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

Percentage Accurate: 87.7% → 99.8%

Time: 8.3s

Alternatives: 11

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: 87.7% 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, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{x + y}{t\_0}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-278} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\frac{y}{t\_0} + \frac{x}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{-\left(x + y\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ (+ x y) t_0)))
   (if (or (<= t_1 -2e-278) (not (<= t_1 0.0)))
     (+ (/ y t_0) (/ x t_0))
     (/ z (/ y (- (+ x y)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = (x + y) / t_0;
	double tmp;
	if ((t_1 <= -2e-278) || !(t_1 <= 0.0)) {
		tmp = (y / t_0) + (x / 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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = (x + y) / t_0
    if ((t_1 <= (-2d-278)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = (y / t_0) + (x / 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 = 1.0 - (y / z);
	double t_1 = (x + y) / t_0;
	double tmp;
	if ((t_1 <= -2e-278) || !(t_1 <= 0.0)) {
		tmp = (y / t_0) + (x / t_0);
	} else {
		tmp = z / (y / -(x + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = (x + y) / t_0
	tmp = 0
	if (t_1 <= -2e-278) or not (t_1 <= 0.0):
		tmp = (y / t_0) + (x / t_0)
	else:
		tmp = z / (y / -(x + y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(Float64(x + y) / t_0)
	tmp = 0.0
	if ((t_1 <= -2e-278) || !(t_1 <= 0.0))
		tmp = Float64(Float64(y / t_0) + Float64(x / 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 = 1.0 - (y / z);
	t_1 = (x + y) / t_0;
	tmp = 0.0;
	if ((t_1 <= -2e-278) || ~((t_1 <= 0.0)))
		tmp = (y / t_0) + (x / t_0);
	else
		tmp = z / (y / -(x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-278], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y / t$95$0), $MachinePrecision] + N[(x / t$95$0), $MachinePrecision]), $MachinePrecision], 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))) < -1.99999999999999988e-278 or 0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 99.8%

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

      1. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   if -1.99999999999999988e-278 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 0.0

