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

Percentage Accurate: 88.3% → 99.6%

Time: 6.5s

Alternatives: 9

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: 88.3% 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: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-268}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{z - y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (<= t_0 -5e-268)
     t_0
     (if (<= t_0 0.0) (* z (/ (- (- x) y) y)) (/ (+ x y) (/ (- z y) z))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if (t_0 <= -5e-268) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = z * ((-x - y) / y);
	} else {
		tmp = (x + y) / ((z - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if (t_0 <= (-5d-268)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = z * ((-x - y) / y)
    else
        tmp = (x + y) / ((z - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if (t_0 <= -5e-268) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = z * ((-x - y) / y);
	} else {
		tmp = (x + y) / ((z - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if t_0 <= -5e-268:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = z * ((-x - y) / y)
	else:
		tmp = (x + y) / ((z - y) / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (t_0 <= -5e-268)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(z * Float64(Float64(Float64(-x) - y) / y));
	else
		tmp = Float64(Float64(x + y) / Float64(Float64(z - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if (t_0 <= -5e-268)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = z * ((-x - y) / y);
	else
		tmp = (x + y) / ((z - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e-268], t$95$0, If[LessEqual[t$95$0, 0.0], N[(z * N[(N[((-x) - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -4.9999999999999999e-268

   1. Initial program 99.8%

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

   if -4.9999999999999999e-268 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 5.4%

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

   3. Taylor expanded in z around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. associate-/l* 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. distribute-neg-frac2 100.0%

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

      5. +-commutative 100.0%

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

   5. Simplified 100.0%

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

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

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-268}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;\frac{x + y}{1 - \frac{y}{z}} \leq 0:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{z - y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-268} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -5e-268) (not (<= t_0 0.0))) t_0 (* z (/ (- (- x) y) y)))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -5e-268) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * ((-x - y) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-5d-268)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = z * ((-x - y) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -5e-268) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * ((-x - y) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -5e-268) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = z * ((-x - y) / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -5e-268) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(Float64(Float64(-x) - y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -5e-268) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = z * ((-x - y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -5e-268], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(z * N[(N[((-x) - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -4.9999999999999999e-268 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 -4.9999999999999999e-268 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 5.4%

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

   3. Taylor expanded in z around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. associate-/l* 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. distribute-neg-frac2 100.0%

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

      5. +-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-268} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+41}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.1e+27)
   (* z (- -1.0 (/ x y)))
   (if (<= y 2.7e+41) (* (+ x y) (+ 1.0 (/ y z))) (* z (/ (- (- x) y) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.1e+27) {
		tmp = z * (-1.0 - (x / y));
	} else if (y <= 2.7e+41) {
		tmp = (x + y) * (1.0 + (y / z));
	} 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 (y <= (-3.1d+27)) then
        tmp = z * ((-1.0d0) - (x / y))
    else if (y <= 2.7d+41) then
        tmp = (x + y) * (1.0d0 + (y / z))
    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 (y <= -3.1e+27) {
		tmp = z * (-1.0 - (x / y));
	} else if (y <= 2.7e+41) {
		tmp = (x + y) * (1.0 + (y / z));
	} else {
		tmp = z * ((-x - y) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.1e+27:
		tmp = z * (-1.0 - (x / y))
	elif y <= 2.7e+41:
		tmp = (x + y) * (1.0 + (y / z))
	else:
		tmp = z * ((-x - y) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.1e+27)
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	elseif (y <= 2.7e+41)
		tmp = Float64(Float64(x + y) * Float64(1.0 + Float64(y / z)));
	else
		tmp = Float64(z * Float64(Float64(Float64(-x) - y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.1e+27)
		tmp = z * (-1.0 - (x / y));
	elseif (y <= 2.7e+41)
		tmp = (x + y) * (1.0 + (y / z));
	else
		tmp = z * ((-x - y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.1e+27], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+41], N[(N[(x + y), $MachinePrecision] * N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[((-x) - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.09999999999999996e27

