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

Percentage Accurate: 88.1% → 98.4%

Time: 8.0s

Alternatives: 14

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: 88.1% 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: 98.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-192}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{z - y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (<= t_0 -1e-192)
     t_0
     (if (<= t_0 0.0) (* z (/ (- (- x) y) y)) (/ (+ x y) (/ (- z y) z))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if (t_0 <= -1e-192) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = z * ((-x - y) / y);
	} else {
		tmp = (x + y) / ((z - 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 = (x + y) / (1.0d0 - (y / z))
    if (t_0 <= (-1d-192)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = z * ((-x - y) / y)
    else
        tmp = (x + y) / ((z - y) / z)
    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-192) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = z * ((-x - y) / y);
	} else {
		tmp = (x + y) / ((z - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if t_0 <= -1e-192:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = z * ((-x - y) / y)
	else:
		tmp = (x + y) / ((z - y) / z)
	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-192)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(z * Float64(Float64(Float64(-x) - y) / y));
	else
		tmp = Float64(Float64(x + y) / Float64(Float64(z - y) / z));
	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-192)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = z * ((-x - y) / y);
	else
		tmp = (x + y) / ((z - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-192], t$95$0, If[LessEqual[t$95$0, 0.0], N[(z * N[(N[((-x) - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -1.0000000000000001e-192

   1. Initial program 99.9%

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

   if -1.0000000000000001e-192 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 0.0

   1. Initial program 22.4%

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

   3. Taylor expanded in z around 0 88.2%

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

      1. *-commutative 88.2%

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

      2. associate-/l* 93.0%

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

      3. associate-*r* 93.0%

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

      4. associate-*l/ 93.0%

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

      5. *-commutative 93.0%

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

      6. neg-mul-1 93.0%

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

      7. distribute-neg-in 93.0%

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

      8. unsub-neg 93.0%

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

   5. Simplified 93.0%

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

   if 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

   3. Taylor expanded in z around 0 99.9%

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

Alternative 2: 64.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{z}{-y}\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{+44}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -0.36:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-17}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-21}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-60}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-60}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+105}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+156}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ z (- y)))))
   (if (<= y -3.3e+44)
     (- z)
     (if (<= y -0.36)
       x
       (if (<= y -7.2e-17)
         t_0
         (if (<= y -1.05e-21)
           (+ x y)
           (if (<= y -4.4e-60)
             t_0
             (if (<= y -2.8e-60)
               (- z)
               (if (<= y 9e+105)
                 (+ x y)
                 (if (<= y 4.4e+156) (/ (* x (- z)) y) (- z)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z / -y);
	double tmp;
	if (y <= -3.3e+44) {
		tmp = -z;
	} else if (y <= -0.36) {
		tmp = x;
	} else if (y <= -7.2e-17) {
		tmp = t_0;
	} else if (y <= -1.05e-21) {
		tmp = x + y;
	} else if (y <= -4.4e-60) {
		tmp = t_0;
	} else if (y <= -2.8e-60) {
		tmp = -z;
	} else if (y <= 9e+105) {
		tmp = x + y;
	} else if (y <= 4.4e+156) {
		tmp = (x * -z) / 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 * (z / -y)
    if (y <= (-3.3d+44)) then
        tmp = -z
    else if (y <= (-0.36d0)) then
        tmp = x
    else if (y <= (-7.2d-17)) then
        tmp = t_0
    else if (y <= (-1.05d-21)) then
        tmp = x + y
    else if (y <= (-4.4d-60)) then
        tmp = t_0
    else if (y <= (-2.8d-60)) then
        tmp = -z
    else if (y <= 9d+105) then
        tmp = x + y
    else if (y <= 4.4d+156) then
        tmp = (x * -z) / 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 * (z / -y);
	double tmp;
	if (y <= -3.3e+44) {
		tmp = -z;
	} else if (y <= -0.36) {
		tmp = x;
	} else if (y <= -7.2e-17) {
		tmp = t_0;
	} else if (y <= -1.05e-21) {
		tmp = x + y;
	} else if (y <= -4.4e-60) {
		tmp = t_0;
	} else if (y <= -2.8e-60) {
		tmp = -z;
	} else if (y <= 9e+105) {
		tmp = x + y;
	} else if (y <= 4.4e+156) {
		tmp = (x * -z) / y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z / -y)
	tmp = 0
	if y <= -3.3e+44:
		tmp = -z
	elif y <= -0.36:
		tmp = x
	elif y <= -7.2e-17:
		tmp = t_0
	elif y <= -1.05e-21:
		tmp = x + y
	elif y <= -4.4e-60:
		tmp = t_0
	elif y <= -2.8e-60:
		tmp = -z
	elif y <= 9e+105:
		tmp = x + y
	elif y <= 4.4e+156:
		tmp = (x * -z) / y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z / Float64(-y)))
	tmp = 0.0
	if (y <= -3.3e+44)
		tmp = Float64(-z);
	elseif (y <= -0.36)
		tmp = x;
	elseif (y <= -7.2e-17)
		tmp = t_0;
	elseif (y <= -1.05e-21)
		tmp = Float64(x + y);
	elseif (y <= -4.4e-60)
		tmp = t_0;
	elseif (y <= -2.8e-60)
		tmp = Float64(-z);
	elseif (y <= 9e+105)
		tmp = Float64(x + y);
	elseif (y <= 4.4e+156)
		tmp = Float64(Float64(x * Float64(-z)) / y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z / -y);
	tmp = 0.0;
	if (y <= -3.3e+44)
		tmp = -z;
	elseif (y <= -0.36)
		tmp = x;
	elseif (y <= -7.2e-17)
		tmp = t_0;
	elseif (y <= -1.05e-21)
		tmp = x + y;
	elseif (y <= -4.4e-60)
		tmp = t_0;
	elseif (y <= -2.8e-60)
		tmp = -z;
	elseif (y <= 9e+105)
		tmp = x + y;
	elseif (y <= 4.4e+156)
		tmp = (x * -z) / y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.3e+44], (-z), If[LessEqual[y, -0.36], x, If[LessEqual[y, -7.2e-17], t$95$0, If[LessEqual[y, -1.05e-21], N[(x + y), $MachinePrecision], If[LessEqual[y, -4.4e-60], t$95$0, If[LessEqual[y, -2.8e-60], (-z), If[LessEqual[y, 9e+105], N[(x + y), $MachinePrecision], If[LessEqual[y, 4.4e+156], N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision], (-z)]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.30000000000000013e44 or -4.3999999999999998e-60 < y < -2.8000000000000002e-60 or 4.40000000000000008e156 < y