   1. Initial program 12.1%

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

   3. Taylor expanded in z around 0 95.3%

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

      1. mul-1-neg 95.3%

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

      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%

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

      1. associate-*r/ 95.3%

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

      2. distribute-frac-neg2 95.3%

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

      3. add-sqr-sqrt 53.7%

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

      4. sqrt-unprod 23.7%

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

      5. sqr-neg 23.7%

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

      6. sqrt-unprod 2.0%

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

      7. add-sqr-sqrt 5.4%

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

      8. associate-*r/ 5.4%

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

      9. clear-num 5.4%

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

      10. un-div-inv 5.4%

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

      11. add-sqr-sqrt 2.0%

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

      12. sqrt-unprod 28.3%

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

      13. sqr-neg 28.3%

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

      14. sqrt-unprod 58.2%

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

      15. add-sqr-sqrt 100.0%

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

   7. Applied egg-rr 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-278} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}} + \frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{-\left(x + y\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 69.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{x}{t\_0}\\ t_2 := \frac{y}{t\_0}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+197}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-197}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-259}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+32}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ x t_0)) (t_2 (/ y t_0)))
   (if (<= y -1.3e+197)
     (- z)
     (if (<= y -2.7e+41)
       t_2
       (if (<= y -2.5e-146)
         t_1
         (if (<= y -8.5e-197)
           (+ x y)
           (if (<= y -1.35e-259)
             t_1
             (if (<= y 1.3e+32)
               (+ x y)
               (if (<= y 2.15e+61) t_2 (if (<= y 1.05e+65) t_1 (- z)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = x / t_0;
	double t_2 = y / t_0;
	double tmp;
	if (y <= -1.3e+197) {
		tmp = -z;
	} else if (y <= -2.7e+41) {
		tmp = t_2;
	} else if (y <= -2.5e-146) {
		tmp = t_1;
	} else if (y <= -8.5e-197) {
		tmp = x + y;
	} else if (y <= -1.35e-259) {
		tmp = t_1;
	} else if (y <= 1.3e+32) {
		tmp = x + y;
	} else if (y <= 2.15e+61) {
		tmp = t_2;
	} else if (y <= 1.05e+65) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = x / t_0
    t_2 = y / t_0
    if (y <= (-1.3d+197)) then
        tmp = -z
    else if (y <= (-2.7d+41)) then
        tmp = t_2
    else if (y <= (-2.5d-146)) then
        tmp = t_1
    else if (y <= (-8.5d-197)) then
        tmp = x + y
    else if (y <= (-1.35d-259)) then
        tmp = t_1
    else if (y <= 1.3d+32) then
        tmp = x + y
    else if (y <= 2.15d+61) then
        tmp = t_2
    else if (y <= 1.05d+65) then
        tmp = t_1
    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 t_1 = x / t_0;
	double t_2 = y / t_0;
	double tmp;
	if (y <= -1.3e+197) {
		tmp = -z;
	} else if (y <= -2.7e+41) {
		tmp = t_2;
	} else if (y <= -2.5e-146) {
		tmp = t_1;
	} else if (y <= -8.5e-197) {
		tmp = x + y;
	} else if (y <= -1.35e-259) {
		tmp = t_1;
	} else if (y <= 1.3e+32) {
		tmp = x + y;
	} else if (y <= 2.15e+61) {
		tmp = t_2;
	} else if (y <= 1.05e+65) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = x / t_0
	t_2 = y / t_0
	tmp = 0
	if y <= -1.3e+197:
		tmp = -z
	elif y <= -2.7e+41:
		tmp = t_2
	elif y <= -2.5e-146:
		tmp = t_1
	elif y <= -8.5e-197:
		tmp = x + y
	elif y <= -1.35e-259:
		tmp = t_1
	elif y <= 1.3e+32:
		tmp = x + y
	elif y <= 2.15e+61:
		tmp = t_2
	elif y <= 1.05e+65:
		tmp = t_1
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(x / t_0)
	t_2 = Float64(y / t_0)
	tmp = 0.0
	if (y <= -1.3e+197)
		tmp = Float64(-z);
	elseif (y <= -2.7e+41)
		tmp = t_2;
	elseif (y <= -2.5e-146)
		tmp = t_1;
	elseif (y <= -8.5e-197)
		tmp = Float64(x + y);
	elseif (y <= -1.35e-259)
		tmp = t_1;
	elseif (y <= 1.3e+32)
		tmp = Float64(x + y);
	elseif (y <= 2.15e+61)
		tmp = t_2;
	elseif (y <= 1.05e+65)
		tmp = t_1;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = x / t_0;
	t_2 = y / t_0;
	tmp = 0.0;
	if (y <= -1.3e+197)
		tmp = -z;
	elseif (y <= -2.7e+41)
		tmp = t_2;
	elseif (y <= -2.5e-146)
		tmp = t_1;
	elseif (y <= -8.5e-197)
		tmp = x + y;
	elseif (y <= -1.35e-259)
		tmp = t_1;
	elseif (y <= 1.3e+32)
		tmp = x + y;
	elseif (y <= 2.15e+61)
		tmp = t_2;
	elseif (y <= 1.05e+65)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(x / t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(y / t$95$0), $MachinePrecision]}, If[LessEqual[y, -1.3e+197], (-z), If[LessEqual[y, -2.7e+41], t$95$2, If[LessEqual[y, -2.5e-146], t$95$1, If[LessEqual[y, -8.5e-197], N[(x + y), $MachinePrecision], If[LessEqual[y, -1.35e-259], t$95$1, If[LessEqual[y, 1.3e+32], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.15e+61], t$95$2, If[LessEqual[y, 1.05e+65], t$95$1, (-z)]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.29999999999999994e197 or 1.04999999999999996e65 < y

   1. Initial program 64.0%

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

   3. Taylor expanded in y around inf 74.0%

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

      1. mul-1-neg 74.0%

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

   5. Simplified 74.0%

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

   if -1.29999999999999994e197 < y < -2.7e41 or 1.3000000000000001e32 < y < 2.1500000000000001e61

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0 68.6%

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

   if -2.7e41 < y < -2.49999999999999979e-146 or -8.5e-197 < y < -1.34999999999999992e-259 or 2.1500000000000001e61 < y < 1.04999999999999996e65

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf 79.4%

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

   if -2.49999999999999979e-146 < y < -8.5e-197 or -1.34999999999999992e-259 < y < 1.3000000000000001e32

