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

Percentage Accurate: 88.2% → 99.8%

Time: 6.1s

Alternatives: 10

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: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-290} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{-y} - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -5e-290) (not (<= t_0 0.0))) t_0 (- (/ (* x 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 <= -5e-290) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = ((x * 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 <= (-5d-290)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = ((x * 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 <= -5e-290) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = ((x * z) / -y) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -5e-290) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = ((x * 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 <= -5e-290) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(x * 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 <= -5e-290) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = ((x * 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, -5e-290], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(N[(N[(x * z), $MachinePrecision] / (-y)), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -5.0000000000000001e-290 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 -5.0000000000000001e-290 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 0.0

   1. Initial program 9.3%

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

   3. Taylor expanded in z around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. associate-/l* 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. distribute-neg-frac2 99.9%

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

      5. +-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-290} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{-y} - z\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 71.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+41}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-21}:\\ \;\;\;\;\frac{z}{\frac{z}{y} + -1}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{-y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.6e+41)
   (+ x y)
   (if (<= z -2.25e-21)
     (/ z (+ (/ z y) -1.0))
     (if (<= z 7.2e+26) (/ (* z (+ x y)) (- y)) (+ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.6e+41) {
		tmp = x + y;
	} else if (z <= -2.25e-21) {
		tmp = z / ((z / y) + -1.0);
	} else if (z <= 7.2e+26) {
		tmp = (z * (x + y)) / -y;
	} 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 <= (-3.6d+41)) then
        tmp = x + y
    else if (z <= (-2.25d-21)) then
        tmp = z / ((z / y) + (-1.0d0))
    else if (z <= 7.2d+26) then
        tmp = (z * (x + y)) / -y
    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 <= -3.6e+41) {
		tmp = x + y;
	} else if (z <= -2.25e-21) {
		tmp = z / ((z / y) + -1.0);
	} else if (z <= 7.2e+26) {
		tmp = (z * (x + y)) / -y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.6e+41:
		tmp = x + y
	elif z <= -2.25e-21:
		tmp = z / ((z / y) + -1.0)
	elif z <= 7.2e+26:
		tmp = (z * (x + y)) / -y
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.6e+41)
		tmp = Float64(x + y);
	elseif (z <= -2.25e-21)
		tmp = Float64(z / Float64(Float64(z / y) + -1.0));
	elseif (z <= 7.2e+26)
		tmp = Float64(Float64(z * Float64(x + y)) / Float64(-y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.6e+41)
		tmp = x + y;
	elseif (z <= -2.25e-21)
		tmp = z / ((z / y) + -1.0);
	elseif (z <= 7.2e+26)
		tmp = (z * (x + y)) / -y;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.6e+41], N[(x + y), $MachinePrecision], If[LessEqual[z, -2.25e-21], N[(z / N[(N[(z / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+26], N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] / (-y)), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.60000000000000025e41 or 7.20000000000000048e26 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 81.6%

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

      1. +-commutative 81.6%

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

   5. Simplified 81.6%

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

   if -3.60000000000000025e41 < z < -2.24999999999999984e-21

   1. Initial program 100.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.5%

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

      2. inv-pow 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in z around 0 95.8%

