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

Percentage Accurate: 88.5% → 99.8%

Time: 8.7s

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: 88.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-289} \lor \neg \left(t_0 \leq 3.5 \cdot 10^{-288}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z\right) - z \cdot \frac{x}{y}\right) - \frac{z}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-289) (not (<= t_0 3.5e-288)))
     t_0
     (- (- (- z) (* z (/ 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-289) || !(t_0 <= 3.5e-288)) {
		tmp = t_0;
	} else {
		tmp = (-z - (z * (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-289)) .or. (.not. (t_0 <= 3.5d-288))) then
        tmp = t_0
    else
        tmp = (-z - (z * (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-289) || !(t_0 <= 3.5e-288)) {
		tmp = t_0;
	} else {
		tmp = (-z - (z * (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-289) or not (t_0 <= 3.5e-288):
		tmp = t_0
	else:
		tmp = (-z - (z * (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-289) || !(t_0 <= 3.5e-288))
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(-z) - Float64(z * Float64(x / y))) - Float64(z / Float64(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-289) || ~((t_0 <= 3.5e-288)))
		tmp = t_0;
	else
		tmp = (-z - (z * (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[Or[LessEqual[t$95$0, -1e-289], N[Not[LessEqual[t$95$0, 3.5e-288]], $MachinePrecision]], t$95$0, N[(N[((-z) - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -1e-289 or 3.5000000000000003e-288 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

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

   if -1e-289 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 3.5000000000000003e-288

   1. Initial program 12.7%

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

   2. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}\right) - \frac{{z}^{2}}{y}} \]
   3. Step-by-step derivation

      1. mul-1-neg 100.0%

         \[\leadsto \left(-1 \cdot z + \color{blue}{\left(-\frac{x \cdot z}{y}\right)}\right) - \frac{{z}^{2}}{y} \]

      2. unsub-neg 100.0%

         \[\leadsto \color{blue}{\left(-1 \cdot z - \frac{x \cdot z}{y}\right)} - \frac{{z}^{2}}{y} \]

      3. mul-1-neg 100.0%

         \[\leadsto \left(\color{blue}{\left(-z\right)} - \frac{x \cdot z}{y}\right) - \frac{{z}^{2}}{y} \]

      4. associate-/l* 84.9%

         \[\leadsto \left(\left(-z\right) - \color{blue}{\frac{x}{\frac{y}{z}}}\right) - \frac{{z}^{2}}{y} \]

      5. associate-/r/ 100.0%

         \[\leadsto \left(\left(-z\right) - \color{blue}{\frac{x}{y} \cdot z}\right) - \frac{{z}^{2}}{y} \]

      6. unpow2 100.0%

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

      7. associate-/l* 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-289} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 3.5 \cdot 10^{-288}\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z\right) - z \cdot \frac{x}{y}\right) - \frac{z}{\frac{y}{z}}\\ \end{array} \]

Alternative 2: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-289} \lor \neg \left(t_0 \leq 3.5 \cdot 10^{-288}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-289) (not (<= t_0 3.5e-288)))
     t_0
     (/ (- z) (/ y (+ x y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-289) || !(t_0 <= 3.5e-288)) {
		tmp = t_0;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-1d-289)) .or. (.not. (t_0 <= 3.5d-288))) then
        tmp = t_0
    else
        tmp = -z / (y / (x + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-289) || !(t_0 <= 3.5e-288)) {
		tmp = t_0;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -1e-289) or not (t_0 <= 3.5e-288):
		tmp = t_0
	else:
		tmp = -z / (y / (x + y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -1e-289) || !(t_0 <= 3.5e-288))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) / Float64(y / Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -1e-289) || ~((t_0 <= 3.5e-288)))
		tmp = t_0;
	else
		tmp = -z / (y / (x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -1e-289], N[Not[LessEqual[t$95$0, 3.5e-288]], $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 1 (/.f64 y z))) < -1e-289 or 3.5000000000000003e-288 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

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

   if -1e-289 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 3.5000000000000003e-288

   1. Initial program 12.7%

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

   2. Taylor expanded in z around 0 94.8%

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

      1. associate-/l* 100.0%

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

      2. associate-*r/ 100.0%

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

      3. mul-1-neg 100.0%

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

      4. +-commutative 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-289} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 3.5 \cdot 10^{-288}\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \]

