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

Percentage Accurate: 88.2% → 99.7%

Time: 6.8s

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: 88.2% 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: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-292} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + y\right) \cdot z}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-292) (not (<= t_0 0.0))) t_0 (/ (* (+ x y) z) (- 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-292) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = ((x + y) * 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 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-1d-292)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = ((x + y) * z) / -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-292) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = ((x + y) * z) / -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -1e-292) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = ((x + y) * z) / -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-292) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(x + y) * z) / Float64(-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-292) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = ((x + y) * z) / -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-292], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] / (-y)), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -1.0000000000000001e-292 or -0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.8%

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

   if -1.0000000000000001e-292 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 6.4%

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

   3. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(x + y\right)}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-292} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + y\right) \cdot z}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 66.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{x}{t\_0}\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+151}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{-54} \lor \neg \left(x \leq 1.8 \cdot 10^{-80}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ x t_0)))
   (if (<= x -1.02e+180)
     t_1
     (if (<= x -5.8e+151)
       (- z)
       (if (or (<= x -9.8e-54) (not (<= x 1.8e-80))) t_1 (/ y t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = x / t_0;
	double tmp;
	if (x <= -1.02e+180) {
		tmp = t_1;
	} else if (x <= -5.8e+151) {
		tmp = -z;
	} else if ((x <= -9.8e-54) || !(x <= 1.8e-80)) {
		tmp = t_1;
	} else {
		tmp = y / t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = x / t_0
    if (x <= (-1.02d+180)) then
        tmp = t_1
    else if (x <= (-5.8d+151)) then
        tmp = -z
    else if ((x <= (-9.8d-54)) .or. (.not. (x <= 1.8d-80))) then
        tmp = t_1
    else
        tmp = y / t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = x / t_0;
	double tmp;
	if (x <= -1.02e+180) {
		tmp = t_1;
	} else if (x <= -5.8e+151) {
		tmp = -z;
	} else if ((x <= -9.8e-54) || !(x <= 1.8e-80)) {
		tmp = t_1;
	} else {
		tmp = y / t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = x / t_0
	tmp = 0
	if x <= -1.02e+180:
		tmp = t_1
	elif x <= -5.8e+151:
		tmp = -z
	elif (x <= -9.8e-54) or not (x <= 1.8e-80):
		tmp = t_1
	else:
		tmp = y / t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(x / t_0)
	tmp = 0.0
	if (x <= -1.02e+180)
		tmp = t_1;
	elseif (x <= -5.8e+151)
		tmp = Float64(-z);
	elseif ((x <= -9.8e-54) || !(x <= 1.8e-80))
		tmp = t_1;
	else
		tmp = Float64(y / t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = x / t_0;
	tmp = 0.0;
	if (x <= -1.02e+180)
		tmp = t_1;
	elseif (x <= -5.8e+151)
		tmp = -z;
	elseif ((x <= -9.8e-54) || ~((x <= 1.8e-80)))
		tmp = t_1;
	else
		tmp = y / t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / t$95$0), $MachinePrecision]}, If[LessEqual[x, -1.02e+180], t$95$1, If[LessEqual[x, -5.8e+151], (-z), If[Or[LessEqual[x, -9.8e-54], N[Not[LessEqual[x, 1.8e-80]], $MachinePrecision]], t$95$1, N[(y / t$95$0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.02e180 or -5.80000000000000036e151 < x < -9.80000000000000042e-54 or 1.8e-80 < x