   1. Initial program 70.0%

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

   3. Taylor expanded in y around inf 74.9%

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

      1. mul-1-neg 74.9%

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

   5. Simplified 74.9%

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

   if -3.30000000000000013e44 < y < -0.35999999999999999

   1. Initial program 88.7%

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

   3. Taylor expanded in y around 0 64.1%

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

   if -0.35999999999999999 < y < -7.1999999999999999e-17 or -1.05000000000000006e-21 < y < -4.3999999999999998e-60

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 68.0%

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

   4. Taylor expanded in y around inf 55.0%

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

      1. mul-1-neg 55.0%

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

      2. associate-*r/ 55.2%

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

      3. distribute-rgt-neg-in 55.2%

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

   6. Simplified 55.2%

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

   if -7.1999999999999999e-17 < y < -1.05000000000000006e-21 or -2.8000000000000002e-60 < y < 9.0000000000000002e105

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 77.3%

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

      1. +-commutative 77.3%

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

   5. Simplified 77.3%

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

   if 9.0000000000000002e105 < y < 4.40000000000000008e156

   1. Initial program 86.0%

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

   3. Taylor expanded in z around 0 86.0%

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

   4. Taylor expanded in x around inf 72.7%

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

      1. associate-/l* 58.9%

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

   6. Simplified 58.9%

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

   7. Taylor expanded in z around 0 72.7%

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

   9. Simplified 72.7%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+44}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -0.36:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-21}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-60}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+105}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+156}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{z}{-y}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+44}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -0.0022:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-60}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-60}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+91}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+156}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ z (- y)))))
   (if (<= y -4.6e+44)
     (- z)
     (if (<= y -0.0022)
       x
       (if (<= y -1e-16)
         t_0
         (if (<= y -2.1e-22)
           (+ x y)
           (if (<= y -3e-60)
             t_0
             (if (<= y -2.8e-60)
               (- z)
               (if (<= y 1.4e+91)
                 (+ x y)
                 (if (<= y 4.4e+156) (* z (/ x (- y))) (- z)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z / -y);
	double tmp;
	if (y <= -4.6e+44) {
		tmp = -z;
	} else if (y <= -0.0022) {
		tmp = x;
	} else if (y <= -1e-16) {
		tmp = t_0;
	} else if (y <= -2.1e-22) {
		tmp = x + y;
	} else if (y <= -3e-60) {
		tmp = t_0;
	} else if (y <= -2.8e-60) {
		tmp = -z;
	} else if (y <= 1.4e+91) {
		tmp = x + y;
	} else if (y <= 4.4e+156) {
		tmp = z * (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 * (z / -y)
    if (y <= (-4.6d+44)) then
        tmp = -z
    else if (y <= (-0.0022d0)) then
        tmp = x
    else if (y <= (-1d-16)) then
        tmp = t_0
    else if (y <= (-2.1d-22)) then
        tmp = x + y
    else if (y <= (-3d-60)) then
        tmp = t_0
    else if (y <= (-2.8d-60)) then
        tmp = -z
    else if (y <= 1.4d+91) then
        tmp = x + y
    else if (y <= 4.4d+156) then
        tmp = z * (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 * (z / -y);
	double tmp;
	if (y <= -4.6e+44) {
		tmp = -z;
	} else if (y <= -0.0022) {
		tmp = x;
	} else if (y <= -1e-16) {
		tmp = t_0;
	} else if (y <= -2.1e-22) {
		tmp = x + y;
	} else if (y <= -3e-60) {
		tmp = t_0;
	} else if (y <= -2.8e-60) {
		tmp = -z;
	} else if (y <= 1.4e+91) {
		tmp = x + y;
	} else if (y <= 4.4e+156) {
		tmp = z * (x / -y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z / -y)
	tmp = 0
	if y <= -4.6e+44:
		tmp = -z
	elif y <= -0.0022:
		tmp = x
	elif y <= -1e-16:
		tmp = t_0
	elif y <= -2.1e-22:
		tmp = x + y
	elif y <= -3e-60:
		tmp = t_0
	elif y <= -2.8e-60:
		tmp = -z
	elif y <= 1.4e+91:
		tmp = x + y
	elif y <= 4.4e+156:
		tmp = z * (x / -y)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z / Float64(-y)))
	tmp = 0.0
	if (y <= -4.6e+44)
		tmp = Float64(-z);
	elseif (y <= -0.0022)
		tmp = x;
	elseif (y <= -1e-16)
		tmp = t_0;
	elseif (y <= -2.1e-22)
		tmp = Float64(x + y);
	elseif (y <= -3e-60)
		tmp = t_0;
	elseif (y <= -2.8e-60)
		tmp = Float64(-z);
	elseif (y <= 1.4e+91)
		tmp = Float64(x + y);
	elseif (y <= 4.4e+156)
		tmp = Float64(z * Float64(x / Float64(-y)));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z / -y);
	tmp = 0.0;
	if (y <= -4.6e+44)
		tmp = -z;
	elseif (y <= -0.0022)
		tmp = x;
	elseif (y <= -1e-16)
		tmp = t_0;
	elseif (y <= -2.1e-22)
		tmp = x + y;
	elseif (y <= -3e-60)
		tmp = t_0;
	elseif (y <= -2.8e-60)
		tmp = -z;
	elseif (y <= 1.4e+91)
		tmp = x + y;
	elseif (y <= 4.4e+156)
		tmp = z * (x / -y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e+44], (-z), If[LessEqual[y, -0.0022], x, If[LessEqual[y, -1e-16], t$95$0, If[LessEqual[y, -2.1e-22], N[(x + y), $MachinePrecision], If[LessEqual[y, -3e-60], t$95$0, If[LessEqual[y, -2.8e-60], (-z), If[LessEqual[y, 1.4e+91], N[(x + y), $MachinePrecision], If[LessEqual[y, 4.4e+156], N[(z * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], (-z)]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.60000000000000009e44 or -3.00000000000000019e-60 < y < -2.8000000000000002e-60 or 4.40000000000000008e156 < y

