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

Percentage Accurate: 88.8% → 99.8%

Time: 6.7s

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: 88.8% 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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-304} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-304) (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 <= -2e-304) || !(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 <= (-2d-304)) .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 <= -2e-304) || !(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 <= -2e-304) 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 <= -2e-304) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(z * Float64(x + y)) / 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 <= -2e-304) || ~((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, -2e-304], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] / (-y)), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -1.99999999999999994e-304 or -0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.9%

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

   if -1.99999999999999994e-304 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 5.8%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. associate-*r/ 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*r* 99.9%

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

      4. neg-mul-1 99.9%

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

      5. distribute-neg-in 99.9%

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

      6. unsub-neg 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-304} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := z \cdot \frac{\left(-x\right) - y}{y}\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-82}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-129}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-7}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (* z (/ (- (- x) y) y))))
   (if (<= y -5.4e+166)
     t_1
     (if (<= y -1.6e-82)
       (/ y t_0)
       (if (<= y 1.42e-129)
         (/ x t_0)
         (if (<= y 1.4e-7) (* (+ x y) (+ 1.0 (/ y z))) t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = z * ((-x - y) / y);
	double tmp;
	if (y <= -5.4e+166) {
		tmp = t_1;
	} else if (y <= -1.6e-82) {
		tmp = y / t_0;
	} else if (y <= 1.42e-129) {
		tmp = x / t_0;
	} else if (y <= 1.4e-7) {
		tmp = (x + y) * (1.0 + (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = z * ((-x - y) / y)
    if (y <= (-5.4d+166)) then
        tmp = t_1
    else if (y <= (-1.6d-82)) then
        tmp = y / t_0
    else if (y <= 1.42d-129) then
        tmp = x / t_0
    else if (y <= 1.4d-7) then
        tmp = (x + y) * (1.0d0 + (y / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = z * ((-x - y) / y);
	double tmp;
	if (y <= -5.4e+166) {
		tmp = t_1;
	} else if (y <= -1.6e-82) {
		tmp = y / t_0;
	} else if (y <= 1.42e-129) {
		tmp = x / t_0;
	} else if (y <= 1.4e-7) {
		tmp = (x + y) * (1.0 + (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = z * ((-x - y) / y)
	tmp = 0
	if y <= -5.4e+166:
		tmp = t_1
	elif y <= -1.6e-82:
		tmp = y / t_0
	elif y <= 1.42e-129:
		tmp = x / t_0
	elif y <= 1.4e-7:
		tmp = (x + y) * (1.0 + (y / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(z * Float64(Float64(Float64(-x) - y) / y))
	tmp = 0.0
	if (y <= -5.4e+166)
		tmp = t_1;
	elseif (y <= -1.6e-82)
		tmp = Float64(y / t_0);
	elseif (y <= 1.42e-129)
		tmp = Float64(x / t_0);
	elseif (y <= 1.4e-7)
		tmp = Float64(Float64(x + y) * Float64(1.0 + Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = z * ((-x - y) / y);
	tmp = 0.0;
	if (y <= -5.4e+166)
		tmp = t_1;
	elseif (y <= -1.6e-82)
		tmp = y / t_0;
	elseif (y <= 1.42e-129)
		tmp = x / t_0;
	elseif (y <= 1.4e-7)
		tmp = (x + y) * (1.0 + (y / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(N[((-x) - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.4e+166], t$95$1, If[LessEqual[y, -1.6e-82], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, 1.42e-129], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 1.4e-7], N[(N[(x + y), $MachinePrecision] * N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.40000000000000023e166 or 1.4000000000000001e-7 < y