   1. Initial program 87.9%

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

   3. Taylor expanded in x around inf 72.0%

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

   if -1.02e180 < x < -5.80000000000000036e151

   1. Initial program 71.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 -9.80000000000000042e-54 < x < 1.8e-80

   1. Initial program 90.6%

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

   3. Taylor expanded in x around 0 76.3%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+180}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+151}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{-54} \lor \neg \left(x \leq 1.8 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-44} \lor \neg \left(y \leq 4.9 \cdot 10^{-5}\right):\\ \;\;\;\;\left(-z\right) \cdot \frac{x + y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8e-44) (not (<= y 4.9e-5)))
   (* (- z) (/ (+ x y) y))
   (/ x (- 1.0 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8e-44) || !(y <= 4.9e-5)) {
		tmp = -z * ((x + y) / y);
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-8d-44)) .or. (.not. (y <= 4.9d-5))) then
        tmp = -z * ((x + y) / y)
    else
        tmp = x / (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8e-44) || !(y <= 4.9e-5)) {
		tmp = -z * ((x + y) / y);
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8e-44) or not (y <= 4.9e-5):
		tmp = -z * ((x + y) / y)
	else:
		tmp = x / (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8e-44) || !(y <= 4.9e-5))
		tmp = Float64(Float64(-z) * Float64(Float64(x + y) / y));
	else
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -8e-44) || ~((y <= 4.9e-5)))
		tmp = -z * ((x + y) / y);
	else
		tmp = x / (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8e-44], N[Not[LessEqual[y, 4.9e-5]], $MachinePrecision]], N[((-z) * N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.99999999999999962e-44 or 4.9e-5 < y

   1. Initial program 78.0%

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

   3. Taylor expanded in z around 0 68.5%

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

      1. *-commutative 68.5%

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

      2. associate-/l* 77.2%

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

      3. associate-*r* 77.2%

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

      4. associate-*l/ 77.2%

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

      5. *-commutative 77.2%

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

      6. neg-mul-1 77.2%

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

      7. distribute-neg-in 77.2%

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

      8. unsub-neg 77.2%

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

   5. Simplified 77.2%

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

   if -7.99999999999999962e-44 < y < 4.9e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 81.5%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-44} \lor \neg \left(y \leq 4.9 \cdot 10^{-5}\right):\\ \;\;\;\;\left(-z\right) \cdot \frac{x + y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+14}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-16}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8e+14)
   (- z)
   (if (<= y -6.4e-16) (/ (* z (- x)) y) (if (<= y 5.3e-5) (+ x y) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e+14) {
		tmp = -z;
	} else if (y <= -6.4e-16) {
		tmp = (z * -x) / y;
	} else if (y <= 5.3e-5) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-8d+14)) then
        tmp = -z
    else if (y <= (-6.4d-16)) then
        tmp = (z * -x) / y
    else if (y <= 5.3d-5) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e+14) {
		tmp = -z;
	} else if (y <= -6.4e-16) {
		tmp = (z * -x) / y;
	} else if (y <= 5.3e-5) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8e+14:
		tmp = -z
	elif y <= -6.4e-16:
		tmp = (z * -x) / y
	elif y <= 5.3e-5:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8e+14)
		tmp = Float64(-z);
	elseif (y <= -6.4e-16)
		tmp = Float64(Float64(z * Float64(-x)) / y);
	elseif (y <= 5.3e-5)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8e+14)
		tmp = -z;
	elseif (y <= -6.4e-16)
		tmp = (z * -x) / y;
	elseif (y <= 5.3e-5)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8e+14], (-z), If[LessEqual[y, -6.4e-16], N[(N[(z * (-x)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 5.3e-5], N[(x + y), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -8e14 or 5.3000000000000001e-5 < y

   1. Initial program 75.7%

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

   3. Taylor expanded in y around inf 60.2%

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

      1. mul-1-neg 60.2%

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

   5. Simplified 60.2%

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

   if -8e14 < y < -6.40000000000000046e-16

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 80.4%

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

   4. Taylor expanded in y around inf 68.4%

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

      1. associate-*r/ 68.4%

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

      2. associate-*r* 68.4%

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

      3. neg-mul-1 68.4%

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

   6. Simplified 68.4%

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

   if -6.40000000000000046e-16 < y < 5.3000000000000001e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 71.7%