   1. Initial program 70.0%

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

   3. Taylor expanded in y around inf 74.9%

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

      1. mul-1-neg 74.9%

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

   5. Simplified 74.9%

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

   if -4.60000000000000009e44 < y < -0.00220000000000000013

   1. Initial program 88.7%

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

   3. Taylor expanded in y around 0 64.1%

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

   if -0.00220000000000000013 < y < -9.9999999999999998e-17 or -2.10000000000000008e-22 < y < -3.00000000000000019e-60

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 68.0%

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

   4. Taylor expanded in y around inf 55.0%

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

      1. mul-1-neg 55.0%

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

      2. associate-*r/ 55.2%

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

      3. distribute-rgt-neg-in 55.2%

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

   6. Simplified 55.2%

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

   if -9.9999999999999998e-17 < y < -2.10000000000000008e-22 or -2.8000000000000002e-60 < y < 1.3999999999999999e91

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 77.3%

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

      1. +-commutative 77.3%

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

   5. Simplified 77.3%

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

   if 1.3999999999999999e91 < y < 4.40000000000000008e156

   1. Initial program 86.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 99.8%

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

      3. associate-*r* 99.8%

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

      4. associate-*l/ 99.8%

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

      5. *-commutative 99.8%

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

      6. neg-mul-1 99.8%

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

      7. distribute-neg-in 99.8%

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

      8. unsub-neg 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around inf 72.5%

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

   8. Simplified 72.5%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+44}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -0.0022:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-60}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+91}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+156}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{z}{-y}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+45}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -11.6:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-60}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-60} \lor \neg \left(y \leq 1.3 \cdot 10^{+27}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ z (- y)))))
   (if (<= y -2.7e+45)
     (- z)
     (if (<= y -11.6)
       x
       (if (<= y -1e-16)
         t_0
         (if (<= y -2.1e-22)
           (+ x y)
           (if (<= y -2.9e-60)
             t_0
             (if (or (<= y -2.8e-60) (not (<= y 1.3e+27)))
               (- z)
               (+ x y)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z / -y);
	double tmp;
	if (y <= -2.7e+45) {
		tmp = -z;
	} else if (y <= -11.6) {
		tmp = x;
	} else if (y <= -1e-16) {
		tmp = t_0;
	} else if (y <= -2.1e-22) {
		tmp = x + y;
	} else if (y <= -2.9e-60) {
		tmp = t_0;
	} else if ((y <= -2.8e-60) || !(y <= 1.3e+27)) {
		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) :: t_0
    real(8) :: tmp
    t_0 = x * (z / -y)
    if (y <= (-2.7d+45)) then
        tmp = -z
    else if (y <= (-11.6d0)) then
        tmp = x
    else if (y <= (-1d-16)) then
        tmp = t_0
    else if (y <= (-2.1d-22)) then
        tmp = x + y
    else if (y <= (-2.9d-60)) then
        tmp = t_0
    else if ((y <= (-2.8d-60)) .or. (.not. (y <= 1.3d+27))) 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 t_0 = x * (z / -y);
	double tmp;
	if (y <= -2.7e+45) {
		tmp = -z;
	} else if (y <= -11.6) {
		tmp = x;
	} else if (y <= -1e-16) {
		tmp = t_0;
	} else if (y <= -2.1e-22) {
		tmp = x + y;
	} else if (y <= -2.9e-60) {
		tmp = t_0;
	} else if ((y <= -2.8e-60) || !(y <= 1.3e+27)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z / -y)
	tmp = 0
	if y <= -2.7e+45:
		tmp = -z
	elif y <= -11.6:
		tmp = x
	elif y <= -1e-16:
		tmp = t_0
	elif y <= -2.1e-22:
		tmp = x + y
	elif y <= -2.9e-60:
		tmp = t_0
	elif (y <= -2.8e-60) or not (y <= 1.3e+27):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z / Float64(-y)))
	tmp = 0.0
	if (y <= -2.7e+45)
		tmp = Float64(-z);
	elseif (y <= -11.6)
		tmp = x;
	elseif (y <= -1e-16)
		tmp = t_0;
	elseif (y <= -2.1e-22)
		tmp = Float64(x + y);
	elseif (y <= -2.9e-60)
		tmp = t_0;
	elseif ((y <= -2.8e-60) || !(y <= 1.3e+27))
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z / -y);
	tmp = 0.0;
	if (y <= -2.7e+45)
		tmp = -z;
	elseif (y <= -11.6)
		tmp = x;
	elseif (y <= -1e-16)
		tmp = t_0;
	elseif (y <= -2.1e-22)
		tmp = x + y;
	elseif (y <= -2.9e-60)
		tmp = t_0;
	elseif ((y <= -2.8e-60) || ~((y <= 1.3e+27)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+45], (-z), If[LessEqual[y, -11.6], x, If[LessEqual[y, -1e-16], t$95$0, If[LessEqual[y, -2.1e-22], N[(x + y), $MachinePrecision], If[LessEqual[y, -2.9e-60], t$95$0, If[Or[LessEqual[y, -2.8e-60], N[Not[LessEqual[y, 1.3e+27]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.69999999999999984e45 or -2.8999999999999999e-60 < y < -2.8000000000000002e-60 or 1.30000000000000004e27 < y