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 83.9%

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

      1. +-commutative 83.9%

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

   5. Simplified 83.9%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+197}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+41}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-146}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-197}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-259}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+32}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+61}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z \cdot \left(x + y\right)}{-y}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+32}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-289}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-199}:\\ \;\;\;\;\frac{z}{\frac{y}{-\left(x + y\right)}}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-45}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+79}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+112}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* z (+ x y)) (- y))))
   (if (<= z -1.5e+32)
     (+ x y)
     (if (<= z -1.5e-289)
       t_0
       (if (<= z 1.12e-199)
         (/ z (/ y (- (+ x y))))
         (if (<= z 1.06e-45)
           t_0
           (if (<= z 1.45e+79)
             (+ x y)
             (if (<= z 6.2e+112)
               (* z (/ (+ x y) (- y)))
               (* (+ x y) (+ 1.0 (/ y z)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * (x + y)) / -y;
	double tmp;
	if (z <= -1.5e+32) {
		tmp = x + y;
	} else if (z <= -1.5e-289) {
		tmp = t_0;
	} else if (z <= 1.12e-199) {
		tmp = z / (y / -(x + y));
	} else if (z <= 1.06e-45) {
		tmp = t_0;
	} else if (z <= 1.45e+79) {
		tmp = x + y;
	} else if (z <= 6.2e+112) {
		tmp = z * ((x + y) / -y);
	} else {
		tmp = (x + y) * (1.0 + (y / 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 = (z * (x + y)) / -y
    if (z <= (-1.5d+32)) then
        tmp = x + y
    else if (z <= (-1.5d-289)) then
        tmp = t_0
    else if (z <= 1.12d-199) then
        tmp = z / (y / -(x + y))
    else if (z <= 1.06d-45) then
        tmp = t_0
    else if (z <= 1.45d+79) then
        tmp = x + y
    else if (z <= 6.2d+112) then
        tmp = z * ((x + y) / -y)
    else
        tmp = (x + y) * (1.0d0 + (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * (x + y)) / -y;
	double tmp;
	if (z <= -1.5e+32) {
		tmp = x + y;
	} else if (z <= -1.5e-289) {
		tmp = t_0;
	} else if (z <= 1.12e-199) {
		tmp = z / (y / -(x + y));
	} else if (z <= 1.06e-45) {
		tmp = t_0;
	} else if (z <= 1.45e+79) {
		tmp = x + y;
	} else if (z <= 6.2e+112) {
		tmp = z * ((x + y) / -y);
	} else {
		tmp = (x + y) * (1.0 + (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * (x + y)) / -y
	tmp = 0
	if z <= -1.5e+32:
		tmp = x + y
	elif z <= -1.5e-289:
		tmp = t_0
	elif z <= 1.12e-199:
		tmp = z / (y / -(x + y))
	elif z <= 1.06e-45:
		tmp = t_0
	elif z <= 1.45e+79:
		tmp = x + y
	elif z <= 6.2e+112:
		tmp = z * ((x + y) / -y)
	else:
		tmp = (x + y) * (1.0 + (y / z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * Float64(x + y)) / Float64(-y))
	tmp = 0.0
	if (z <= -1.5e+32)
		tmp = Float64(x + y);
	elseif (z <= -1.5e-289)
		tmp = t_0;
	elseif (z <= 1.12e-199)
		tmp = Float64(z / Float64(y / Float64(-Float64(x + y))));
	elseif (z <= 1.06e-45)
		tmp = t_0;
	elseif (z <= 1.45e+79)
		tmp = Float64(x + y);
	elseif (z <= 6.2e+112)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(-y)));
	else
		tmp = Float64(Float64(x + y) * Float64(1.0 + Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * (x + y)) / -y;
	tmp = 0.0;
	if (z <= -1.5e+32)
		tmp = x + y;
	elseif (z <= -1.5e-289)
		tmp = t_0;
	elseif (z <= 1.12e-199)
		tmp = z / (y / -(x + y));
	elseif (z <= 1.06e-45)
		tmp = t_0;
	elseif (z <= 1.45e+79)
		tmp = x + y;
	elseif (z <= 6.2e+112)
		tmp = z * ((x + y) / -y);
	else
		tmp = (x + y) * (1.0 + (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] / (-y)), $MachinePrecision]}, If[LessEqual[z, -1.5e+32], N[(x + y), $MachinePrecision], If[LessEqual[z, -1.5e-289], t$95$0, If[LessEqual[z, 1.12e-199], N[(z / N[(y / (-N[(x + y), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e-45], t$95$0, If[LessEqual[z, 1.45e+79], N[(x + y), $MachinePrecision], If[LessEqual[z, 6.2e+112], N[(z * N[(N[(x + y), $MachinePrecision] / (-y)), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] * N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.5e32 or 1.06000000000000004e-45 < z < 1.44999999999999996e79

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 80.3%

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

      1. +-commutative 80.3%

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

   5. Simplified 80.3%

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

   if -1.5e32 < z < -1.4999999999999999e-289 or 1.12000000000000003e-199 < z < 1.06000000000000004e-45

   1. Initial program 79.7%

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

   3. Taylor expanded in z around 0 78.7%

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

      1. mul-1-neg 78.7%

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

      2. +-commutative 78.7%

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

   5. Simplified 78.7%

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

   if -1.4999999999999999e-289 < z < 1.12000000000000003e-199

   1. Initial program 58.1%

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

   3. Taylor expanded in z around 0 77.1%

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

      1. mul-1-neg 77.1%

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

      2. associate-/l* 91.1%

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

      3. distribute-rgt-neg-in 91.1%

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

      4. distribute-neg-frac2 91.1%

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

      5. +-commutative 91.1%

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

   5. Simplified 91.1%

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

      1. associate-*r/ 77.1%

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

      2. distribute-frac-neg2 77.1%

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

      3. add-sqr-sqrt 36.9%

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

      4. sqrt-unprod 21.9%

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

      5. sqr-neg 21.9%

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

      6. sqrt-unprod 3.1%

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

      7. add-sqr-sqrt 6.1%

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

      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 2.8%

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

      12. sqrt-unprod 27.0%

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

      13. sqr-neg 27.0%

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

      14. sqrt-unprod 44.7%

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

      15. add-sqr-sqrt 91.2%

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

   7. Applied egg-rr 91.2%

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

   if 1.44999999999999996e79 < z < 6.19999999999999965e112

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 17.9%

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

      1. mul-1-neg 17.9%

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

      2. associate-/l* 86.3%

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

      3. distribute-rgt-neg-in 86.3%

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

      4. distribute-neg-frac2 86.3%

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

      5. +-commutative 86.3%

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

   5. Simplified 86.3%

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

   if 6.19999999999999965e112 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 74.0%