Alternative 3: 60.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -16000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-14}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-95}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-272}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-202}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-75}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -16000000000000.0)
   (+ x y)
   (if (<= z -7.6e-14)
     (- z)
     (if (<= z -1.3e-95)
       (+ x y)
       (if (<= z 5.5e-272)
         (- z)
         (if (<= z 1.35e-202)
           (/ x (- 1.0 (/ y z)))
           (if (<= z 1.8e-75) (- z) (+ x y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -16000000000000.0) {
		tmp = x + y;
	} else if (z <= -7.6e-14) {
		tmp = -z;
	} else if (z <= -1.3e-95) {
		tmp = x + y;
	} else if (z <= 5.5e-272) {
		tmp = -z;
	} else if (z <= 1.35e-202) {
		tmp = x / (1.0 - (y / z));
	} else if (z <= 1.8e-75) {
		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 (z <= (-16000000000000.0d0)) then
        tmp = x + y
    else if (z <= (-7.6d-14)) then
        tmp = -z
    else if (z <= (-1.3d-95)) then
        tmp = x + y
    else if (z <= 5.5d-272) then
        tmp = -z
    else if (z <= 1.35d-202) then
        tmp = x / (1.0d0 - (y / z))
    else if (z <= 1.8d-75) 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 (z <= -16000000000000.0) {
		tmp = x + y;
	} else if (z <= -7.6e-14) {
		tmp = -z;
	} else if (z <= -1.3e-95) {
		tmp = x + y;
	} else if (z <= 5.5e-272) {
		tmp = -z;
	} else if (z <= 1.35e-202) {
		tmp = x / (1.0 - (y / z));
	} else if (z <= 1.8e-75) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -16000000000000.0:
		tmp = x + y
	elif z <= -7.6e-14:
		tmp = -z
	elif z <= -1.3e-95:
		tmp = x + y
	elif z <= 5.5e-272:
		tmp = -z
	elif z <= 1.35e-202:
		tmp = x / (1.0 - (y / z))
	elif z <= 1.8e-75:
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -16000000000000.0)
		tmp = Float64(x + y);
	elseif (z <= -7.6e-14)
		tmp = Float64(-z);
	elseif (z <= -1.3e-95)
		tmp = Float64(x + y);
	elseif (z <= 5.5e-272)
		tmp = Float64(-z);
	elseif (z <= 1.35e-202)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (z <= 1.8e-75)
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -16000000000000.0)
		tmp = x + y;
	elseif (z <= -7.6e-14)
		tmp = -z;
	elseif (z <= -1.3e-95)
		tmp = x + y;
	elseif (z <= 5.5e-272)
		tmp = -z;
	elseif (z <= 1.35e-202)
		tmp = x / (1.0 - (y / z));
	elseif (z <= 1.8e-75)
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -16000000000000.0], N[(x + y), $MachinePrecision], If[LessEqual[z, -7.6e-14], (-z), If[LessEqual[z, -1.3e-95], N[(x + y), $MachinePrecision], If[LessEqual[z, 5.5e-272], (-z), If[LessEqual[z, 1.35e-202], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-75], (-z), N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6e13 or -7.6000000000000004e-14 < z < -1.3e-95 or 1.8e-75 < z

   1. Initial program 98.8%

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

   2. Taylor expanded in z around inf 76.1%

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

      1. +-commutative 76.1%

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

   4. Simplified 76.1%

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

   if -1.6e13 < z < -7.6000000000000004e-14 or -1.3e-95 < z < 5.4999999999999999e-272 or 1.3499999999999999e-202 < z < 1.8e-75

