y) * (1.0 + (y / z));
	} else if (y <= 2.5e+27) {
		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 / (y / (-x - y))
    if (y <= (-6.2d+41)) then
        tmp = t_0
    else if (y <= 3.9d-107) then
        tmp = (x + y) * (1.0d0 + (y / z))
    else if (y <= 2.5d+27) 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 / (y / (-x - y));
	double tmp;
	if (y <= -6.2e+41) {
		tmp = t_0;
	} else if (y <= 3.9e-107) {
		tmp = (x + y) * (1.0 + (y / z));
	} else if (y <= 2.5e+27) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z / (y / (-x - y))
	tmp = 0
	if y <= -6.2e+41:
		tmp = t_0
	elif y <= 3.9e-107:
		tmp = (x + y) * (1.0 + (y / z))
	elif y <= 2.5e+27:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z / Float64(y / Float64(Float64(-x) - y)))
	tmp = 0.0
	if (y <= -6.2e+41)
		tmp = t_0;
	elseif (y <= 3.9e-107)
		tmp = Float64(Float64(x + y) * Float64(1.0 + Float64(y / z)));
	elseif (y <= 2.5e+27)
		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 / (y / (-x - y));
	tmp = 0.0;
	if (y <= -6.2e+41)
		tmp = t_0;
	elseif (y <= 3.9e-107)
		tmp = (x + y) * (1.0 + (y / z));
	elseif (y <= 2.5e+27)
		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[(y / N[((-x) - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+41], t$95$0, If[LessEqual[y, 3.9e-107], N[(N[(x + y), $MachinePrecision] * N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+27], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.2e41 or 2.4999999999999999e27 < y