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

      1. associate-+r+ 74.0%

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

      2. *-rgt-identity 74.0%

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

      3. *-commutative 74.0%

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

      4. associate-/l* 89.1%

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

      5. distribute-lft-in 89.1%

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

      6. +-commutative 89.1%

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

   5. Simplified 89.1%

      \[\leadsto \color{blue}{\left(y + x\right) \cdot \left(1 + \frac{y}{z}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+32}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-289}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{-y}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-199}:\\ \;\;\;\;\frac{z}{\frac{y}{-\left(x + y\right)}}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-45}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{-y}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+79}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+112}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z \cdot \left(x + y\right)}{-y}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+30}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-289}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-199}:\\ \;\;\;\;\frac{z}{\frac{y}{-\left(x + y\right)}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-39}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+83} \lor \neg \left(z \leq 6.2 \cdot 10^{+112}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* z (+ x y)) (- y))))
   (if (<= z -9e+30)
     (+ x y)
     (if (<= z -1.4e-289)
       t_0
       (if (<= z 4.8e-199)
         (/ z (/ y (- (+ x y))))
         (if (<= z 8.2e-39)
           t_0
           (if (or (<= z 2.15e+83) (not (<= z 6.2e+112)))
             (+ x y)
             (* z (/ (+ x y) (- y))))))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * (x + y)) / -y;
	double tmp;
	if (z <= -9e+30) {
		tmp = x + y;
	} else if (z <= -1.4e-289) {
		tmp = t_0;
	} else if (z <= 4.8e-199) {
		tmp = z / (y / -(x + y));
	} else if (z <= 8.2e-39) {
		tmp = t_0;
	} else if ((z <= 2.15e+83) || !(z <= 6.2e+112)) {
		tmp = x + y;
	} else {
		tmp = z * ((x + y) / -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 = (z * (x + y)) / -y
    if (z <= (-9d+30)) then
        tmp = x + y
    else if (z <= (-1.4d-289)) then
        tmp = t_0
    else if (z <= 4.8d-199) then
        tmp = z / (y / -(x + y))
    else if (z <= 8.2d-39) then
        tmp = t_0
    else if ((z <= 2.15d+83) .or. (.not. (z <= 6.2d+112))) then
        tmp = x + y
    else
        tmp = z * ((x + y) / -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * (x + y)) / -y;
	double tmp;
	if (z <= -9e+30) {
		tmp = x + y;
	} else if (z <= -1.4e-289) {
		tmp = t_0;
	} else if (z <= 4.8e-199) {
		tmp = z / (y / -(x + y));
	} else if (z <= 8.2e-39) {
		tmp = t_0;
	} else if ((z <= 2.15e+83) || !(z <= 6.2e+112)) {
		tmp = x + y;
	} else {
		tmp = z * ((x + y) / -y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * (x + y)) / -y
	tmp = 0
	if z <= -9e+30:
		tmp = x + y
	elif z <= -1.4e-289:
		tmp = t_0
	elif z <= 4.8e-199:
		tmp = z / (y / -(x + y))
	elif z <= 8.2e-39:
		tmp = t_0
	elif (z <= 2.15e+83) or not (z <= 6.2e+112):
		tmp = x + y
	else:
		tmp = z * ((x + y) / -y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * Float64(x + y)) / Float64(-y))
	tmp = 0.0
	if (z <= -9e+30)
		tmp = Float64(x + y);
	elseif (z <= -1.4e-289)
		tmp = t_0;
	elseif (z <= 4.8e-199)
		tmp = Float64(z / Float64(y / Float64(-Float64(x + y))));
	elseif (z <= 8.2e-39)
		tmp = t_0;
	elseif ((z <= 2.15e+83) || !(z <= 6.2e+112))
		tmp = Float64(x + y);
	else
		tmp = Float64(z * Float64(Float64(x + y) / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * (x + y)) / -y;
	tmp = 0.0;
	if (z <= -9e+30)
		tmp = x + y;
	elseif (z <= -1.4e-289)
		tmp = t_0;
	elseif (z <= 4.8e-199)
		tmp = z / (y / -(x + y));
	elseif (z <= 8.2e-39)
		tmp = t_0;
	elseif ((z <= 2.15e+83) || ~((z <= 6.2e+112)))
		tmp = x + y;
	else
		tmp = z * ((x + y) / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] / (-y)), $MachinePrecision]}, If[LessEqual[z, -9e+30], N[(x + y), $MachinePrecision], If[LessEqual[z, -1.4e-289], t$95$0, If[LessEqual[z, 4.8e-199], N[(z / N[(y / (-N[(x + y), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-39], t$95$0, If[Or[LessEqual[z, 2.15e+83], N[Not[LessEqual[z, 6.2e+112]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(z * N[(N[(x + y), $MachinePrecision] / (-y)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.9999999999999999e30 or 8.2e-39 < z < 2.15e83 or 6.19999999999999965e112 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 83.3%