   1. Initial program 75.5%

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

   3. Taylor expanded in z around 0 65.6%

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

      1. mul-1-neg 65.6%

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

      2. associate-/l* 83.1%

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

      3. distribute-rgt-neg-in 83.1%

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

      4. distribute-neg-frac2 83.1%

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

      5. +-commutative 83.1%

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

   5. Simplified 83.1%

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

   if -5.40000000000000023e166 < y < -1.6000000000000001e-82

   1. Initial program 98.2%

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

   3. Taylor expanded in x around 0 68.5%

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

   if -1.6000000000000001e-82 < y < 1.42e-129

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 87.9%

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

   if 1.42e-129 < y < 1.4000000000000001e-7

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 69.9%

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

      1. associate-+r+ 69.9%

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

      2. *-rgt-identity 69.9%

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

      3. *-commutative 69.9%

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

      4. associate-/l* 69.9%

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

      5. distribute-lft-in 69.9%

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

      6. +-commutative 69.9%

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

   5. Simplified 69.9%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+166}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-82}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-129}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-7}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := z \cdot \frac{\left(-x\right) - y}{y}\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+165}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-78}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-129}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-7}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (* z (/ (- (- x) y) y))))
   (if (<= y -4.8e+165)
     t_1
     (if (<= y -1.45e-78)
       (/ y t_0)
       (if (<= y 5.4e-129) (/ x t_0) (if (<= y 9.2e-7) (+ x y) t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = z * ((-x - y) / y);
	double tmp;
	if (y <= -4.8e+165) {
		tmp = t_1;
	} else if (y <= -1.45e-78) {
		tmp = y / t_0;
	} else if (y <= 5.4e-129) {
		tmp = x / t_0;
	} else if (y <= 9.2e-7) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = z * ((-x - y) / y)
    if (y <= (-4.8d+165)) then
        tmp = t_1
    else if (y <= (-1.45d-78)) then
        tmp = y / t_0
    else if (y <= 5.4d-129) then
        tmp = x / t_0
    else if (y <= 9.2d-7) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = z * ((-x - y) / y);
	double tmp;
	if (y <= -4.8e+165) {
		tmp = t_1;
	} else if (y <= -1.45e-78) {
		tmp = y / t_0;
	} else if (y <= 5.4e-129) {
		tmp = x / t_0;
	} else if (y <= 9.2e-7) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = z * ((-x - y) / y)
	tmp = 0
	if y <= -4.8e+165:
		tmp = t_1
	elif y <= -1.45e-78:
		tmp = y / t_0
	elif y <= 5.4e-129:
		tmp = x / t_0
	elif y <= 9.2e-7:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(z * Float64(Float64(Float64(-x) - y) / y))
	tmp = 0.0
	if (y <= -4.8e+165)
		tmp = t_1;
	elseif (y <= -1.45e-78)
		tmp = Float64(y / t_0);
	elseif (y <= 5.4e-129)
		tmp = Float64(x / t_0);
	elseif (y <= 9.2e-7)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = z * ((-x - y) / y);
	tmp = 0.0;
	if (y <= -4.8e+165)
		tmp = t_1;
	elseif (y <= -1.45e-78)
		tmp = y / t_0;
	elseif (y <= 5.4e-129)
		tmp = x / t_0;
	elseif (y <= 9.2e-7)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(N[((-x) - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+165], t$95$1, If[LessEqual[y, -1.45e-78], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, 5.4e-129], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 9.2e-7], N[(x + y), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.80000000000000001e165 or 9.1999999999999998e-7 < y