   1. Initial program 71.4%

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

   3. Taylor expanded in z around 0 66.6%

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

      1. mul-1-neg 66.6%

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

      2. associate-/l* 82.4%

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

      3. distribute-rgt-neg-in 82.4%

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

      4. distribute-neg-frac2 82.4%

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

      5. +-commutative 82.4%

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

   5. Simplified 82.4%

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

      1. associate-*r/ 66.6%

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

      2. distribute-frac-neg2 66.6%

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

      3. add-sqr-sqrt 31.0%

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

      4. sqrt-unprod 19.5%

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

      5. sqr-neg 19.5%

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

      6. sqrt-unprod 1.2%

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

      7. add-sqr-sqrt 2.9%

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

      8. associate-*r/ 3.0%

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

      9. clear-num 3.0%

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

      10. un-div-inv 3.0%

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

      11. add-sqr-sqrt 1.3%

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

      12. sqrt-unprod 20.0%

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

      13. sqr-neg 20.0%

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

      14. sqrt-unprod 36.7%

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

      15. add-sqr-sqrt 82.4%

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

      16. +-commutative 82.4%

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

   7. Applied egg-rr 82.4%

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

   if -6.2e41 < y < 3.9000000000000001e-107

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 77.0%

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

      1. associate-+r+ 77.0%

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

      2. *-rgt-identity 77.0%

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

      3. *-commutative 77.0%

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

      4. associate-/l* 77.5%

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

      5. distribute-lft-in 77.5%

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

      6. +-commutative 77.5%

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

   5. Simplified 77.5%

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

   if 3.9000000000000001e-107 < y < 2.4999999999999999e27

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 76.1%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+41}:\\ \;\;\;\;\frac{z}{\frac{y}{\left(-x\right) - y}}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-107}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{\left(-x\right) - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{\frac{y}{\left(-x\right) - y}}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+42}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-107}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ z (/ y (- (- x) y)))))
   (if (<= y -1e+42)
     t_0
     (if (<= y 4.5e-107)
       (+ x y)
       (if (<= y 2.3e+28) (/ x (- 1.0 (/ y z))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z / (y / (-x - y));
	double tmp;
	if (y <= -1e+42) {
		tmp = t_0;
	} else if (y <= 4.5e-107) {
		tmp = x + y;
	} else if (y <= 2.3e+28) {
		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 / (y / (-x - y))
    if (y <= (-1d+42)) then
        tmp = t_0
    else if (y <= 4.5d-107) then
        tmp = x + y
    else if (y <= 2.3d+28) 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 / (y / (-x - y));
	double tmp;
	if (y <= -1e+42) {
		tmp = t_0;
	} else if (y <= 4.5e-107) {
		tmp = x + y;
	} else if (y <= 2.3e+28) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z / (y / (-x - y))
	tmp = 0
	if y <= -1e+42:
		tmp = t_0
	elif y <= 4.5e-107:
		tmp = x + y
	elif y <= 2.3e+28:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z / Float64(y / Float64(Float64(-x) - y)))
	tmp = 0.0
	if (y <= -1e+42)
		tmp = t_0;
	elseif (y <= 4.5e-107)
		tmp = Float64(x + y);
	elseif (y <= 2.3e+28)
		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 / (y / (-x - y));
	tmp = 0.0;
	if (y <= -1e+42)
		tmp = t_0;
	elseif (y <= 4.5e-107)
		tmp = x + y;
	elseif (y <= 2.3e+28)
		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[(y / N[((-x) - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+42], t$95$0, If[LessEqual[y, 4.5e-107], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.3e+28], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.00000000000000004e42 or 2.29999999999999984e28 < y

   1. Initial program 71.4%

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

   3. Taylor expanded in z around 0 66.6%

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

      1. mul-1-neg 66.6%

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

      2. associate-/l* 82.4%

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

      3. distribute-rgt-neg-in 82.4%

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

      4. distribute-neg-frac2 82.4%

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

      5. +-commutative 82.4%

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

   5. Simplified 82.4%

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

      1. associate-*r/ 66.6%

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

      2. distribute-frac-neg2 66.6%

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

      3. add-sqr-sqrt 31.0%

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

      4. sqrt-unprod 19.5%

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

      5. sqr-neg 19.5%

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

      6. sqrt-unprod 1.2%

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

      7. add-sqr-sqrt 2.9%

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

      8. associate-*r/ 3.0%

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

      9. clear-num 3.0%

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

      10. un-div-inv 3.0%

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

      11. add-sqr-sqrt 1.3%

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

      12. sqrt-unprod 20.0%

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

      13. sqr-neg 20.0%

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

      14. sqrt-unprod 36.7%

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

      15. add-sqr-sqrt 82.4%

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

      16. +-commutative 82.4%

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

   7. Applied egg-rr 82.4%

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

   if -1.00000000000000004e42 < y < 4.50000000000000016e-107

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 77.1%

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

      1. +-commutative 77.1%

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

   5. Simplified 77.1%

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

   if 4.50000000000000016e-107 < y < 2.29999999999999984e28

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 76.1%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+42}:\\ \;\;\;\;\frac{z}{\frac{y}{\left(-x\right) - y}}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-107}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{\left(-x\right) - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+61}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-54}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+44}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+48}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.7e+61)
   (- z)
   (if (<= y 5.5e-54)
     (+ x y)
     (if (<= y 6e+44) (/ (* x (- z)) y) (if (<= y 3.1e+48) y (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.7e+61) {
		tmp = -z;
	} else if (y <= 5.5e-54) {
		tmp = x + y;
	} else if (y <= 6e+44) {
		tmp = (x * -z) / y;
	} else if (y <= 3.1e+48) {
		tmp = 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 <= (-3.7d+61)) then
        tmp = -z
    else if (y <= 5.5d-54) then
        tmp = x + y
    else if (y <= 6d+44) then
        tmp = (x * -z) / y
    else if (y <= 3.1d+48) then
        tmp = 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 <= -3.7e+61) {
		tmp = -z;
	} else if (y <= 5.5e-54) {
		tmp = x + y;
	} else if (y <= 6e+44) {
		tmp = (x * -z) / y;
	} else if (y <= 3.1e+48) {
		tmp = y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.7e+61:
		tmp = -z
	elif y <= 5.5e-54:
		tmp = x + y
	elif y <= 6e+44:
		tmp = (x * -z) / y
	elif y <= 3.1e+48:
		tmp = y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.7e+61)
		tmp = Float64(-z);
	elseif (y <= 5.5e-54)
		tmp = Float64(x + y);
	elseif (y <= 6e+44)
		tmp = Float64(Float64(x * Float64(-z)) / y);
	elseif (y <= 3.1e+48)
		tmp = y;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.7e+61)
		tmp = -z;
	elseif (y <= 5.5e-54)
		tmp = x + y;
	elseif (y <= 6e+44)
		tmp = (x * -z) / y;
	elseif (y <= 3.1e+48)
		tmp = y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.7e+61], (-z), If[LessEqual[y, 5.5e-54], N[(x + y), $MachinePrecision], If[LessEqual[y, 6e+44], N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 3.1e+48], y, (-z)]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.70000000000000003e61 or 3.10000000000000005e48 < y