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

      1. +-commutative 83.3%

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

   5. Simplified 83.3%

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

   if -8.9999999999999999e30 < z < -1.39999999999999993e-289 or 4.79999999999999991e-199 < z < 8.2e-39

   1. Initial program 79.7%

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

   3. Taylor expanded in z around 0 78.7%

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

      1. mul-1-neg 78.7%

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

      2. +-commutative 78.7%

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

   5. Simplified 78.7%

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

   if -1.39999999999999993e-289 < z < 4.79999999999999991e-199

   1. Initial program 58.1%

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

   3. Taylor expanded in z around 0 77.1%

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

      1. mul-1-neg 77.1%

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

      2. associate-/l* 91.1%

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

      3. distribute-rgt-neg-in 91.1%

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

      4. distribute-neg-frac2 91.1%

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

      5. +-commutative 91.1%

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

   5. Simplified 91.1%

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

      1. associate-*r/ 77.1%

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

      2. distribute-frac-neg2 77.1%

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

      3. add-sqr-sqrt 36.9%

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

      4. sqrt-unprod 21.9%

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

      5. sqr-neg 21.9%

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

      6. sqrt-unprod 3.1%

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

      7. add-sqr-sqrt 6.1%

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

      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 2.8%

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

      12. sqrt-unprod 27.0%

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

      13. sqr-neg 27.0%

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

      14. sqrt-unprod 44.7%

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

      15. add-sqr-sqrt 91.2%

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

   7. Applied egg-rr 91.2%

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

   if 2.15e83 < z < 6.19999999999999965e112

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 17.9%

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

      1. mul-1-neg 17.9%

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

      2. associate-/l* 86.3%

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

      3. distribute-rgt-neg-in 86.3%

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

      4. distribute-neg-frac2 86.3%

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

      5. +-commutative 86.3%

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

   5. Simplified 86.3%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+30}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-289}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{-y}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-199}:\\ \;\;\;\;\frac{z}{\frac{y}{-\left(x + y\right)}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-39}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{-y}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+83} \lor \neg \left(z \leq 6.2 \cdot 10^{+112}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{\frac{y}{-\left(x + y\right)}}\\ t_1 := \frac{z \cdot \left(x + y\right)}{-y}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+31}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-198}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+83} \lor \neg \left(z \leq 6.2 \cdot 10^{+112}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ z (/ y (- (+ x y))))) (t_1 (/ (* z (+ x y)) (- y))))
   (if (<= z -3.1e+31)
     (+ x y)
     (if (<= z -1.75e-287)
       t_1
       (if (<= z 1e-198)
         t_0
         (if (<= z 2.35e-39)
           t_1
           (if (or (<= z 2.15e+83) (not (<= z 6.2e+112))) (+ x y) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z / (y / -(x + y));
	double t_1 = (z * (x + y)) / -y;
	double tmp;
	if (z <= -3.1e+31) {
		tmp = x + y;
	} else if (z <= -1.75e-287) {
		tmp = t_1;
	} else if (z <= 1e-198) {
		tmp = t_0;
	} else if (z <= 2.35e-39) {
		tmp = t_1;
	} else if ((z <= 2.15e+83) || !(z <= 6.2e+112)) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = z / (y / -(x + y))
    t_1 = (z * (x + y)) / -y
    if (z <= (-3.1d+31)) then
        tmp = x + y
    else if (z <= (-1.75d-287)) then
        tmp = t_1
    else if (z <= 1d-198) then
        tmp = t_0
    else if (z <= 2.35d-39) then
        tmp = t_1
    else if ((z <= 2.15d+83) .or. (.not. (z <= 6.2d+112))) then
        tmp = x + y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z / (y / -(x + y));
	double t_1 = (z * (x + y)) / -y;
	double tmp;
	if (z <= -3.1e+31) {
		tmp = x + y;
	} else if (z <= -1.75e-287) {
		tmp = t_1;
	} else if (z <= 1e-198) {
		tmp = t_0;
	} else if (z <= 2.35e-39) {
		tmp = t_1;
	} else if ((z <= 2.15e+83) || !(z <= 6.2e+112)) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z / (y / -(x + y))
	t_1 = (z * (x + y)) / -y
	tmp = 0
	if z <= -3.1e+31:
		tmp = x + y
	elif z <= -1.75e-287:
		tmp = t_1
	elif z <= 1e-198:
		tmp = t_0
	elif z <= 2.35e-39:
		tmp = t_1
	elif (z <= 2.15e+83) or not (z <= 6.2e+112):
		tmp = x + y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z / Float64(y / Float64(-Float64(x + y))))
	t_1 = Float64(Float64(z * Float64(x + y)) / Float64(-y))
	tmp = 0.0
	if (z <= -3.1e+31)
		tmp = Float64(x + y);
	elseif (z <= -1.75e-287)
		tmp = t_1;
	elseif (z <= 1e-198)
		tmp = t_0;
	elseif (z <= 2.35e-39)
		tmp = t_1;
	elseif ((z <= 2.15e+83) || !(z <= 6.2e+112))
		tmp = Float64(x + y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z / (y / -(x + y));
	t_1 = (z * (x + y)) / -y;
	tmp = 0.0;
	if (z <= -3.1e+31)
		tmp = x + y;
	elseif (z <= -1.75e-287)
		tmp = t_1;
	elseif (z <= 1e-198)
		tmp = t_0;
	elseif (z <= 2.35e-39)
		tmp = t_1;
	elseif ((z <= 2.15e+83) || ~((z <= 6.2e+112)))
		tmp = x + y;
	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]}, Block[{t$95$1 = N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] / (-y)), $MachinePrecision]}, If[LessEqual[z, -3.1e+31], N[(x + y), $MachinePrecision], If[LessEqual[z, -1.75e-287], t$95$1, If[LessEqual[z, 1e-198], t$95$0, If[LessEqual[z, 2.35e-39], t$95$1, If[Or[LessEqual[z, 2.15e+83], N[Not[LessEqual[z, 6.2e+112]], $MachinePrecision]], N[(x + y), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1000000000000002e31 or 2.3500000000000001e-39 < z < 2.15e83 or 6.19999999999999965e112 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 83.3%