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

      1. +-commutative 95.8%

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

      2. mul-1-neg 95.8%

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

      3. unsub-neg 95.8%

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

   7. Simplified 95.8%

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

   8. Taylor expanded in x around 0 83.6%

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

   if -2.24999999999999984e-21 < z < 7.20000000000000048e26

   1. Initial program 72.4%

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

   3. Taylor expanded in z around 0 79.1%

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

      1. mul-1-neg 79.1%

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

      2. +-commutative 79.1%

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

   5. Simplified 79.1%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+41}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-21}:\\ \;\;\;\;\frac{z}{\frac{z}{y} + -1}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{-y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.3 \cdot 10^{+55}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-264}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.3e+55)
   (- z)
   (if (<= y -1.75e-264)
     (+ x y)
     (if (<= y 2.7e+97) (/ x (- 1.0 (/ y z))) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.3e+55) {
		tmp = -z;
	} else if (y <= -1.75e-264) {
		tmp = x + y;
	} else if (y <= 2.7e+97) {
		tmp = x / (1.0 - (y / z));
	} 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 <= (-9.3d+55)) then
        tmp = -z
    else if (y <= (-1.75d-264)) then
        tmp = x + y
    else if (y <= 2.7d+97) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.3e+55) {
		tmp = -z;
	} else if (y <= -1.75e-264) {
		tmp = x + y;
	} else if (y <= 2.7e+97) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.3e+55:
		tmp = -z
	elif y <= -1.75e-264:
		tmp = x + y
	elif y <= 2.7e+97:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.3e+55)
		tmp = Float64(-z);
	elseif (y <= -1.75e-264)
		tmp = Float64(x + y);
	elseif (y <= 2.7e+97)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.3e+55)
		tmp = -z;
	elseif (y <= -1.75e-264)
		tmp = x + y;
	elseif (y <= 2.7e+97)
		tmp = x / (1.0 - (y / z));
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.3e+55], (-z), If[LessEqual[y, -1.75e-264], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.7e+97], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.30000000000000035e55 or 2.69999999999999993e97 < y

   1. Initial program 69.9%

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

   3. Taylor expanded in y around inf 69.0%

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

      1. mul-1-neg 69.0%

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

   5. Simplified 69.0%

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

   if -9.30000000000000035e55 < y < -1.75e-264

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf 74.0%

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

      1. +-commutative 74.0%

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

   5. Simplified 74.0%

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

   if -1.75e-264 < y < 2.69999999999999993e97

   1. Initial program 96.6%

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

   3. Taylor expanded in x around inf 68.7%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.3 \cdot 10^{+55}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-264}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;y \leq -5 \cdot 10^{+165}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -9.1 \cdot 10^{-66}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+98}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (<= y -5e+165)
     (- z)
     (if (<= y -9.1e-66) (/ y t_0) (if (<= y 6.5e+98) (/ x t_0) (- z))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -5e+165) {
		tmp = -z;
	} else if (y <= -9.1e-66) {
		tmp = y / t_0;
	} else if (y <= 6.5e+98) {
		tmp = x / t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    if (y <= (-5d+165)) then
        tmp = -z
    else if (y <= (-9.1d-66)) then
        tmp = y / t_0
    else if (y <= 6.5d+98) then
        tmp = x / t_0
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -5e+165) {
		tmp = -z;
	} else if (y <= -9.1e-66) {
		tmp = y / t_0;
	} else if (y <= 6.5e+98) {
		tmp = x / t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if y <= -5e+165:
		tmp = -z
	elif y <= -9.1e-66:
		tmp = y / t_0
	elif y <= 6.5e+98:
		tmp = x / t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if (y <= -5e+165)
		tmp = Float64(-z);
	elseif (y <= -9.1e-66)
		tmp = Float64(y / t_0);
	elseif (y <= 6.5e+98)
		tmp = Float64(x / t_0);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	tmp = 0.0;
	if (y <= -5e+165)
		tmp = -z;
	elseif (y <= -9.1e-66)
		tmp = y / t_0;
	elseif (y <= 6.5e+98)
		tmp = x / t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+165], (-z), If[LessEqual[y, -9.1e-66], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, 6.5e+98], N[(x / t$95$0), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9999999999999997e165 or 6.4999999999999999e98 < y