   1. Initial program 71.4%

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

   2. Taylor expanded in y around inf 66.4%

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

      1. mul-1-neg 66.4%

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

   4. Simplified 66.4%

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

   if 5.4999999999999999e-272 < z < 1.3499999999999999e-202

   1. Initial program 72.0%

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

   2. Taylor expanded in x around inf 66.4%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -16000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-14}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-95}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-272}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-202}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-75}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{-z}{\frac{y}{x + y}}\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -42:\\ \;\;\;\;\frac{y}{t_0}\\ \mathbf{elif}\;y \leq -1.24 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{t_0}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-47}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ (- z) (/ y (+ x y)))))
   (if (<= y -3.7e+68)
     t_1
     (if (<= y -42.0)
       (/ y t_0)
       (if (<= y -1.24e-116)
         (/ x t_0)
         (if (<= y 3e-47) (* (+ x y) (+ 1.0 (/ y z))) t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = -z / (y / (x + y));
	double tmp;
	if (y <= -3.7e+68) {
		tmp = t_1;
	} else if (y <= -42.0) {
		tmp = y / t_0;
	} else if (y <= -1.24e-116) {
		tmp = x / t_0;
	} else if (y <= 3e-47) {
		tmp = (x + y) * (1.0 + (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = -z / (y / (x + y))
    if (y <= (-3.7d+68)) then
        tmp = t_1
    else if (y <= (-42.0d0)) then
        tmp = y / t_0
    else if (y <= (-1.24d-116)) then
        tmp = x / t_0
    else if (y <= 3d-47) then
        tmp = (x + y) * (1.0d0 + (y / z))
    else
        tmp = t_1
    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 = -z / (y / (x + y));
	double tmp;
	if (y <= -3.7e+68) {
		tmp = t_1;
	} else if (y <= -42.0) {
		tmp = y / t_0;
	} else if (y <= -1.24e-116) {
		tmp = x / t_0;
	} else if (y <= 3e-47) {
		tmp = (x + y) * (1.0 + (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = -z / (y / (x + y))
	tmp = 0
	if y <= -3.7e+68:
		tmp = t_1
	elif y <= -42.0:
		tmp = y / t_0
	elif y <= -1.24e-116:
		tmp = x / t_0
	elif y <= 3e-47:
		tmp = (x + y) * (1.0 + (y / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(Float64(-z) / Float64(y / Float64(x + y)))
	tmp = 0.0
	if (y <= -3.7e+68)
		tmp = t_1;
	elseif (y <= -42.0)
		tmp = Float64(y / t_0);
	elseif (y <= -1.24e-116)
		tmp = Float64(x / t_0);
	elseif (y <= 3e-47)
		tmp = Float64(Float64(x + y) * Float64(1.0 + Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = -z / (y / (x + y));
	tmp = 0.0;
	if (y <= -3.7e+68)
		tmp = t_1;
	elseif (y <= -42.0)
		tmp = y / t_0;
	elseif (y <= -1.24e-116)
		tmp = x / t_0;
	elseif (y <= 3e-47)
		tmp = (x + y) * (1.0 + (y / z));
	else
		tmp = t_1;
	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[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.7e+68], t$95$1, If[LessEqual[y, -42.0], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, -1.24e-116], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 3e-47], N[(N[(x + y), $MachinePrecision] * N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.69999999999999998e68 or 3.00000000000000017e-47 < y

   1. Initial program 75.9%

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

   2. Taylor expanded in z around 0 63.1%

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

      1. associate-/l* 76.1%

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

      2. associate-*r/ 76.1%

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

      3. mul-1-neg 76.1%

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

      4. +-commutative 76.1%

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

   4. Simplified 76.1%

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

   if -3.69999999999999998e68 < y < -42

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 86.2%

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

   if -42 < y < -1.24000000000000004e-116

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 68.3%

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

   if -1.24000000000000004e-116 < y < 3.00000000000000017e-47

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 89.6%

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

      1. associate-+r+ 89.6%

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

      2. *-lft-identity 89.6%

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

      3. associate-*l/ 90.1%

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

      4. distribute-rgt-in 90.1%

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

      5. +-commutative 90.1%

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

   4. Simplified 90.1%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+68}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{elif}\;y \leq -42:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -1.24 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-47}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \]