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

      1. +-commutative 83.3%

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

   5. Simplified 83.3%

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

   if -3.1000000000000002e31 < z < -1.75e-287 or 9.9999999999999991e-199 < z < 2.3500000000000001e-39

   1. Initial program 79.7%

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

   3. Taylor expanded in z around 0 78.7%

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

      1. mul-1-neg 78.7%

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

      2. +-commutative 78.7%

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

   5. Simplified 78.7%

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

   if -1.75e-287 < z < 9.9999999999999991e-199 or 2.15e83 < z < 6.19999999999999965e112

   1. Initial program 65.8%

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

   3. Taylor expanded in z around 0 66.2%

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

      1. mul-1-neg 66.2%

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

      2. associate-/l* 90.2%

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

      3. distribute-rgt-neg-in 90.2%

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

      4. distribute-neg-frac2 90.2%

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

      5. +-commutative 90.2%

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

   5. Simplified 90.2%

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

      1. associate-*r/ 66.2%

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

      2. distribute-frac-neg2 66.2%

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

      3. add-sqr-sqrt 30.2%

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

      4. sqrt-unprod 17.9%

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

      5. sqr-neg 17.9%

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

      6. sqrt-unprod 2.6%

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

      7. add-sqr-sqrt 5.1%

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

      8. associate-*r/ 4.9%

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

      9. clear-num 4.9%

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

      10. un-div-inv 4.9%

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

      11. add-sqr-sqrt 2.5%

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

      12. sqrt-unprod 22.4%

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

      13. sqr-neg 22.4%

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

      14. sqrt-unprod 39.1%

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

      15. add-sqr-sqrt 90.2%

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

   7. Applied egg-rr 90.2%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+31}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-287}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{-y}\\ \mathbf{elif}\;z \leq 10^{-198}:\\ \;\;\;\;\frac{z}{\frac{y}{-\left(x + y\right)}}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-39}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{-y}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+83} \lor \neg \left(z \leq 6.2 \cdot 10^{+112}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{-\left(x + y\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-278} \lor \neg \left(t\_0 \leq 2 \cdot 10^{-271}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{-\left(x + y\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-278) (not (<= t_0 2e-271)))
     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 <= -2e-278) || !(t_0 <= 2e-271)) {
		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 <= (-2d-278)) .or. (.not. (t_0 <= 2d-271))) 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 <= -2e-278) || !(t_0 <= 2e-271)) {
		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 <= -2e-278) or not (t_0 <= 2e-271):
		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 <= -2e-278) || !(t_0 <= 2e-271))
		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 <= -2e-278) || ~((t_0 <= 2e-271)))
		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, -2e-278], N[Not[LessEqual[t$95$0, 2e-271]], $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))) < -1.99999999999999988e-278 or 1.99999999999999993e-271 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.8%

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

   if -1.99999999999999988e-278 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 1.99999999999999993e-271