   1. Initial program 73.1%

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

   3. Taylor expanded in y around inf 66.7%

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

      1. mul-1-neg 66.7%

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

   5. Simplified 66.7%

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

   if -2.69999999999999984e45 < y < -11.5999999999999996

   1. Initial program 88.7%

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

   3. Taylor expanded in y around 0 64.1%

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

   if -11.5999999999999996 < y < -9.9999999999999998e-17 or -2.10000000000000008e-22 < y < -2.8999999999999999e-60

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 68.0%

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

   4. Taylor expanded in y around inf 55.0%

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

      1. mul-1-neg 55.0%

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

      2. associate-*r/ 55.2%

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

      3. distribute-rgt-neg-in 55.2%

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

   6. Simplified 55.2%

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

   if -9.9999999999999998e-17 < y < -2.10000000000000008e-22 or -2.8000000000000002e-60 < y < 1.30000000000000004e27

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 79.2%

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

      1. +-commutative 79.2%

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

   5. Simplified 79.2%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+45}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -11.6:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-60} \lor \neg \left(y \leq 1.3 \cdot 10^{+27}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{1 - \frac{y}{z}}\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+109}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 10^{-43}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-15}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+60}:\\ \;\;\;\;\frac{z}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+113}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (- 1.0 (/ y z)))))
   (if (<= y -6.4e+109)
     (- z)
     (if (<= y 1e-43)
       (* x (/ z (- z y)))
       (if (<= y 3.4e-15)
         t_0
         (if (<= y 3.5e+60)
           (/ z (/ (- z y) x))
           (if (<= y 3.8e+113)
             t_0
             (if (<= y 1.2e+114) (* x (/ z (- y))) (- z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y / (1.0 - (y / z));
	double tmp;
	if (y <= -6.4e+109) {
		tmp = -z;
	} else if (y <= 1e-43) {
		tmp = x * (z / (z - y));
	} else if (y <= 3.4e-15) {
		tmp = t_0;
	} else if (y <= 3.5e+60) {
		tmp = z / ((z - y) / x);
	} else if (y <= 3.8e+113) {
		tmp = t_0;
	} else if (y <= 1.2e+114) {
		tmp = x * (z / -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 = y / (1.0d0 - (y / z))
    if (y <= (-6.4d+109)) then
        tmp = -z
    else if (y <= 1d-43) then
        tmp = x * (z / (z - y))
    else if (y <= 3.4d-15) then
        tmp = t_0
    else if (y <= 3.5d+60) then
        tmp = z / ((z - y) / x)
    else if (y <= 3.8d+113) then
        tmp = t_0
    else if (y <= 1.2d+114) then
        tmp = x * (z / -y)
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y / (1.0 - (y / z));
	double tmp;
	if (y <= -6.4e+109) {
		tmp = -z;
	} else if (y <= 1e-43) {
		tmp = x * (z / (z - y));
	} else if (y <= 3.4e-15) {
		tmp = t_0;
	} else if (y <= 3.5e+60) {
		tmp = z / ((z - y) / x);
	} else if (y <= 3.8e+113) {
		tmp = t_0;
	} else if (y <= 1.2e+114) {
		tmp = x * (z / -y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / (1.0 - (y / z))
	tmp = 0
	if y <= -6.4e+109:
		tmp = -z
	elif y <= 1e-43:
		tmp = x * (z / (z - y))
	elif y <= 3.4e-15:
		tmp = t_0
	elif y <= 3.5e+60:
		tmp = z / ((z - y) / x)
	elif y <= 3.8e+113:
		tmp = t_0
	elif y <= 1.2e+114:
		tmp = x * (z / -y)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (y <= -6.4e+109)
		tmp = Float64(-z);
	elseif (y <= 1e-43)
		tmp = Float64(x * Float64(z / Float64(z - y)));
	elseif (y <= 3.4e-15)
		tmp = t_0;
	elseif (y <= 3.5e+60)
		tmp = Float64(z / Float64(Float64(z - y) / x));
	elseif (y <= 3.8e+113)
		tmp = t_0;
	elseif (y <= 1.2e+114)
		tmp = Float64(x * Float64(z / Float64(-y)));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / (1.0 - (y / z));
	tmp = 0.0;
	if (y <= -6.4e+109)
		tmp = -z;
	elseif (y <= 1e-43)
		tmp = x * (z / (z - y));
	elseif (y <= 3.4e-15)
		tmp = t_0;
	elseif (y <= 3.5e+60)
		tmp = z / ((z - y) / x);
	elseif (y <= 3.8e+113)
		tmp = t_0;
	elseif (y <= 1.2e+114)
		tmp = x * (z / -y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.4e+109], (-z), If[LessEqual[y, 1e-43], N[(x * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-15], t$95$0, If[LessEqual[y, 3.5e+60], N[(z / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+113], t$95$0, If[LessEqual[y, 1.2e+114], N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision], (-z)]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.4000000000000002e109 or 1.2e114 < y