   1. Initial program 66.3%

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

   3. Taylor expanded in y around inf 72.4%

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

      1. mul-1-neg 72.4%

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

   5. Simplified 72.4%

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

   if -4.9999999999999997e165 < y < -9.1000000000000001e-66

   1. Initial program 94.1%

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

   3. Taylor expanded in x around 0 70.1%

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

   if -9.1000000000000001e-66 < y < 6.4999999999999999e98

   1. Initial program 97.7%

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

   3. Taylor expanded in x around inf 72.3%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+165}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -9.1 \cdot 10^{-66}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+98}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+41} \lor \neg \left(z \leq 2.1 \cdot 10^{+27}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x + y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.26e+41) (not (<= z 2.1e+27)))
   (+ x y)
   (* (- z) (/ (+ x y) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.26e+41) || !(z <= 2.1e+27)) {
		tmp = x + y;
	} else {
		tmp = -z * ((x + y) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.26d+41)) .or. (.not. (z <= 2.1d+27))) then
        tmp = x + y
    else
        tmp = -z * ((x + y) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.26e+41) || !(z <= 2.1e+27)) {
		tmp = x + y;
	} else {
		tmp = -z * ((x + y) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.26e+41) or not (z <= 2.1e+27):
		tmp = x + y
	else:
		tmp = -z * ((x + y) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.26e+41) || !(z <= 2.1e+27))
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(-z) * Float64(Float64(x + y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.26e+41) || ~((z <= 2.1e+27)))
		tmp = x + y;
	else
		tmp = -z * ((x + y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.26e+41], N[Not[LessEqual[z, 2.1e+27]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[((-z) * N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.26000000000000001e41 or 2.09999999999999995e27 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 81.7%

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

      1. +-commutative 81.7%

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

   5. Simplified 81.7%

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

   if -1.26000000000000001e41 < z < 2.09999999999999995e27

   1. Initial program 74.7%

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

   3. Taylor expanded in z around 0 75.7%

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

      1. mul-1-neg 75.7%

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

      2. associate-/l* 80.1%

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

      3. distribute-rgt-neg-in 80.1%

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

      4. distribute-neg-frac2 80.1%

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

      5. +-commutative 80.1%

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

   5. Simplified 80.1%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+41} \lor \neg \left(z \leq 2.1 \cdot 10^{+27}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x + y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -300000000000:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-114}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -300000000000.0)
   (- z)
   (if (<= y -1.3e-114) y (if (<= y 3.5e-15) x (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -300000000000.0) {
		tmp = -z;
	} else if (y <= -1.3e-114) {
		tmp = y;
	} else if (y <= 3.5e-15) {
		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 <= (-300000000000.0d0)) then
        tmp = -z
    else if (y <= (-1.3d-114)) then
        tmp = y
    else if (y <= 3.5d-15) 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 <= -300000000000.0) {
		tmp = -z;
	} else if (y <= -1.3e-114) {
		tmp = y;
	} else if (y <= 3.5e-15) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -300000000000.0:
		tmp = -z
	elif y <= -1.3e-114:
		tmp = y
	elif y <= 3.5e-15:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -300000000000.0)
		tmp = Float64(-z);
	elseif (y <= -1.3e-114)
		tmp = y;
	elseif (y <= 3.5e-15)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -300000000000.0)
		tmp = -z;
	elseif (y <= -1.3e-114)
		tmp = y;
	elseif (y <= 3.5e-15)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -300000000000.0], (-z), If[LessEqual[y, -1.3e-114], y, If[LessEqual[y, 3.5e-15], x, (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -3e11 or 3.5000000000000001e-15 < y