   1. Initial program 73.8%

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

   3. Taylor expanded in y around inf 57.5%

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

      1. neg-mul-1 57.5%

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

      2. distribute-neg-frac 57.5%

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

   5. Simplified 57.5%

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

   6. Taylor expanded in x around 0 78.0%

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

      1. distribute-lft-out 78.0%

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

      2. mul-1-neg 78.0%

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

      3. associate-*l/ 83.6%

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

      4. *-lft-identity 83.6%

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

      5. distribute-rgt-in 83.6%

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

      6. distribute-rgt-neg-in 83.6%

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

      7. distribute-neg-in 83.6%

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

      8. metadata-eval 83.6%

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

      9. unsub-neg 83.6%

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

   8. Simplified 83.6%

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

   if -3.09999999999999996e27 < y < 2.7e41

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 81.9%

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

      1. associate-+r+ 81.9%

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

      2. *-rgt-identity 81.9%

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

      3. *-commutative 81.9%

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

      4. associate-/l* 82.6%

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

      5. distribute-lft-in 82.6%

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

      6. +-commutative 82.6%

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

   5. Simplified 82.6%

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

   if 2.7e41 < y

   1. Initial program 74.8%

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

   3. Taylor expanded in z around 0 65.9%

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

      1. mul-1-neg 65.9%

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

      2. associate-/l* 80.8%

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

      3. distribute-rgt-neg-in 80.8%

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

      4. distribute-neg-frac2 80.8%

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

      5. +-commutative 80.8%

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

   5. Simplified 80.8%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+41}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+41}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.25e-19)
   (* z (- -1.0 (/ x y)))
   (if (<= y 5.2e+41) (+ x y) (* z (/ (- (- x) y) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.25e-19) {
		tmp = z * (-1.0 - (x / y));
	} else if (y <= 5.2e+41) {
		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 (y <= (-1.25d-19)) then
        tmp = z * ((-1.0d0) - (x / y))
    else if (y <= 5.2d+41) 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 (y <= -1.25e-19) {
		tmp = z * (-1.0 - (x / y));
	} else if (y <= 5.2e+41) {
		tmp = x + y;
	} else {
		tmp = z * ((-x - y) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.25e-19:
		tmp = z * (-1.0 - (x / y))
	elif y <= 5.2e+41:
		tmp = x + y
	else:
		tmp = z * ((-x - y) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.25e-19)
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	elseif (y <= 5.2e+41)
		tmp = Float64(x + y);
	else
		tmp = Float64(z * Float64(Float64(Float64(-x) - y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.25e-19)
		tmp = z * (-1.0 - (x / y));
	elseif (y <= 5.2e+41)
		tmp = x + y;
	else
		tmp = z * ((-x - y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.25e-19], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+41], N[(x + y), $MachinePrecision], N[(z * N[(N[((-x) - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2500000000000001e-19

   1. Initial program 76.9%

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

   3. Taylor expanded in y around inf 56.0%

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

      1. neg-mul-1 56.0%

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

      2. distribute-neg-frac 56.0%

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

   5. Simplified 56.0%

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

   6. Taylor expanded in x around 0 74.1%

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

      1. distribute-lft-out 74.1%

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

      2. mul-1-neg 74.1%

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

      3. associate-*l/ 79.0%

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

      4. *-lft-identity 79.0%

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

      5. distribute-rgt-in 79.0%

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

      6. distribute-rgt-neg-in 79.0%

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

      7. distribute-neg-in 79.0%

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

      8. metadata-eval 79.0%

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

      9. unsub-neg 79.0%

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

   8. Simplified 79.0%

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

   if -1.2500000000000001e-19 < y < 5.2000000000000001e41

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 84.2%

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

      1. +-commutative 84.2%

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

   5. Simplified 84.2%

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

   if 5.2000000000000001e41 < y

   1. Initial program 74.8%

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

   3. Taylor expanded in z around 0 65.9%

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

      1. mul-1-neg 65.9%

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

      2. associate-/l* 80.8%

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

      3. distribute-rgt-neg-in 80.8%

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

      4. distribute-neg-frac2 80.8%

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

      5. +-commutative 80.8%

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

   5. Simplified 80.8%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+41}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-20} \lor \neg \left(y \leq 1.45 \cdot 10^{+45}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.5e-20) (not (<= y 1.45e+45)))
   (* z (- -1.0 (/ x y)))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.5e-20) || !(y <= 1.45e+45)) {
		tmp = z * (-1.0 - (x / 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 ((y <= (-3.5d-20)) .or. (.not. (y <= 1.45d+45))) then
        tmp = z * ((-1.0d0) - (x / 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 ((y <= -3.5e-20) || !(y <= 1.45e+45)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.5e-20) or not (y <= 1.45e+45):
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.5e-20) || !(y <= 1.45e+45))
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.5e-20) || ~((y <= 1.45e+45)))
		tmp = z * (-1.0 - (x / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.5e-20], N[Not[LessEqual[y, 1.45e+45]], $MachinePrecision]], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.50000000000000003e-20 or 1.4499999999999999e45 < y