   1. Initial program 70.0%

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

   3. Taylor expanded in y around inf 75.6%

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

      1. mul-1-neg 75.6%

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

   5. Simplified 75.6%

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

   if -6.4000000000000002e109 < y < 1.00000000000000008e-43

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 96.8%

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

   4. Taylor expanded in x around inf 59.9%

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

      1. associate-/l* 79.8%

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

   6. Simplified 79.8%

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

   if 1.00000000000000008e-43 < y < 3.4e-15 or 3.5000000000000002e60 < y < 3.8000000000000003e113

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 91.0%

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

   if 3.4e-15 < y < 3.5000000000000002e60

   1. Initial program 84.0%

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

   3. Taylor expanded in x around inf 43.9%

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

   4. Taylor expanded in z around 0 43.9%

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

      1. associate-/r/ 59.7%

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

      2. add-sqr-sqrt 25.5%

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

      3. associate-*r* 25.5%

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

   6. Applied egg-rr 25.5%

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

      1. associate-*l* 25.5%

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

      2. clear-num 25.5%

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

      3. add-sqr-sqrt 59.6%

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

      4. associate-*l/ 59.6%

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

      5. *-un-lft-identity 59.6%

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

   8. Applied egg-rr 59.6%

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

   if 3.8000000000000003e113 < y < 1.2e114

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-*r/ 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+109}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 10^{-43}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-15}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+60}:\\ \;\;\;\;\frac{z}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+113}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{1 - \frac{y}{z}}\\ t_1 := x \cdot \frac{z}{z - y}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+116}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-15}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+113}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (- 1.0 (/ y z)))) (t_1 (* x (/ z (- z y)))))
   (if (<= y -1.2e+116)
     (- z)
     (if (<= y 7.4e-44)
       t_1
       (if (<= y 6.5e-15)
         t_0
         (if (<= y 4e+58)
           t_1
           (if (<= y 3.8e+113)
             t_0
             (if (<= y 1.45e+114) (* x (/ z (- y))) (- z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y / (1.0 - (y / z));
	double t_1 = x * (z / (z - y));
	double tmp;
	if (y <= -1.2e+116) {
		tmp = -z;
	} else if (y <= 7.4e-44) {
		tmp = t_1;
	} else if (y <= 6.5e-15) {
		tmp = t_0;
	} else if (y <= 4e+58) {
		tmp = t_1;
	} else if (y <= 3.8e+113) {
		tmp = t_0;
	} else if (y <= 1.45e+114) {
		tmp = x * (z / -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) :: t_1
    real(8) :: tmp
    t_0 = y / (1.0d0 - (y / z))
    t_1 = x * (z / (z - y))
    if (y <= (-1.2d+116)) then
        tmp = -z
    else if (y <= 7.4d-44) then
        tmp = t_1
    else if (y <= 6.5d-15) then
        tmp = t_0
    else if (y <= 4d+58) then
        tmp = t_1
    else if (y <= 3.8d+113) then
        tmp = t_0
    else if (y <= 1.45d+114) then
        tmp = x * (z / -y)
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y / (1.0 - (y / z));
	double t_1 = x * (z / (z - y));
	double tmp;
	if (y <= -1.2e+116) {
		tmp = -z;
	} else if (y <= 7.4e-44) {
		tmp = t_1;
	} else if (y <= 6.5e-15) {
		tmp = t_0;
	} else if (y <= 4e+58) {
		tmp = t_1;
	} else if (y <= 3.8e+113) {
		tmp = t_0;
	} else if (y <= 1.45e+114) {
		tmp = x * (z / -y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / (1.0 - (y / z))
	t_1 = x * (z / (z - y))
	tmp = 0
	if y <= -1.2e+116:
		tmp = -z
	elif y <= 7.4e-44:
		tmp = t_1
	elif y <= 6.5e-15:
		tmp = t_0
	elif y <= 4e+58:
		tmp = t_1
	elif y <= 3.8e+113:
		tmp = t_0
	elif y <= 1.45e+114:
		tmp = x * (z / -y)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(1.0 - Float64(y / z)))
	t_1 = Float64(x * Float64(z / Float64(z - y)))
	tmp = 0.0
	if (y <= -1.2e+116)
		tmp = Float64(-z);
	elseif (y <= 7.4e-44)
		tmp = t_1;
	elseif (y <= 6.5e-15)
		tmp = t_0;
	elseif (y <= 4e+58)
		tmp = t_1;
	elseif (y <= 3.8e+113)
		tmp = t_0;
	elseif (y <= 1.45e+114)
		tmp = Float64(x * Float64(z / Float64(-y)));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / (1.0 - (y / z));
	t_1 = x * (z / (z - y));
	tmp = 0.0;
	if (y <= -1.2e+116)
		tmp = -z;
	elseif (y <= 7.4e-44)
		tmp = t_1;
	elseif (y <= 6.5e-15)
		tmp = t_0;
	elseif (y <= 4e+58)
		tmp = t_1;
	elseif (y <= 3.8e+113)
		tmp = t_0;
	elseif (y <= 1.45e+114)
		tmp = x * (z / -y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e+116], (-z), If[LessEqual[y, 7.4e-44], t$95$1, If[LessEqual[y, 6.5e-15], t$95$0, If[LessEqual[y, 4e+58], t$95$1, If[LessEqual[y, 3.8e+113], t$95$0, If[LessEqual[y, 1.45e+114], N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision], (-z)]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.2e116 or 1.45e114 < y