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

      1. +-commutative 71.7%

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

   5. Simplified 71.7%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+14}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-16}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+22}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-16}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.6e+22)
   (- z)
   (if (<= y -7.5e-16) (* z (/ x (- y))) (if (<= y 5.3e-5) (+ x y) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.6e+22) {
		tmp = -z;
	} else if (y <= -7.5e-16) {
		tmp = z * (x / -y);
	} else if (y <= 5.3e-5) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.6d+22)) then
        tmp = -z
    else if (y <= (-7.5d-16)) then
        tmp = z * (x / -y)
    else if (y <= 5.3d-5) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.6e+22) {
		tmp = -z;
	} else if (y <= -7.5e-16) {
		tmp = z * (x / -y);
	} else if (y <= 5.3e-5) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.6e+22:
		tmp = -z
	elif y <= -7.5e-16:
		tmp = z * (x / -y)
	elif y <= 5.3e-5:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.6e+22)
		tmp = Float64(-z);
	elseif (y <= -7.5e-16)
		tmp = Float64(z * Float64(x / Float64(-y)));
	elseif (y <= 5.3e-5)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.6e+22)
		tmp = -z;
	elseif (y <= -7.5e-16)
		tmp = z * (x / -y);
	elseif (y <= 5.3e-5)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.6e+22], (-z), If[LessEqual[y, -7.5e-16], N[(z * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.3e-5], N[(x + y), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e22 or 5.3000000000000001e-5 < y

   1. Initial program 75.7%

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

   3. Taylor expanded in y around inf 60.2%

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

      1. mul-1-neg 60.2%

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

   5. Simplified 60.2%

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

   if -2.6e22 < y < -7.5e-16

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 80.4%

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

   4. Taylor expanded in y around inf 68.4%

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

      1. mul-1-neg 68.4%

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

      2. associate-/l* 68.3%

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

      3. distribute-rgt-neg-in 68.3%

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

      4. distribute-neg-frac2 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in x around 0 68.4%

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

      1. associate-*r/ 68.3%

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

      2. *-commutative 68.3%

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

      3. associate-*l/ 68.4%

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

      4. associate-*r/ 68.3%

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

      5. neg-mul-1 68.3%

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

      6. distribute-rgt-neg-in 68.3%

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

   9. Simplified 68.3%

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

   if -7.5e-16 < y < 5.3000000000000001e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 71.7%

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

      1. +-commutative 71.7%

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

   5. Simplified 71.7%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+22}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-16}:\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+23}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e+23)
   (- z)
   (if (<= y -4.3e-17) (* x (/ z (- y))) (if (<= y 5.3e-5) (+ x y) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+23) {
		tmp = -z;
	} else if (y <= -4.3e-17) {
		tmp = x * (z / -y);
	} else if (y <= 5.3e-5) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2d+23)) then
        tmp = -z
    else if (y <= (-4.3d-17)) then
        tmp = x * (z / -y)
    else if (y <= 5.3d-5) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+23) {
		tmp = -z;
	} else if (y <= -4.3e-17) {
		tmp = x * (z / -y);
	} else if (y <= 5.3e-5) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e+23:
		tmp = -z
	elif y <= -4.3e-17:
		tmp = x * (z / -y)
	elif y <= 5.3e-5:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e+23)
		tmp = Float64(-z);
	elseif (y <= -4.3e-17)
		tmp = Float64(x * Float64(z / Float64(-y)));
	elseif (y <= 5.3e-5)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2e+23)
		tmp = -z;
	elseif (y <= -4.3e-17)
		tmp = x * (z / -y);
	elseif (y <= 5.3e-5)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e+23], (-z), If[LessEqual[y, -4.3e-17], N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.3e-5], N[(x + y), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9999999999999998e23 or 5.3000000000000001e-5 < y

   1. Initial program 75.7%

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

   3. Taylor expanded in y around inf 60.2%

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

      1. mul-1-neg 60.2%

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

   5. Simplified 60.2%

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

   if -1.9999999999999998e23 < y < -4.30000000000000023e-17

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 80.4%

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

   4. Taylor expanded in y around inf 68.4%

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

      1. mul-1-neg 68.4%

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

      2. associate-/l* 68.3%

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

      3. distribute-rgt-neg-in 68.3%

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

      4. distribute-neg-frac2 68.3%

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

   6. Simplified 68.3%

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

   if -4.30000000000000023e-17 < y < 5.3000000000000001e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 71.7%