   1. Initial program 75.9%

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

   3. Taylor expanded in y around inf 55.9%

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

      1. neg-mul-1 55.9%

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

      2. distribute-neg-frac 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in x around 0 74.9%

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

      1. distribute-lft-out 74.9%

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

      2. mul-1-neg 74.9%

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

      3. associate-*l/ 79.9%

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

      4. *-lft-identity 79.9%

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

      5. distribute-rgt-in 79.9%

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

      6. distribute-rgt-neg-in 79.9%

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

      7. distribute-neg-in 79.9%

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

      8. metadata-eval 79.9%

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

      9. unsub-neg 79.9%

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

   8. Simplified 79.9%

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

   if -3.50000000000000003e-20 < y < 1.4499999999999999e45

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 84.2%

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

      1. +-commutative 84.2%

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

   5. Simplified 84.2%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-20} \lor \neg \left(y \leq 1.45 \cdot 10^{+45}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+59} \lor \neg \left(y \leq 7 \cdot 10^{+62}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.6e+59) (not (<= y 7e+62))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.6e+59) || !(y <= 7e+62)) {
		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 <= (-1.6d+59)) .or. (.not. (y <= 7d+62))) 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 <= -1.6e+59) || !(y <= 7e+62)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.6e+59) or not (y <= 7e+62):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.6e+59) || !(y <= 7e+62))
		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 <= -1.6e+59) || ~((y <= 7e+62)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.6e+59], N[Not[LessEqual[y, 7e+62]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.59999999999999991e59 or 6.99999999999999967e62 < y

   1. Initial program 72.3%

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

   3. Taylor expanded in y around inf 69.1%

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

      1. neg-mul-1 69.1%

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

   5. Simplified 69.1%

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

   if -1.59999999999999991e59 < y < 6.99999999999999967e62

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 80.1%

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

      1. +-commutative 80.1%

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

   5. Simplified 80.1%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+59} \lor \neg \left(y \leq 7 \cdot 10^{+62}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-20} \lor \neg \left(y \leq 3.5 \cdot 10^{+35}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.45e-20) (not (<= y 3.5e+35))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.45e-20) || !(y <= 3.5e+35)) {
		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 <= (-2.45d-20)) .or. (.not. (y <= 3.5d+35))) 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 <= -2.45e-20) || !(y <= 3.5e+35)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.45e-20) or not (y <= 3.5e+35):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.45e-20) || !(y <= 3.5e+35))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.45e-20) || ~((y <= 3.5e+35)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.45e-20], N[Not[LessEqual[y, 3.5e+35]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -2.4500000000000001e-20 or 3.5000000000000001e35 < y

   1. Initial program 76.3%

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

   3. Taylor expanded in y around inf 63.8%

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

      1. neg-mul-1 63.8%

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

   5. Simplified 63.8%

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

   if -2.4500000000000001e-20 < y < 3.5000000000000001e35

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 66.3%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-20} \lor \neg \left(y \leq 3.5 \cdot 10^{+35}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 41.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-169}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6e-126) x (if (<= x 4.2e-169) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6e-126) {
		tmp = x;
	} else if (x <= 4.2e-169) {
		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 <= (-6d-126)) then
        tmp = x
    else if (x <= 4.2d-169) 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 <= -6e-126) {
		tmp = x;
	} else if (x <= 4.2e-169) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6e-126:
		tmp = x
	elif x <= 4.2e-169:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6e-126)
		tmp = x;
	elseif (x <= 4.2e-169)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6e-126)
		tmp = x;
	elseif (x <= 4.2e-169)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6e-126], x, If[LessEqual[x, 4.2e-169], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.0000000000000003e-126 or 4.2000000000000001e-169 < x

   1. Initial program 88.5%

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

   3. Taylor expanded in y around 0 47.4%

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

   if -6.0000000000000003e-126 < x < 4.2000000000000001e-169

   1. Initial program 91.5%

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

   3. Taylor expanded in z around inf 56.3%

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

      1. +-commutative 56.3%

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

   5. Simplified 56.3%

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

   6. Taylor expanded in y around inf 43.4%

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

Alternative 9: 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 89.2%

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

3. Taylor expanded in y around 0 40.5%

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

Developer Target 1: 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 2024130 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -3742931076268985600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* (/ (+ y x) (- y)) z) (if (< y 3553466245608673400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ x y) (- 1 (/ y z))) (* (/ (+ y x) (- y)) z))))

  (/ (+ x y) (- 1.0 (/ y z))))