   1. Initial program 70.0%

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

   3. Taylor expanded in y around inf 75.6%

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

      1. mul-1-neg 75.6%

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

   5. Simplified 75.6%

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

   if -1.2e116 < y < 7.4e-44 or 6.49999999999999991e-15 < y < 3.99999999999999978e58

   1. Initial program 95.9%

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

   3. Taylor expanded in z around 0 95.9%

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

   4. Taylor expanded in x around inf 59.3%

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

      1. associate-/l* 78.2%

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

   6. Simplified 78.2%

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

   if 7.4e-44 < y < 6.49999999999999991e-15 or 3.99999999999999978e58 < y < 3.8000000000000003e113

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 91.0%

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

   if 3.8000000000000003e113 < y < 1.45e114

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-*r/ 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+116}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-15}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+113}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-192} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-192) (not (<= t_0 0.0))) t_0 (* z (/ (- (- x) y) 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-192) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} 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 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-1d-192)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    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 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-192) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * ((-x - y) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -1e-192) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = z * ((-x - y) / 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-192) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(Float64(Float64(-x) - y) / 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-192) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = z * ((-x - y) / 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-192], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(z * N[(N[((-x) - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -1.0000000000000001e-192 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 -1.0000000000000001e-192 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 0.0

   1. Initial program 22.4%

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

   3. Taylor expanded in z around 0 88.2%

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

      1. *-commutative 88.2%

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

      2. associate-/l* 93.0%

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

      3. associate-*r* 93.0%

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

      4. associate-*l/ 93.0%

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

      5. *-commutative 93.0%

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

      6. neg-mul-1 93.0%

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

      7. distribute-neg-in 93.0%

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

      8. unsub-neg 93.0%

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

   5. Simplified 93.0%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-192} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{\left(-x\right) - y}{y}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+44}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-153}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-188}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{\frac{z - y}{z}}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-14}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ (- (- x) y) y))))
   (if (<= y -1.2e+44)
     t_0
     (if (<= y -2.4e-153)
       (* x (/ z (- z y)))
       (if (<= y -1.05e-188)
         (+ x y)
         (if (<= y 8.5e-44)
           (/ x (/ (- z y) z))
           (if (<= y 1.02e-14) (/ y (- 1.0 (/ y z))) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((-x - y) / y);
	double tmp;
	if (y <= -1.2e+44) {
		tmp = t_0;
	} else if (y <= -2.4e-153) {
		tmp = x * (z / (z - y));
	} else if (y <= -1.05e-188) {
		tmp = x + y;
	} else if (y <= 8.5e-44) {
		tmp = x / ((z - y) / z);
	} else if (y <= 1.02e-14) {
		tmp = 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 = z * ((-x - y) / y)
    if (y <= (-1.2d+44)) then
        tmp = t_0
    else if (y <= (-2.4d-153)) then
        tmp = x * (z / (z - y))
    else if (y <= (-1.05d-188)) then
        tmp = x + y
    else if (y <= 8.5d-44) then
        tmp = x / ((z - y) / z)
    else if (y <= 1.02d-14) then
        tmp = 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 = z * ((-x - y) / y);
	double tmp;
	if (y <= -1.2e+44) {
		tmp = t_0;
	} else if (y <= -2.4e-153) {
		tmp = x * (z / (z - y));
	} else if (y <= -1.05e-188) {
		tmp = x + y;
	} else if (y <= 8.5e-44) {
		tmp = x / ((z - y) / z);
	} else if (y <= 1.02e-14) {
		tmp = y / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((-x - y) / y)
	tmp = 0
	if y <= -1.2e+44:
		tmp = t_0
	elif y <= -2.4e-153:
		tmp = x * (z / (z - y))
	elif y <= -1.05e-188:
		tmp = x + y
	elif y <= 8.5e-44:
		tmp = x / ((z - y) / z)
	elif y <= 1.02e-14:
		tmp = y / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(Float64(-x) - y) / y))
	tmp = 0.0
	if (y <= -1.2e+44)
		tmp = t_0;
	elseif (y <= -2.4e-153)
		tmp = Float64(x * Float64(z / Float64(z - y)));
	elseif (y <= -1.05e-188)
		tmp = Float64(x + y);
	elseif (y <= 8.5e-44)
		tmp = Float64(x / Float64(Float64(z - y) / z));
	elseif (y <= 1.02e-14)
		tmp = Float64(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 = z * ((-x - y) / y);
	tmp = 0.0;
	if (y <= -1.2e+44)
		tmp = t_0;
	elseif (y <= -2.4e-153)
		tmp = x * (z / (z - y));
	elseif (y <= -1.05e-188)
		tmp = x + y;
	elseif (y <= 8.5e-44)
		tmp = x / ((z - y) / z);
	elseif (y <= 1.02e-14)
		tmp = y / (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[(N[((-x) - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e+44], t$95$0, If[LessEqual[y, -2.4e-153], N[(x * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.05e-188], N[(x + y), $MachinePrecision], If[LessEqual[y, 8.5e-44], N[(x / N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e-14], N[(y / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.20000000000000007e44 or 1.02e-14 < y