Alternative 5: 69.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{1 - \frac{y}{z}}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+141}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -11800000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-17}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+178}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (- 1.0 (/ y z)))))
   (if (<= y -4.6e+141)
     (- z)
     (if (<= y -11800000000.0)
       t_0
       (if (<= y 5.3e-17)
         (+ x y)
         (if (<= y 3e+178) t_0 (- (- z) (* z (/ z y)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y / (1.0 - (y / z));
	double tmp;
	if (y <= -4.6e+141) {
		tmp = -z;
	} else if (y <= -11800000000.0) {
		tmp = t_0;
	} else if (y <= 5.3e-17) {
		tmp = x + y;
	} else if (y <= 3e+178) {
		tmp = t_0;
	} else {
		tmp = -z - (z * (z / 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 = y / (1.0d0 - (y / z))
    if (y <= (-4.6d+141)) then
        tmp = -z
    else if (y <= (-11800000000.0d0)) then
        tmp = t_0
    else if (y <= 5.3d-17) then
        tmp = x + y
    else if (y <= 3d+178) then
        tmp = t_0
    else
        tmp = -z - (z * (z / y))
    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 <= -4.6e+141) {
		tmp = -z;
	} else if (y <= -11800000000.0) {
		tmp = t_0;
	} else if (y <= 5.3e-17) {
		tmp = x + y;
	} else if (y <= 3e+178) {
		tmp = t_0;
	} else {
		tmp = -z - (z * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / (1.0 - (y / z))
	tmp = 0
	if y <= -4.6e+141:
		tmp = -z
	elif y <= -11800000000.0:
		tmp = t_0
	elif y <= 5.3e-17:
		tmp = x + y
	elif y <= 3e+178:
		tmp = t_0
	else:
		tmp = -z - (z * (z / y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (y <= -4.6e+141)
		tmp = Float64(-z);
	elseif (y <= -11800000000.0)
		tmp = t_0;
	elseif (y <= 5.3e-17)
		tmp = Float64(x + y);
	elseif (y <= 3e+178)
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) - Float64(z * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / (1.0 - (y / z));
	tmp = 0.0;
	if (y <= -4.6e+141)
		tmp = -z;
	elseif (y <= -11800000000.0)
		tmp = t_0;
	elseif (y <= 5.3e-17)
		tmp = x + y;
	elseif (y <= 3e+178)
		tmp = t_0;
	else
		tmp = -z - (z * (z / y));
	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, -4.6e+141], (-z), If[LessEqual[y, -11800000000.0], t$95$0, If[LessEqual[y, 5.3e-17], N[(x + y), $MachinePrecision], If[LessEqual[y, 3e+178], t$95$0, N[((-z) - N[(z * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.6000000000000003e141

   1. Initial program 53.9%

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

   2. Taylor expanded in y around inf 74.3%

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

      1. mul-1-neg 74.3%

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

   4. Simplified 74.3%

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

   if -4.6000000000000003e141 < y < -1.18e10 or 5.2999999999999998e-17 < y < 3.00000000000000016e178

   1. Initial program 90.7%

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

   2. Taylor expanded in x around 0 67.1%

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

   if -1.18e10 < y < 5.2999999999999998e-17

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 80.2%

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

      1. +-commutative 80.2%

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

   4. Simplified 80.2%

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

   if 3.00000000000000016e178 < y

   1. Initial program 73.1%

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

   2. Taylor expanded in x around 0 67.3%

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

   3. Taylor expanded in y around inf 88.3%

      \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{{z}^{2}}{y}} \]
   4. Step-by-step derivation

      1. distribute-lft-in 88.3%

         \[\leadsto \color{blue}{-1 \cdot \left(z + \frac{{z}^{2}}{y}\right)} \]

      2. mul-1-neg 88.3%

         \[\leadsto \color{blue}{-\left(z + \frac{{z}^{2}}{y}\right)} \]

      3. unpow2 88.3%

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

      4. associate-*r/ 94.2%

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

   5. Simplified 94.2%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+141}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -11800000000:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-17}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+178}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{z}{y}\\ \end{array} \]