   1. Initial program 21.3%

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

   3. Taylor expanded in z around 0 86.4%

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

      1. mul-1-neg 86.4%

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

      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/ 86.4%

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

      2. distribute-frac-neg2 86.4%

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

      3. add-sqr-sqrt 48.3%

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

      4. sqrt-unprod 22.1%

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

      5. sqr-neg 22.1%

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

      6. sqrt-unprod 2.7%

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

      7. add-sqr-sqrt 6.0%

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

      8. associate-*r/ 5.8%

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

      9. clear-num 5.8%

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

      10. un-div-inv 5.8%

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

      11. add-sqr-sqrt 2.6%

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

      12. sqrt-unprod 26.1%

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

      13. sqr-neg 26.1%

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

      14. sqrt-unprod 54.7%

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

      15. add-sqr-sqrt 100.0%

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

   7. Applied egg-rr 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-278} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 2 \cdot 10^{-271}\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{-\left(x + y\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+32} \lor \neg \left(z \leq 1.06 \cdot 10^{-41} \lor \neg \left(z \leq 1.6 \cdot 10^{+83}\right) \land z \leq 6.2 \cdot 10^{+112}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{-\left(x + y\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.8e+32)
         (not (or (<= z 1.06e-41) (and (not (<= z 1.6e+83)) (<= z 6.2e+112)))))
   (+ x y)
   (/ z (/ y (- (+ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e+32) || !((z <= 1.06e-41) || (!(z <= 1.6e+83) && (z <= 6.2e+112)))) {
		tmp = x + y;
	} 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) :: tmp
    if ((z <= (-1.8d+32)) .or. (.not. (z <= 1.06d-41) .or. (.not. (z <= 1.6d+83)) .and. (z <= 6.2d+112))) then
        tmp = x + y
    else
        tmp = z / (y / -(x + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e+32) || !((z <= 1.06e-41) || (!(z <= 1.6e+83) && (z <= 6.2e+112)))) {
		tmp = x + y;
	} else {
		tmp = z / (y / -(x + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.8e+32) or not ((z <= 1.06e-41) or (not (z <= 1.6e+83) and (z <= 6.2e+112))):
		tmp = x + y
	else:
		tmp = z / (y / -(x + y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.8e+32) || !((z <= 1.06e-41) || (!(z <= 1.6e+83) && (z <= 6.2e+112))))
		tmp = Float64(x + y);
	else
		tmp = Float64(z / Float64(y / Float64(-Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.8e+32) || ~(((z <= 1.06e-41) || (~((z <= 1.6e+83)) && (z <= 6.2e+112)))))
		tmp = x + y;
	else
		tmp = z / (y / -(x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.8e+32], N[Not[Or[LessEqual[z, 1.06e-41], And[N[Not[LessEqual[z, 1.6e+83]], $MachinePrecision], LessEqual[z, 6.2e+112]]]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(z / N[(y / (-N[(x + y), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7999999999999998e32 or 1.06e-41 < z < 1.5999999999999999e83 or 6.19999999999999965e112 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 83.3%

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

      1. +-commutative 83.3%

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

   5. Simplified 83.3%

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

   if -1.7999999999999998e32 < z < 1.06e-41 or 1.5999999999999999e83 < z < 6.19999999999999965e112