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

      1. +-commutative 71.7%

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

   5. Simplified 71.7%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+23}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+24} \lor \neg \left(y \leq 1.55 \cdot 10^{+109}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.8e+24) (not (<= y 1.55e+109))) (- z) (/ x (- 1.0 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.8e+24) || !(y <= 1.55e+109)) {
		tmp = -z;
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-7.8d+24)) .or. (.not. (y <= 1.55d+109))) then
        tmp = -z
    else
        tmp = x / (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.8e+24) || !(y <= 1.55e+109)) {
		tmp = -z;
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.8e+24) or not (y <= 1.55e+109):
		tmp = -z
	else:
		tmp = x / (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.8e+24) || !(y <= 1.55e+109))
		tmp = Float64(-z);
	else
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.8e+24) || ~((y <= 1.55e+109)))
		tmp = -z;
	else
		tmp = x / (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.8e+24], N[Not[LessEqual[y, 1.55e+109]], $MachinePrecision]], (-z), N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.7999999999999995e24 or 1.54999999999999996e109 < y

   1. Initial program 69.7%

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

   3. Taylor expanded in y around inf 67.7%

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

      1. mul-1-neg 67.7%

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

   5. Simplified 67.7%

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

   if -7.7999999999999995e24 < y < 1.54999999999999996e109

   1. Initial program 98.2%

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

   3. Taylor expanded in x around inf 73.6%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+24} \lor \neg \left(y \leq 1.55 \cdot 10^{+109}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -120000000 \lor \neg \left(y \leq 5.3 \cdot 10^{-5}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -120000000.0) (not (<= y 5.3e-5))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -120000000.0) || !(y <= 5.3e-5)) {
		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 <= (-120000000.0d0)) .or. (.not. (y <= 5.3d-5))) 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 <= -120000000.0) || !(y <= 5.3e-5)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -120000000.0) or not (y <= 5.3e-5):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -120000000.0) || !(y <= 5.3e-5))
		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 <= -120000000.0) || ~((y <= 5.3e-5)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -120000000.0], N[Not[LessEqual[y, 5.3e-5]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e8 or 5.3000000000000001e-5 < y

   1. Initial program 76.1%

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

   3. Taylor expanded in y around inf 59.4%

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

      1. mul-1-neg 59.4%

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

   5. Simplified 59.4%

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

   if -1.2e8 < y < 5.3000000000000001e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 68.9%

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

      1. +-commutative 68.9%

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

   5. Simplified 68.9%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -120000000 \lor \neg \left(y \leq 5.3 \cdot 10^{-5}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-65} \lor \neg \left(y \leq 1.1 \cdot 10^{-5}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.15e-65) (not (<= y 1.1e-5))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.15e-65) || !(y <= 1.1e-5)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.15d-65)) .or. (.not. (y <= 1.1d-5))) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.15e-65) || !(y <= 1.1e-5)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.15e-65) or not (y <= 1.1e-5):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.15e-65) || !(y <= 1.1e-5))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.15e-65) || ~((y <= 1.1e-5)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.15e-65], N[Not[LessEqual[y, 1.1e-5]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e-65 or 1.1e-5 < y

   1. Initial program 78.6%

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

   3. Taylor expanded in y around inf 55.5%

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

      1. mul-1-neg 55.5%

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

   5. Simplified 55.5%

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

   if -1.15e-65 < y < 1.1e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 64.1%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-65} \lor \neg \left(y \leq 1.1 \cdot 10^{-5}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 41.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-140}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-81}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.4e-140) x (if (<= x 3.2e-81) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.4e-140) {
		tmp = x;
	} else if (x <= 3.2e-81) {
		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 <= (-3.4d-140)) then
        tmp = x
    else if (x <= 3.2d-81) 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 <= -3.4e-140) {
		tmp = x;
	} else if (x <= 3.2e-81) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.4e-140:
		tmp = x
	elif x <= 3.2e-81:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.4e-140)
		tmp = x;
	elseif (x <= 3.2e-81)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.4e-140)
		tmp = x;
	elseif (x <= 3.2e-81)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.4e-140], x, If[LessEqual[x, 3.2e-81], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.40000000000000008e-140 or 3.2e-81 < x

   1. Initial program 86.1%

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

   3. Taylor expanded in y around 0 40.9%

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

   if -3.40000000000000008e-140 < x < 3.2e-81

   1. Initial program 94.2%

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

   3. Taylor expanded in x around 0 82.4%

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

   4. Taylor expanded in y around 0 33.2%

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

Alternative 11: 35.5% 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 88.2%

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

3. Taylor expanded in y around 0 34.0%

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

Developer target: 93.5% 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 2024091 
(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))))