Alternative 6: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{-z}{\frac{y}{x + y}}\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -70:\\ \;\;\;\;\frac{y}{t_0}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{t_0}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-47}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ (- z) (/ y (+ x y)))))
   (if (<= y -4.3e+70)
     t_1
     (if (<= y -70.0)
       (/ y t_0)
       (if (<= y -4.4e-115) (/ x t_0) (if (<= y 2.9e-47) (+ x y) t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = -z / (y / (x + y));
	double tmp;
	if (y <= -4.3e+70) {
		tmp = t_1;
	} else if (y <= -70.0) {
		tmp = y / t_0;
	} else if (y <= -4.4e-115) {
		tmp = x / t_0;
	} else if (y <= 2.9e-47) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = -z / (y / (x + y))
    if (y <= (-4.3d+70)) then
        tmp = t_1
    else if (y <= (-70.0d0)) then
        tmp = y / t_0
    else if (y <= (-4.4d-115)) then
        tmp = x / t_0
    else if (y <= 2.9d-47) then
        tmp = x + y
    else
        tmp = t_1
    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 = -z / (y / (x + y));
	double tmp;
	if (y <= -4.3e+70) {
		tmp = t_1;
	} else if (y <= -70.0) {
		tmp = y / t_0;
	} else if (y <= -4.4e-115) {
		tmp = x / t_0;
	} else if (y <= 2.9e-47) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = -z / (y / (x + y))
	tmp = 0
	if y <= -4.3e+70:
		tmp = t_1
	elif y <= -70.0:
		tmp = y / t_0
	elif y <= -4.4e-115:
		tmp = x / t_0
	elif y <= 2.9e-47:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(Float64(-z) / Float64(y / Float64(x + y)))
	tmp = 0.0
	if (y <= -4.3e+70)
		tmp = t_1;
	elseif (y <= -70.0)
		tmp = Float64(y / t_0);
	elseif (y <= -4.4e-115)
		tmp = Float64(x / t_0);
	elseif (y <= 2.9e-47)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = -z / (y / (x + y));
	tmp = 0.0;
	if (y <= -4.3e+70)
		tmp = t_1;
	elseif (y <= -70.0)
		tmp = y / t_0;
	elseif (y <= -4.4e-115)
		tmp = x / t_0;
	elseif (y <= 2.9e-47)
		tmp = x + y;
	else
		tmp = t_1;
	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[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.3e+70], t$95$1, If[LessEqual[y, -70.0], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, -4.4e-115], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 2.9e-47], N[(x + y), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.3000000000000001e70 or 2.9e-47 < y

   1. Initial program 75.9%

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

   2. Taylor expanded in z around 0 63.1%

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

      1. associate-/l* 76.1%

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

      2. associate-*r/ 76.1%

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

      3. mul-1-neg 76.1%

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

      4. +-commutative 76.1%

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

   4. Simplified 76.1%

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

   if -4.3000000000000001e70 < y < -70

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 86.2%

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

   if -70 < y < -4.3999999999999999e-115

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 68.3%

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

   if -4.3999999999999999e-115 < y < 2.9e-47

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 89.7%

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

      1. +-commutative 89.7%

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

   4. Simplified 89.7%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+70}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{elif}\;y \leq -70:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-47}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \]

Alternative 7: 69.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{1 - \frac{y}{z}}\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+140}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1750000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-17}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+177}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (- 1.0 (/ y z)))))
   (if (<= y -2.1e+140)
     (- z)
     (if (<= y -1750000.0)
       t_0
       (if (<= y 7e-17) (+ x y) (if (<= y 4.6e+177) t_0 (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = y / (1.0 - (y / z));
	double tmp;
	if (y <= -2.1e+140) {
		tmp = -z;
	} else if (y <= -1750000.0) {
		tmp = t_0;
	} else if (y <= 7e-17) {
		tmp = x + y;
	} else if (y <= 4.6e+177) {
		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 = y / (1.0d0 - (y / z))
    if (y <= (-2.1d+140)) then
        tmp = -z
    else if (y <= (-1750000.0d0)) then
        tmp = t_0
    else if (y <= 7d-17) then
        tmp = x + y
    else if (y <= 4.6d+177) 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 = y / (1.0 - (y / z));
	double tmp;
	if (y <= -2.1e+140) {
		tmp = -z;
	} else if (y <= -1750000.0) {
		tmp = t_0;
	} else if (y <= 7e-17) {
		tmp = x + y;
	} else if (y <= 4.6e+177) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / (1.0 - (y / z))
	tmp = 0
	if y <= -2.1e+140:
		tmp = -z
	elif y <= -1750000.0:
		tmp = t_0
	elif y <= 7e-17:
		tmp = x + y
	elif y <= 4.6e+177:
		tmp = t_0
	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 <= -2.1e+140)
		tmp = Float64(-z);
	elseif (y <= -1750000.0)
		tmp = t_0;
	elseif (y <= 7e-17)
		tmp = Float64(x + y);
	elseif (y <= 4.6e+177)
		tmp = t_0;
	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 <= -2.1e+140)
		tmp = -z;
	elseif (y <= -1750000.0)
		tmp = t_0;
	elseif (y <= 7e-17)
		tmp = x + y;
	elseif (y <= 4.6e+177)
		tmp = t_0;
	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, -2.1e+140], (-z), If[LessEqual[y, -1750000.0], t$95$0, If[LessEqual[y, 7e-17], N[(x + y), $MachinePrecision], If[LessEqual[y, 4.6e+177], t$95$0, (-z)]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1000000000000002e140 or 4.5999999999999998e177 < y