   1. Initial program 75.5%

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

   3. Taylor expanded in z around 0 65.6%

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

      1. mul-1-neg 65.6%

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

      2. associate-/l* 83.1%

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

      3. distribute-rgt-neg-in 83.1%

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

      4. distribute-neg-frac2 83.1%

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

      5. +-commutative 83.1%

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

   5. Simplified 83.1%

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

   if -4.80000000000000001e165 < y < -1.45e-78

   1. Initial program 98.2%

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

   3. Taylor expanded in x around 0 68.5%

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

   if -1.45e-78 < y < 5.39999999999999998e-129

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 87.9%

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

   if 5.39999999999999998e-129 < y < 9.1999999999999998e-7

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 69.0%

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

      1. +-commutative 69.0%

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

   5. Simplified 69.0%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+165}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-78}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-129}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-7}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{y}{t\_0}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+170}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+168}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ y t_0)))
   (if (<= y -3.5e+170)
     (- z)
     (if (<= y -1.5e-78)
       t_1
       (if (<= y 5e-26) (/ x t_0) (if (<= y 8.5e+168) t_1 (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = y / t_0;
	double tmp;
	if (y <= -3.5e+170) {
		tmp = -z;
	} else if (y <= -1.5e-78) {
		tmp = t_1;
	} else if (y <= 5e-26) {
		tmp = x / t_0;
	} else if (y <= 8.5e+168) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = y / t_0
    if (y <= (-3.5d+170)) then
        tmp = -z
    else if (y <= (-1.5d-78)) then
        tmp = t_1
    else if (y <= 5d-26) then
        tmp = x / t_0
    else if (y <= 8.5d+168) then
        tmp = t_1
    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 t_1 = y / t_0;
	double tmp;
	if (y <= -3.5e+170) {
		tmp = -z;
	} else if (y <= -1.5e-78) {
		tmp = t_1;
	} else if (y <= 5e-26) {
		tmp = x / t_0;
	} else if (y <= 8.5e+168) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = y / t_0
	tmp = 0
	if y <= -3.5e+170:
		tmp = -z
	elif y <= -1.5e-78:
		tmp = t_1
	elif y <= 5e-26:
		tmp = x / t_0
	elif y <= 8.5e+168:
		tmp = t_1
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(y / t_0)
	tmp = 0.0
	if (y <= -3.5e+170)
		tmp = Float64(-z);
	elseif (y <= -1.5e-78)
		tmp = t_1;
	elseif (y <= 5e-26)
		tmp = Float64(x / t_0);
	elseif (y <= 8.5e+168)
		tmp = t_1;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = y / t_0;
	tmp = 0.0;
	if (y <= -3.5e+170)
		tmp = -z;
	elseif (y <= -1.5e-78)
		tmp = t_1;
	elseif (y <= 5e-26)
		tmp = x / t_0;
	elseif (y <= 8.5e+168)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(y / t$95$0), $MachinePrecision]}, If[LessEqual[y, -3.5e+170], (-z), If[LessEqual[y, -1.5e-78], t$95$1, If[LessEqual[y, 5e-26], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 8.5e+168], t$95$1, (-z)]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.50000000000000005e170 or 8.50000000000000069e168 < y

   1. Initial program 64.8%

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

   3. Taylor expanded in y around inf 78.0%

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

      1. neg-mul-1 78.0%

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

   5. Simplified 78.0%

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

   if -3.50000000000000005e170 < y < -1.49999999999999994e-78 or 5.00000000000000019e-26 < y < 8.50000000000000069e168

   1. Initial program 93.7%

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

   3. Taylor expanded in x around 0 68.1%

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

   if -1.49999999999999994e-78 < y < 5.00000000000000019e-26

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 80.8%

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

Alternative 5: 66.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.9 \cdot 10^{+149}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-71}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-129}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-19}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.9e+149)
   (- z)
   (if (<= y -1.35e-71)
     (+ x y)
     (if (<= y 1.12e-129)
       (/ x (- 1.0 (/ y z)))
       (if (<= y 8.2e-19) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.9e+149) {
		tmp = -z;
	} else if (y <= -1.35e-71) {
		tmp = x + y;
	} else if (y <= 1.12e-129) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 8.2e-19) {
		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 <= (-7.9d+149)) then
        tmp = -z
    else if (y <= (-1.35d-71)) then
        tmp = x + y
    else if (y <= 1.12d-129) then
        tmp = x / (1.0d0 - (y / z))
    else if (y <= 8.2d-19) 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 <= -7.9e+149) {
		tmp = -z;
	} else if (y <= -1.35e-71) {
		tmp = x + y;
	} else if (y <= 1.12e-129) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 8.2e-19) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.9e+149:
		tmp = -z
	elif y <= -1.35e-71:
		tmp = x + y
	elif y <= 1.12e-129:
		tmp = x / (1.0 - (y / z))
	elif y <= 8.2e-19:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.9e+149)
		tmp = Float64(-z);
	elseif (y <= -1.35e-71)
		tmp = Float64(x + y);
	elseif (y <= 1.12e-129)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (y <= 8.2e-19)
		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 <= -7.9e+149)
		tmp = -z;
	elseif (y <= -1.35e-71)
		tmp = x + y;
	elseif (y <= 1.12e-129)
		tmp = x / (1.0 - (y / z));
	elseif (y <= 8.2e-19)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.9e+149], (-z), If[LessEqual[y, -1.35e-71], N[(x + y), $MachinePrecision], If[LessEqual[y, 1.12e-129], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e-19], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.89999999999999965e149 or 8.1999999999999997e-19 < y