   1. Initial program 73.5%

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

   3. Taylor expanded in z around 0 59.6%

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

      1. *-commutative 59.6%

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

      2. associate-/l* 80.7%

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

      3. associate-*r* 80.7%

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

      4. associate-*l/ 80.7%

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

      5. *-commutative 80.7%

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

      6. neg-mul-1 80.7%

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

      7. distribute-neg-in 80.7%

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

      8. unsub-neg 80.7%

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

   5. Simplified 80.7%

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

   if -1.20000000000000007e44 < y < -2.4000000000000002e-153

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0 98.0%

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

   4. Taylor expanded in x around inf 63.6%

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

      1. associate-/l* 81.2%

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

   6. Simplified 81.2%

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

   if -2.4000000000000002e-153 < y < -1.05e-188

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -1.05e-188 < y < 8.5000000000000002e-44

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 83.9%

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

   4. Taylor expanded in z around 0 83.9%

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

   if 8.5000000000000002e-44 < y < 1.02e-14

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{y}{z}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+44}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-153}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-188}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{\frac{z - y}{z}}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-14}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+43}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -26:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-43}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-14}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e+43)
   (- z)
   (if (<= y -26.0)
     x
     (if (<= y -3.5e-43) y (if (<= y 1e-49) x (if (<= y 3.5e-14) y (- z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+43) {
		tmp = -z;
	} else if (y <= -26.0) {
		tmp = x;
	} else if (y <= -3.5e-43) {
		tmp = y;
	} else if (y <= 1e-49) {
		tmp = x;
	} else if (y <= 3.5e-14) {
		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 <= (-3.8d+43)) then
        tmp = -z
    else if (y <= (-26.0d0)) then
        tmp = x
    else if (y <= (-3.5d-43)) then
        tmp = y
    else if (y <= 1d-49) then
        tmp = x
    else if (y <= 3.5d-14) 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 <= -3.8e+43) {
		tmp = -z;
	} else if (y <= -26.0) {
		tmp = x;
	} else if (y <= -3.5e-43) {
		tmp = y;
	} else if (y <= 1e-49) {
		tmp = x;
	} else if (y <= 3.5e-14) {
		tmp = y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.8e+43:
		tmp = -z
	elif y <= -26.0:
		tmp = x
	elif y <= -3.5e-43:
		tmp = y
	elif y <= 1e-49:
		tmp = x
	elif y <= 3.5e-14:
		tmp = y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e+43)
		tmp = Float64(-z);
	elseif (y <= -26.0)
		tmp = x;
	elseif (y <= -3.5e-43)
		tmp = y;
	elseif (y <= 1e-49)
		tmp = x;
	elseif (y <= 3.5e-14)
		tmp = y;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.8e+43)
		tmp = -z;
	elseif (y <= -26.0)
		tmp = x;
	elseif (y <= -3.5e-43)
		tmp = y;
	elseif (y <= 1e-49)
		tmp = x;
	elseif (y <= 3.5e-14)
		tmp = y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.8e+43], (-z), If[LessEqual[y, -26.0], x, If[LessEqual[y, -3.5e-43], y, If[LessEqual[y, 1e-49], x, If[LessEqual[y, 3.5e-14], y, (-z)]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.80000000000000008e43 or 3.5000000000000002e-14 < y

   1. Initial program 73.2%

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

   3. Taylor expanded in y around inf 64.5%

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

      1. mul-1-neg 64.5%

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

   5. Simplified 64.5%

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

   if -3.80000000000000008e43 < y < -26 or -3.49999999999999997e-43 < y < 9.99999999999999936e-50

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 68.5%

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

   if -26 < y < -3.49999999999999997e-43 or 9.99999999999999936e-50 < y < 3.5000000000000002e-14