   1. Initial program 70.9%

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

   3. Taylor expanded in y around inf 70.0%

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

      1. mul-1-neg 70.0%

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

   5. Simplified 70.0%

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

   if -3.70000000000000003e61 < y < 5.50000000000000046e-54

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf 74.0%

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

      1. +-commutative 74.0%

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

   5. Simplified 74.0%

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

   if 5.50000000000000046e-54 < y < 5.99999999999999974e44

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0 61.1%

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

      1. mul-1-neg 61.1%

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

      2. associate-/l* 57.0%

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

      3. distribute-rgt-neg-in 57.0%

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

      4. distribute-neg-frac2 57.0%

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

      5. +-commutative 57.0%

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

   5. Simplified 57.0%

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

   6. Taylor expanded in y around 0 54.5%

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

      1. associate-*r/ 54.5%

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

      2. associate-*r* 54.5%

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

      3. mul-1-neg 54.5%

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

   8. Simplified 54.5%

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

   if 5.99999999999999974e44 < y < 3.10000000000000005e48

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+61}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-54}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+44}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+48}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+63}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+45}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+49}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.5e+63)
   (- z)
   (if (<= y 3.1e-10)
     (+ x y)
     (if (<= y 7e+45) (* z (/ x (- y))) (if (<= y 2.2e+49) y (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.5e+63) {
		tmp = -z;
	} else if (y <= 3.1e-10) {
		tmp = x + y;
	} else if (y <= 7e+45) {
		tmp = z * (x / -y);
	} else if (y <= 2.2e+49) {
		tmp = 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 <= (-4.5d+63)) then
        tmp = -z
    else if (y <= 3.1d-10) then
        tmp = x + y
    else if (y <= 7d+45) then
        tmp = z * (x / -y)
    else if (y <= 2.2d+49) then
        tmp = 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 <= -4.5e+63) {
		tmp = -z;
	} else if (y <= 3.1e-10) {
		tmp = x + y;
	} else if (y <= 7e+45) {
		tmp = z * (x / -y);
	} else if (y <= 2.2e+49) {
		tmp = y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.5e+63:
		tmp = -z
	elif y <= 3.1e-10:
		tmp = x + y
	elif y <= 7e+45:
		tmp = z * (x / -y)
	elif y <= 2.2e+49:
		tmp = y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.5e+63)
		tmp = Float64(-z);
	elseif (y <= 3.1e-10)
		tmp = Float64(x + y);
	elseif (y <= 7e+45)
		tmp = Float64(z * Float64(x / Float64(-y)));
	elseif (y <= 2.2e+49)
		tmp = y;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.5e+63)
		tmp = -z;
	elseif (y <= 3.1e-10)
		tmp = x + y;
	elseif (y <= 7e+45)
		tmp = z * (x / -y);
	elseif (y <= 2.2e+49)
		tmp = y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.5e+63], (-z), If[LessEqual[y, 3.1e-10], N[(x + y), $MachinePrecision], If[LessEqual[y, 7e+45], N[(z * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+49], y, (-z)]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.50000000000000017e63 or 2.2000000000000001e49 < y