   1. Initial program 76.6%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 -7.89999999999999965e149 < y < -1.3500000000000001e-71 or 1.12000000000000006e-129 < y < 8.1999999999999997e-19

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf 65.3%

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

      1. +-commutative 65.3%

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

   5. Simplified 65.3%

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

   if -1.3500000000000001e-71 < y < 1.12000000000000006e-129

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 85.1%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.9 \cdot 10^{+149}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-71}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-129}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-19}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+108}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-78}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e+108) (- z) (if (<= y -3.6e-78) y (if (<= y 2.8e-56) x (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+108) {
		tmp = -z;
	} else if (y <= -3.6e-78) {
		tmp = y;
	} else if (y <= 2.8e-56) {
		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 <= (-2d+108)) then
        tmp = -z
    else if (y <= (-3.6d-78)) then
        tmp = y
    else if (y <= 2.8d-56) 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 <= -2e+108) {
		tmp = -z;
	} else if (y <= -3.6e-78) {
		tmp = y;
	} else if (y <= 2.8e-56) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e+108:
		tmp = -z
	elif y <= -3.6e-78:
		tmp = y
	elif y <= 2.8e-56:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e+108)
		tmp = Float64(-z);
	elseif (y <= -3.6e-78)
		tmp = y;
	elseif (y <= 2.8e-56)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2e+108)
		tmp = -z;
	elseif (y <= -3.6e-78)
		tmp = y;
	elseif (y <= 2.8e-56)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e+108], (-z), If[LessEqual[y, -3.6e-78], y, If[LessEqual[y, 2.8e-56], x, (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0000000000000001e108 or 2.79999999999999993e-56 < y

   1. Initial program 79.2%

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

   3. Taylor expanded in y around inf 62.3%

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

      1. neg-mul-1 62.3%

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

   5. Simplified 62.3%

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

   if -2.0000000000000001e108 < y < -3.6000000000000002e-78

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 59.3%

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

      1. +-commutative 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in y around inf 50.1%

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

   if -3.6000000000000002e-78 < y < 2.79999999999999993e-56

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 64.7%

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

Alternative 7: 66.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+143} \lor \neg \left(y \leq 5.8 \cdot 10^{-18}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.6e+143) (not (<= y 5.8e-18))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.6e+143) || !(y <= 5.8e-18)) {
		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 <= (-4.6d+143)) .or. (.not. (y <= 5.8d-18))) 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 <= -4.6e+143) || !(y <= 5.8e-18)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.6e+143) or not (y <= 5.8e-18):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.6e+143) || !(y <= 5.8e-18))
		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 <= -4.6e+143) || ~((y <= 5.8e-18)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.6e+143], N[Not[LessEqual[y, 5.8e-18]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5999999999999999e143 or 5.8e-18 < y

   1. Initial program 76.6%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 -4.5999999999999999e143 < y < 5.8e-18

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 70.1%

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

      1. +-commutative 70.1%

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

   5. Simplified 70.1%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+143} \lor \neg \left(y \leq 5.8 \cdot 10^{-18}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-12}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.45e-5) x (if (<= x 2.2e-12) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.45e-5) {
		tmp = x;
	} else if (x <= 2.2e-12) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2.45d-5)) then
        tmp = x
    else if (x <= 2.2d-12) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.45e-5) {
		tmp = x;
	} else if (x <= 2.2e-12) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.45e-5:
		tmp = x
	elif x <= 2.2e-12:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.45e-5)
		tmp = x;
	elseif (x <= 2.2e-12)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.45e-5)
		tmp = x;
	elseif (x <= 2.2e-12)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.45e-5], x, If[LessEqual[x, 2.2e-12], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.45e-5 or 2.19999999999999992e-12 < x

   1. Initial program 91.5%

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

   3. Taylor expanded in y around 0 45.7%

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

   if -2.45e-5 < x < 2.19999999999999992e-12

   1. Initial program 90.7%

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

   3. Taylor expanded in z around inf 54.9%

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

      1. +-commutative 54.9%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in y around inf 40.2%

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

Alternative 9: 34.6% 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 91.1%

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

3. Taylor expanded in y around 0 31.6%

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

Developer Target 1: 94.0% 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 2024163 
(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))))