   1. Initial program 59.8%

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

   2. Taylor expanded in y around inf 79.8%

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

      1. mul-1-neg 79.8%

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

   4. Simplified 79.8%

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

   if -2.1000000000000002e140 < y < -1.75e6 or 7.0000000000000003e-17 < y < 4.5999999999999998e177

   1. Initial program 90.7%

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

   2. Taylor expanded in x around 0 67.1%

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

   if -1.75e6 < y < 7.0000000000000003e-17

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 80.2%

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

      1. +-commutative 80.2%

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

   4. Simplified 80.2%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+140}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1750000:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-17}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+177}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 8: 60.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+17}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-14} \lor \neg \left(z \leq -7.8 \cdot 10^{-94}\right) \land z \leq 2.1 \cdot 10^{-69}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.2e+17)
   (+ x y)
   (if (or (<= z -8e-14) (and (not (<= z -7.8e-94)) (<= z 2.1e-69)))
     (- z)
     (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.2e+17) {
		tmp = x + y;
	} else if ((z <= -8e-14) || (!(z <= -7.8e-94) && (z <= 2.1e-69))) {
		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 (z <= (-1.2d+17)) then
        tmp = x + y
    else if ((z <= (-8d-14)) .or. (.not. (z <= (-7.8d-94))) .and. (z <= 2.1d-69)) 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 (z <= -1.2e+17) {
		tmp = x + y;
	} else if ((z <= -8e-14) || (!(z <= -7.8e-94) && (z <= 2.1e-69))) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.2e+17:
		tmp = x + y
	elif (z <= -8e-14) or (not (z <= -7.8e-94) and (z <= 2.1e-69)):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.2e+17)
		tmp = Float64(x + y);
	elseif ((z <= -8e-14) || (!(z <= -7.8e-94) && (z <= 2.1e-69)))
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.2e+17)
		tmp = x + y;
	elseif ((z <= -8e-14) || (~((z <= -7.8e-94)) && (z <= 2.1e-69)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.2e+17], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, -8e-14], And[N[Not[LessEqual[z, -7.8e-94]], $MachinePrecision], LessEqual[z, 2.1e-69]]], (-z), N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e17 or -7.99999999999999999e-14 < z < -7.8000000000000004e-94 or 2.1e-69 < z

   1. Initial program 98.8%

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

   2. Taylor expanded in z around inf 76.1%

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

      1. +-commutative 76.1%

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

   4. Simplified 76.1%

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

   if -1.2e17 < z < -7.99999999999999999e-14 or -7.8000000000000004e-94 < z < 2.1e-69