   1. Initial program 70.9%

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

   3. Taylor expanded in y around inf 70.0%

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

      1. mul-1-neg 70.0%

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

   5. Simplified 70.0%

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

   if -4.50000000000000017e63 < y < 3.10000000000000015e-10

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf 71.5%

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

      1. +-commutative 71.5%

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

   5. Simplified 71.5%

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

   if 3.10000000000000015e-10 < y < 7.00000000000000046e45

   1. Initial program 81.5%

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

   3. Taylor expanded in z around 0 71.0%

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

      1. mul-1-neg 71.0%

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

      2. associate-/l* 71.2%

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

      3. distribute-rgt-neg-in 71.2%

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

      4. distribute-neg-frac2 71.2%

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

      5. +-commutative 71.2%

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

   5. Simplified 71.2%

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

   6. Taylor expanded in y around 0 66.7%

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

      1. associate-*r/ 66.7%

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

      2. mul-1-neg 66.7%

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

   8. Simplified 66.7%

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

   if 7.00000000000000046e45 < y < 2.2000000000000001e49

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+63}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+45}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+49}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+65}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-11}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{z}{\frac{y}{-x}}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+51}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.6e+65)
   (- z)
   (if (<= y 5.8e-11)
     (+ x y)
     (if (<= y 5.2e+45) (/ z (/ y (- x))) (if (<= y 8.8e+51) y (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.6e+65) {
		tmp = -z;
	} else if (y <= 5.8e-11) {
		tmp = x + y;
	} else if (y <= 5.2e+45) {
		tmp = z / (y / -x);
	} else if (y <= 8.8e+51) {
		tmp = 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 <= (-1.6d+65)) then
        tmp = -z
    else if (y <= 5.8d-11) then
        tmp = x + y
    else if (y <= 5.2d+45) then
        tmp = z / (y / -x)
    else if (y <= 8.8d+51) then
        tmp = 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 <= -1.6e+65) {
		tmp = -z;
	} else if (y <= 5.8e-11) {
		tmp = x + y;
	} else if (y <= 5.2e+45) {
		tmp = z / (y / -x);
	} else if (y <= 8.8e+51) {
		tmp = y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.6e+65:
		tmp = -z
	elif y <= 5.8e-11:
		tmp = x + y
	elif y <= 5.2e+45:
		tmp = z / (y / -x)
	elif y <= 8.8e+51:
		tmp = y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.6e+65)
		tmp = Float64(-z);
	elseif (y <= 5.8e-11)
		tmp = Float64(x + y);
	elseif (y <= 5.2e+45)
		tmp = Float64(z / Float64(y / Float64(-x)));
	elseif (y <= 8.8e+51)
		tmp = y;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.6e+65)
		tmp = -z;
	elseif (y <= 5.8e-11)
		tmp = x + y;
	elseif (y <= 5.2e+45)
		tmp = z / (y / -x);
	elseif (y <= 8.8e+51)
		tmp = y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.6e+65], (-z), If[LessEqual[y, 5.8e-11], N[(x + y), $MachinePrecision], If[LessEqual[y, 5.2e+45], N[(z / N[(y / (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.8e+51], y, (-z)]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.60000000000000003e65 or 8.79999999999999967e51 < y