   1. Initial program 75.4%

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

   3. Taylor expanded in z around 0 74.8%

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

      1. mul-1-neg 74.8%

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

      2. associate-/l* 76.8%

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

      3. distribute-rgt-neg-in 76.8%

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

      4. distribute-neg-frac2 76.8%

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

      5. +-commutative 76.8%

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

   5. Simplified 76.8%

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

      1. associate-*r/ 74.8%

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

      2. distribute-frac-neg2 74.8%

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

      3. add-sqr-sqrt 33.8%

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

      4. sqrt-unprod 23.3%

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

      5. sqr-neg 23.3%

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

      6. sqrt-unprod 2.0%

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

      7. add-sqr-sqrt 3.5%

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

      8. associate-*r/ 3.3%

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

      9. clear-num 3.3%

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

      10. un-div-inv 3.3%

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

      11. add-sqr-sqrt 1.8%

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

      12. sqrt-unprod 24.0%

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

      13. sqr-neg 24.0%

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

      14. sqrt-unprod 35.8%

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

      15. add-sqr-sqrt 76.9%

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

   7. Applied egg-rr 76.9%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+32} \lor \neg \left(z \leq 1.06 \cdot 10^{-41} \lor \neg \left(z \leq 1.6 \cdot 10^{+83}\right) \land z \leq 6.2 \cdot 10^{+112}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{-\left(x + y\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - \frac{y}{z}}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+71}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-147}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-197}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-257}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+35}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 (/ y z)))))
   (if (<= y -1.3e+71)
     (- z)
     (if (<= y -1.12e-147)
       t_0
       (if (<= y -8.8e-197)
         (+ x y)
         (if (<= y -2.4e-257) t_0 (if (<= y 4.8e+35) (+ x y) (- z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -1.3e+71) {
		tmp = -z;
	} else if (y <= -1.12e-147) {
		tmp = t_0;
	} else if (y <= -8.8e-197) {
		tmp = x + y;
	} else if (y <= -2.4e-257) {
		tmp = t_0;
	} else if (y <= 4.8e+35) {
		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) :: t_0
    real(8) :: tmp
    t_0 = x / (1.0d0 - (y / z))
    if (y <= (-1.3d+71)) then
        tmp = -z
    else if (y <= (-1.12d-147)) then
        tmp = t_0
    else if (y <= (-8.8d-197)) then
        tmp = x + y
    else if (y <= (-2.4d-257)) then
        tmp = t_0
    else if (y <= 4.8d+35) 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 t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -1.3e+71) {
		tmp = -z;
	} else if (y <= -1.12e-147) {
		tmp = t_0;
	} else if (y <= -8.8e-197) {
		tmp = x + y;
	} else if (y <= -2.4e-257) {
		tmp = t_0;
	} else if (y <= 4.8e+35) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (1.0 - (y / z))
	tmp = 0
	if y <= -1.3e+71:
		tmp = -z
	elif y <= -1.12e-147:
		tmp = t_0
	elif y <= -8.8e-197:
		tmp = x + y
	elif y <= -2.4e-257:
		tmp = t_0
	elif y <= 4.8e+35:
		tmp = x + y
	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 <= -1.3e+71)
		tmp = Float64(-z);
	elseif (y <= -1.12e-147)
		tmp = t_0;
	elseif (y <= -8.8e-197)
		tmp = Float64(x + y);
	elseif (y <= -2.4e-257)
		tmp = t_0;
	elseif (y <= 4.8e+35)
		tmp = Float64(x + y);
	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 <= -1.3e+71)
		tmp = -z;
	elseif (y <= -1.12e-147)
		tmp = t_0;
	elseif (y <= -8.8e-197)
		tmp = x + y;
	elseif (y <= -2.4e-257)
		tmp = t_0;
	elseif (y <= 4.8e+35)
		tmp = x + y;
	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, -1.3e+71], (-z), If[LessEqual[y, -1.12e-147], t$95$0, If[LessEqual[y, -8.8e-197], N[(x + y), $MachinePrecision], If[LessEqual[y, -2.4e-257], t$95$0, If[LessEqual[y, 4.8e+35], N[(x + y), $MachinePrecision], (-z)]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.29999999999999996e71 or 4.80000000000000029e35 < y

   1. Initial program 72.4%

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

   3. Taylor expanded in y around inf 65.2%

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

      1. mul-1-neg 65.2%

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

   5. Simplified 65.2%

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

   if -1.29999999999999996e71 < y < -1.12e-147 or -8.8000000000000001e-197 < y < -2.40000000000000017e-257

   1. Initial program 98.5%

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

   3. Taylor expanded in x around inf 75.6%

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

   if -1.12e-147 < y < -8.8000000000000001e-197 or -2.40000000000000017e-257 < y < 4.80000000000000029e35

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 84.1%

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

      1. +-commutative 84.1%

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

   5. Simplified 84.1%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+71}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-147}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-197}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-257}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+35}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+72} \lor \neg \left(y \leq 4 \cdot 10^{+35}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.2e+72) (not (<= y 4e+35))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e+72) || !(y <= 4e+35)) {
		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 <= (-5.2d+72)) .or. (.not. (y <= 4d+35))) 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 <= -5.2e+72) || !(y <= 4e+35)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.2e+72) or not (y <= 4e+35):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.2e+72) || !(y <= 4e+35))
		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 <= -5.2e+72) || ~((y <= 4e+35)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.2e+72], N[Not[LessEqual[y, 4e+35]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.19999999999999963e72 or 3.9999999999999999e35 < y

   1. Initial program 72.4%

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

   3. Taylor expanded in y around inf 65.2%

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

      1. mul-1-neg 65.2%

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

   5. Simplified 65.2%

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

   if -5.19999999999999963e72 < y < 3.9999999999999999e35

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 71.3%

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

      1. +-commutative 71.3%

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

   5. Simplified 71.3%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+72} \lor \neg \left(y \leq 4 \cdot 10^{+35}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+18} \lor \neg \left(y \leq 0.000155\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.2e+18) (not (<= y 0.000155))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.2e+18) || !(y <= 0.000155)) {
		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 <= (-3.2d+18)) .or. (.not. (y <= 0.000155d0))) 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 <= -3.2e+18) || !(y <= 0.000155)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.2e+18) or not (y <= 0.000155):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.2e+18) || !(y <= 0.000155))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.2e+18) || ~((y <= 0.000155)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.2e+18], N[Not[LessEqual[y, 0.000155]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -3.2e18 or 1.55e-4 < y

   1. Initial program 76.4%

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

   3. Taylor expanded in y around inf 59.4%

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

      1. mul-1-neg 59.4%

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

   5. Simplified 59.4%

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

   if -3.2e18 < y < 1.55e-4

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 57.6%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+18} \lor \neg \left(y \leq 0.000155\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 35.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 88.1%

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

3. Taylor expanded in y around 0 33.3%

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

Developer target: 93.3% 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 2024101 
(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))))