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 54.4%

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

   4. Taylor expanded in y around 0 45.5%

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

Alternative 10: 68.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{z}{z - y}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+109}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-87}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-13}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+53}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ z (- z y)))))
   (if (<= y -1.15e+109)
     (- z)
     (if (<= y 5.2e-87)
       t_0
       (if (<= y 2e-13) (+ x y) (if (<= y 4.8e+53) t_0 (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z / (z - y));
	double tmp;
	if (y <= -1.15e+109) {
		tmp = -z;
	} else if (y <= 5.2e-87) {
		tmp = t_0;
	} else if (y <= 2e-13) {
		tmp = x + y;
	} else if (y <= 4.8e+53) {
		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 * (z / (z - y))
    if (y <= (-1.15d+109)) then
        tmp = -z
    else if (y <= 5.2d-87) then
        tmp = t_0
    else if (y <= 2d-13) then
        tmp = x + y
    else if (y <= 4.8d+53) 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 * (z / (z - y));
	double tmp;
	if (y <= -1.15e+109) {
		tmp = -z;
	} else if (y <= 5.2e-87) {
		tmp = t_0;
	} else if (y <= 2e-13) {
		tmp = x + y;
	} else if (y <= 4.8e+53) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z / (z - y))
	tmp = 0
	if y <= -1.15e+109:
		tmp = -z
	elif y <= 5.2e-87:
		tmp = t_0
	elif y <= 2e-13:
		tmp = x + y
	elif y <= 4.8e+53:
		tmp = t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z / Float64(z - y)))
	tmp = 0.0
	if (y <= -1.15e+109)
		tmp = Float64(-z);
	elseif (y <= 5.2e-87)
		tmp = t_0;
	elseif (y <= 2e-13)
		tmp = Float64(x + y);
	elseif (y <= 4.8e+53)
		tmp = t_0;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z / (z - y));
	tmp = 0.0;
	if (y <= -1.15e+109)
		tmp = -z;
	elseif (y <= 5.2e-87)
		tmp = t_0;
	elseif (y <= 2e-13)
		tmp = x + y;
	elseif (y <= 4.8e+53)
		tmp = t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e+109], (-z), If[LessEqual[y, 5.2e-87], t$95$0, If[LessEqual[y, 2e-13], N[(x + y), $MachinePrecision], If[LessEqual[y, 4.8e+53], t$95$0, (-z)]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15000000000000005e109 or 4.8e53 < y

   1. Initial program 72.9%

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

   3. Taylor expanded in y around inf 71.7%

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

      1. mul-1-neg 71.7%

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

   5. Simplified 71.7%

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

   if -1.15000000000000005e109 < y < 5.20000000000000005e-87 or 2.0000000000000001e-13 < y < 4.8e53

   1. Initial program 95.6%

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

   3. Taylor expanded in z around 0 95.6%

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

   4. Taylor expanded in x around inf 60.3%

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

      1. associate-/l* 79.3%

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

   6. Simplified 79.3%

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

   if 5.20000000000000005e-87 < y < 2.0000000000000001e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 68.2%

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

      1. +-commutative 68.2%

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

   5. Simplified 68.2%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+109}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-87}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-13}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+73} \lor \neg \left(y \leq 2.05 \cdot 10^{+28}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.6e+73) (not (<= y 2.05e+28))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.6e+73) || !(y <= 2.05e+28)) {
		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 <= (-3.6d+73)) .or. (.not. (y <= 2.05d+28))) 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 <= -3.6e+73) || !(y <= 2.05e+28)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.6e+73) or not (y <= 2.05e+28):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.6e+73) || !(y <= 2.05e+28))
		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 <= -3.6e+73) || ~((y <= 2.05e+28)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.6e+73], N[Not[LessEqual[y, 2.05e+28]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5999999999999999e73 or 2.0499999999999999e28 < y

   1. Initial program 72.4%

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

   3. Taylor expanded in y around inf 66.7%

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

      1. mul-1-neg 66.7%

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

   5. Simplified 66.7%

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

   if -3.5999999999999999e73 < y < 2.0499999999999999e28

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf 72.6%

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

      1. +-commutative 72.6%

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

   5. Simplified 72.6%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+73} \lor \neg \left(y \leq 2.05 \cdot 10^{+28}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 40.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-148}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.5e-63) x (if (<= x 7.6e-148) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.5e-63) {
		tmp = x;
	} else if (x <= 7.6e-148) {
		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 <= (-2.5d-63)) then
        tmp = x
    else if (x <= 7.6d-148) 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 <= -2.5e-63) {
		tmp = x;
	} else if (x <= 7.6e-148) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.5e-63:
		tmp = x
	elif x <= 7.6e-148:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.5e-63)
		tmp = x;
	elseif (x <= 7.6e-148)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.5e-63)
		tmp = x;
	elseif (x <= 7.6e-148)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.5e-63], x, If[LessEqual[x, 7.6e-148], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5000000000000001e-63 or 7.60000000000000028e-148 < x

   1. Initial program 89.3%

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

   3. Taylor expanded in y around 0 49.0%

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

   if -2.5000000000000001e-63 < x < 7.60000000000000028e-148

   1. Initial program 84.4%

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

   3. Taylor expanded in x around 0 70.4%

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

   4. Taylor expanded in y around 0 36.4%

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

Alternative 13: 35.3% 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 87.8%

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

3. Taylor expanded in y around 0 37.8%

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

Alternative 14: 3.7% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 87.8%

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

3. Taylor expanded in z around 0 39.4%

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

   1. *-commutative 39.4%

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

   2. associate-/l* 49.1%

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

   3. associate-*r* 49.1%

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

   4. associate-*l/ 49.1%

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

   5. *-commutative 49.1%

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

   6. neg-mul-1 49.1%

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

   7. distribute-neg-in 49.1%

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

   8. unsub-neg 49.1%

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

5. Simplified 49.1%

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

7. Applied egg-rr 3.6%

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

8. Taylor expanded in x around 0 4.0%

   \[\leadsto \color{blue}{1} \]
9. Add Preprocessing

Developer target: 93.8% 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 2024105 
(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))))