   1. Initial program 71.5%

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

   2. Taylor expanded in y around inf 59.3%

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

      1. mul-1-neg 59.3%

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

   4. Simplified 59.3%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+17}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-14} \lor \neg \left(z \leq -7.8 \cdot 10^{-94}\right) \land z \leq 2.1 \cdot 10^{-69}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9: 40.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-162}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-212}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-90}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.5e-162)
   x
   (if (<= x 1.12e-212) y (if (<= x 1e-143) x (if (<= x 7.2e-90) y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.5e-162) {
		tmp = x;
	} else if (x <= 1.12e-212) {
		tmp = y;
	} else if (x <= 1e-143) {
		tmp = x;
	} else if (x <= 7.2e-90) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.5d-162)) then
        tmp = x
    else if (x <= 1.12d-212) then
        tmp = y
    else if (x <= 1d-143) then
        tmp = x
    else if (x <= 7.2d-90) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.5e-162) {
		tmp = x;
	} else if (x <= 1.12e-212) {
		tmp = y;
	} else if (x <= 1e-143) {
		tmp = x;
	} else if (x <= 7.2e-90) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.5e-162:
		tmp = x
	elif x <= 1.12e-212:
		tmp = y
	elif x <= 1e-143:
		tmp = x
	elif x <= 7.2e-90:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.5e-162)
		tmp = x;
	elseif (x <= 1.12e-212)
		tmp = y;
	elseif (x <= 1e-143)
		tmp = x;
	elseif (x <= 7.2e-90)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.5e-162)
		tmp = x;
	elseif (x <= 1.12e-212)
		tmp = y;
	elseif (x <= 1e-143)
		tmp = x;
	elseif (x <= 7.2e-90)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.5e-162], x, If[LessEqual[x, 1.12e-212], y, If[LessEqual[x, 1e-143], x, If[LessEqual[x, 7.2e-90], y, x]]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.49999999999999999e-162 or 1.12e-212 < x < 9.9999999999999995e-144 or 7.19999999999999961e-90 < x

   1. Initial program 88.8%

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

   2. Taylor expanded in y around 0 47.1%

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

   if -1.49999999999999999e-162 < x < 1.12e-212 or 9.9999999999999995e-144 < x < 7.19999999999999961e-90

   1. Initial program 88.3%

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

   2. Taylor expanded in x around 0 79.9%

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

   3. Taylor expanded in y around 0 45.7%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-162}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-212}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-90}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 57.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -35:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -35.0) (- z) (if (<= y 5e-18) x (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -35.0) {
		tmp = -z;
	} else if (y <= 5e-18) {
		tmp = x;
	} 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 <= (-35.0d0)) then
        tmp = -z
    else if (y <= 5d-18) then
        tmp = x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -35.0) {
		tmp = -z;
	} else if (y <= 5e-18) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -35.0:
		tmp = -z
	elif y <= 5e-18:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -35.0)
		tmp = Float64(-z);
	elseif (y <= 5e-18)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -35.0)
		tmp = -z;
	elseif (y <= 5e-18)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -35.0], (-z), If[LessEqual[y, 5e-18], x, (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -35 or 5.00000000000000036e-18 < y

   1. Initial program 77.0%

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

   2. Taylor expanded in y around inf 60.4%

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

      1. mul-1-neg 60.4%

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

   4. Simplified 60.4%

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

   if -35 < y < 5.00000000000000036e-18

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 64.4%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -35:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 11: 35.0% 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 88.6%

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

2. Taylor expanded in y around 0 37.3%

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

3. Final simplification 37.3%

   \[\leadsto x \]

Developer target: 93.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y + x}{-y} \cdot z\\ \mathbf{if}\;y < -3.7429310762689856 \cdot 10^{+171}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y < 3.5534662456086734 \cdot 10^{+168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ (+ y x) (- y)) z)))
   (if (< y -3.7429310762689856e+171)
     t_0
     (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y + x) / -y) * z
    if (y < (-3.7429310762689856d+171)) then
        tmp = t_0
    else if (y < 3.5534662456086734d+168) then
        tmp = (x + y) / (1.0d0 - (y / z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y + x) / -y) * z
	tmp = 0
	if y < -3.7429310762689856e+171:
		tmp = t_0
	elif y < 3.5534662456086734e+168:
		tmp = (x + y) / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y + x) / Float64(-y)) * z)
	tmp = 0.0
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y + x) / -y) * z;
	tmp = 0.0;
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = (x + y) / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y + x), $MachinePrecision] / (-y)), $MachinePrecision] * z), $MachinePrecision]}, If[Less[y, -3.7429310762689856e+171], t$95$0, If[Less[y, 3.5534662456086734e+168], N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :herbie-target
  (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))))