   1. Initial program 70.9%

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

   3. Taylor expanded in y around inf 70.0%

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

      1. mul-1-neg 70.0%

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

   5. Simplified 70.0%

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

   if -1.60000000000000003e65 < y < 5.8e-11

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf 71.5%

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

      1. +-commutative 71.5%

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

   5. Simplified 71.5%

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

   if 5.8e-11 < y < 5.20000000000000014e45

   1. Initial program 81.5%

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

   3. Taylor expanded in z around 0 71.0%

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

      1. mul-1-neg 71.0%

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

      2. associate-/l* 71.2%

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

      3. distribute-rgt-neg-in 71.2%

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

      4. distribute-neg-frac2 71.2%

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

      5. +-commutative 71.2%

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

   5. Simplified 71.2%

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

      1. associate-*r/ 71.0%

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

      2. distribute-frac-neg2 71.0%

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

      3. add-sqr-sqrt 70.9%

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

      4. sqrt-unprod 71.0%

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

      5. sqr-neg 71.0%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 3.0%

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

      8. associate-*r/ 3.0%

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

      9. clear-num 3.0%

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

      10. un-div-inv 3.0%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 71.0%

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

      13. sqr-neg 71.0%

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

      14. sqrt-unprod 70.9%

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

      15. add-sqr-sqrt 71.0%

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

      16. +-commutative 71.0%

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

   7. Applied egg-rr 71.0%

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

   8. Taylor expanded in y around 0 66.5%

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

      1. associate-*r/ 52.3%

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

      2. *-commutative 52.3%

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

      3. associate-/r/ 66.5%

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

   10. Simplified 66.5%

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

   if 5.20000000000000014e45 < y < 8.79999999999999967e51

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+65}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-11}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{z}{\frac{y}{-x}}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+51}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+63} \lor \neg \left(y \leq 3.2 \cdot 10^{+48}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.5e+63) (not (<= y 3.2e+48))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.5e+63) || !(y <= 3.2e+48)) {
		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 <= (-5.5d+63)) .or. (.not. (y <= 3.2d+48))) 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 <= -5.5e+63) || !(y <= 3.2e+48)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.5e+63) or not (y <= 3.2e+48):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.5e+63) || !(y <= 3.2e+48))
		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 <= -5.5e+63) || ~((y <= 3.2e+48)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.5e+63], N[Not[LessEqual[y, 3.2e+48]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.50000000000000004e63 or 3.2000000000000001e48 < y

   1. Initial program 70.9%

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

   3. Taylor expanded in y around inf 70.0%

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

      1. mul-1-neg 70.0%

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

   5. Simplified 70.0%

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

   if -5.50000000000000004e63 < y < 3.2000000000000001e48

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf 69.3%

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

      1. +-commutative 69.3%

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

   5. Simplified 69.3%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+63} \lor \neg \left(y \leq 3.2 \cdot 10^{+48}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+41} \lor \neg \left(y \leq 3.6 \cdot 10^{+28}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.4e+41) (not (<= y 3.6e+28))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.4e+41) || !(y <= 3.6e+28)) {
		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 <= (-6.4d+41)) .or. (.not. (y <= 3.6d+28))) 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 <= -6.4e+41) || !(y <= 3.6e+28)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.4e+41) or not (y <= 3.6e+28):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.4e+41) || !(y <= 3.6e+28))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.4e+41) || ~((y <= 3.6e+28)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.4e+41], N[Not[LessEqual[y, 3.6e+28]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -6.40000000000000019e41 or 3.5999999999999999e28 < y

   1. Initial program 71.4%

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

   3. Taylor expanded in y around inf 64.0%

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

      1. mul-1-neg 64.0%

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

   5. Simplified 64.0%

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

   if -6.40000000000000019e41 < y < 3.5999999999999999e28

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0 54.2%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+41} \lor \neg \left(y \leq 3.6 \cdot 10^{+28}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-172}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-204}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.3e-172) x (if (<= x 3.7e-204) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.3e-172) {
		tmp = x;
	} else if (x <= 3.7e-204) {
		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 <= (-2.3d-172)) then
        tmp = x
    else if (x <= 3.7d-204) 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 <= -2.3e-172) {
		tmp = x;
	} else if (x <= 3.7e-204) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.3e-172:
		tmp = x
	elif x <= 3.7e-204:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.3e-172)
		tmp = x;
	elseif (x <= 3.7e-204)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.3e-172)
		tmp = x;
	elseif (x <= 3.7e-204)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.3e-172], x, If[LessEqual[x, 3.7e-204], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.29999999999999995e-172 or 3.6999999999999997e-204 < x

   1. Initial program 88.8%

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

   3. Taylor expanded in y around 0 41.0%

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

   if -2.29999999999999995e-172 < x < 3.6999999999999997e-204

   1. Initial program 84.8%

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

   3. Taylor expanded in x around 0 76.2%

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

   4. Taylor expanded in y around 0 44.1%

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

Alternative 12: 35.2% 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 87.9%

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

3. Taylor expanded in y around 0 34.4%

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

Developer target: 93.4% 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 2024096 
(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))))