   1. Initial program 73.7%

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

   3. Taylor expanded in y around inf 61.0%

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

      1. mul-1-neg 61.0%

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

   5. Simplified 61.0%

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

   if -3e11 < y < -1.30000000000000007e-114

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 66.7%

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

   4. Taylor expanded in y around 0 48.8%

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

   if -1.30000000000000007e-114 < y < 3.5000000000000001e-15

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 62.6%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -300000000000:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-114}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.1 \cdot 10^{-66} \lor \neg \left(y \leq 6.4 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{z}{\frac{z}{y} + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9.1e-66) (not (<= y 6.4e-20)))
   (/ z (+ (/ z y) -1.0))
   (/ x (- 1.0 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.1e-66) || !(y <= 6.4e-20)) {
		tmp = z / ((z / y) + -1.0);
	} 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 <= (-9.1d-66)) .or. (.not. (y <= 6.4d-20))) then
        tmp = z / ((z / y) + (-1.0d0))
    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 <= -9.1e-66) || !(y <= 6.4e-20)) {
		tmp = z / ((z / y) + -1.0);
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9.1e-66) or not (y <= 6.4e-20):
		tmp = z / ((z / y) + -1.0)
	else:
		tmp = x / (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9.1e-66) || !(y <= 6.4e-20))
		tmp = Float64(z / Float64(Float64(z / y) + -1.0));
	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 <= -9.1e-66) || ~((y <= 6.4e-20)))
		tmp = z / ((z / y) + -1.0);
	else
		tmp = x / (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9.1e-66], N[Not[LessEqual[y, 6.4e-20]], $MachinePrecision]], N[(z / N[(N[(z / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.1000000000000001e-66 or 6.39999999999999941e-20 < y

   1. Initial program 77.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 77.2%

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

      2. inv-pow 77.2%

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

   4. Applied egg-rr 77.2%

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

   5. Taylor expanded in z around 0 99.0%

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

      1. +-commutative 99.0%

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

      2. mul-1-neg 99.0%

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

      3. unsub-neg 99.0%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in x around 0 77.6%

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

   if -9.1000000000000001e-66 < y < 6.39999999999999941e-20

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 77.0%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.1 \cdot 10^{-66} \lor \neg \left(y \leq 6.4 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{z}{\frac{z}{y} + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+55} \lor \neg \left(y \leq 9.2 \cdot 10^{+97}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.6e+55) (not (<= y 9.2e+97))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.6e+55) || !(y <= 9.2e+97)) {
		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 <= (-7.6d+55)) .or. (.not. (y <= 9.2d+97))) 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 <= -7.6e+55) || !(y <= 9.2e+97)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.6e+55) or not (y <= 9.2e+97):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.6e+55) || !(y <= 9.2e+97))
		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 <= -7.6e+55) || ~((y <= 9.2e+97)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.6e+55], N[Not[LessEqual[y, 9.2e+97]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5999999999999999e55 or 9.20000000000000022e97 < y

   1. Initial program 69.9%

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

   3. Taylor expanded in y around inf 69.0%

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

      1. mul-1-neg 69.0%

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

   5. Simplified 69.0%

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

   if -7.5999999999999999e55 < y < 9.20000000000000022e97

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf 68.6%

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

      1. +-commutative 68.6%

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

   5. Simplified 68.6%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+55} \lor \neg \left(y \leq 9.2 \cdot 10^{+97}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 38.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 105:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5e-169) x (if (<= x 105.0) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5e-169) {
		tmp = x;
	} else if (x <= 105.0) {
		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 <= (-5.5d-169)) then
        tmp = x
    else if (x <= 105.0d0) 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 <= -5.5e-169) {
		tmp = x;
	} else if (x <= 105.0) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5e-169:
		tmp = x
	elif x <= 105.0:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5e-169)
		tmp = x;
	elseif (x <= 105.0)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5e-169)
		tmp = x;
	elseif (x <= 105.0)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5e-169], x, If[LessEqual[x, 105.0], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.4999999999999994e-169 or 105 < x

   1. Initial program 87.1%

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

   3. Taylor expanded in y around 0 44.5%

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

   if -5.4999999999999994e-169 < x < 105

   1. Initial program 87.2%

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

   3. Taylor expanded in x around 0 75.1%

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

   4. Taylor expanded in y around 0 42.4%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 105:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.1% 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 87.1%

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

3. Taylor expanded in y around 0 31.7%

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

4. Final simplification 31.7%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 93.9% 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 2024075 
(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))))