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

Percentage Accurate: 88.5% → 99.4%

Time: 6.8s

Alternatives: 12

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-247}:\\ \;\;\;\;\frac{x + y}{\frac{z - y}{z}}\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (<= t_0 -5e-247)
     (/ (+ x y) (/ (- z y) z))
     (if (<= t_0 0.0) (* z (/ (- (- x) y) y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if (t_0 <= -5e-247) {
		tmp = (x + y) / ((z - y) / z);
	} else if (t_0 <= 0.0) {
		tmp = z * ((-x - y) / y);
	} 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 = (x + y) / (1.0d0 - (y / z))
    if (t_0 <= (-5d-247)) then
        tmp = (x + y) / ((z - y) / z)
    else if (t_0 <= 0.0d0) then
        tmp = z * ((-x - y) / y)
    else
        tmp = t_0
    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-247) {
		tmp = (x + y) / ((z - y) / z);
	} else if (t_0 <= 0.0) {
		tmp = z * ((-x - y) / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if t_0 <= -5e-247:
		tmp = (x + y) / ((z - y) / z)
	elif t_0 <= 0.0:
		tmp = z * ((-x - y) / y)
	else:
		tmp = t_0
	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-247)
		tmp = Float64(Float64(x + y) / Float64(Float64(z - y) / z));
	elseif (t_0 <= 0.0)
		tmp = Float64(z * Float64(Float64(Float64(-x) - y) / y));
	else
		tmp = t_0;
	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-247)
		tmp = (x + y) / ((z - y) / z);
	elseif (t_0 <= 0.0)
		tmp = z * ((-x - y) / y);
	else
		tmp = t_0;
	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-247], N[(N[(x + y), $MachinePrecision] / N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(z * N[(N[((-x) - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -4.99999999999999978e-247

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 99.8%

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

   if -4.99999999999999978e-247 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 0.0

   1. Initial program 12.1%

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

   3. Taylor expanded in z around 0 94.0%

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

      1. mul-1-neg 94.0%

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

      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. Recombined 3 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-247}:\\ \;\;\;\;\frac{x + y}{\frac{z - y}{z}}\\ \mathbf{elif}\;\frac{x + y}{1 - \frac{y}{z}} \leq 0:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-247} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -5e-247) (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-247) || !(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-247)) .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-247) || !(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-247) 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-247) || !(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-247) || ~((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-247], 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))) < -4.99999999999999978e-247 or 0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.8%

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

   if -4.99999999999999978e-247 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 0.0

   1. Initial program 12.1%

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

   3. Taylor expanded in z around 0 94.0%

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

      1. mul-1-neg 94.0%

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

      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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-247} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-25} \lor \neg \left(z \leq 4.5 \cdot 10^{-14}\right):\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(\left(-x\right) - y\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.5e-25) (not (<= z 4.5e-14)))
   (* (+ x y) (+ 1.0 (/ y z)))
   (/ (* z (- (- x) y)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.5e-25) || !(z <= 4.5e-14)) {
		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 ((z <= (-7.5d-25)) .or. (.not. (z <= 4.5d-14))) 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 ((z <= -7.5e-25) || !(z <= 4.5e-14)) {
		tmp = (x + y) * (1.0 + (y / z));
	} else {
		tmp = (z * (-x - y)) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.5e-25) or not (z <= 4.5e-14):
		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 ((z <= -7.5e-25) || !(z <= 4.5e-14))
		tmp = Float64(Float64(x + y) * Float64(1.0 + Float64(y / z)));
	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 <= -7.5e-25) || ~((z <= 4.5e-14)))
		tmp = (x + y) * (1.0 + (y / z));
	else
		tmp = (z * (-x - y)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.5e-25], N[Not[LessEqual[z, 4.5e-14]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] * N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[((-x) - y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999989e-25 or 4.4999999999999998e-14 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 74.0%

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

      1. associate-+r+ 74.0%

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

      2. *-rgt-identity 74.0%

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

      3. *-commutative 74.0%

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

      4. associate-/l* 78.3%

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

      5. distribute-lft-in 78.3%

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

      6. +-commutative 78.3%

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

   5. Simplified 78.3%

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

   if -7.49999999999999989e-25 < z < 4.4999999999999998e-14

   1. Initial program 77.6%

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

   3. Taylor expanded in z around 0 76.8%

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

      1. associate-*r/ 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*r* 76.8%

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

      4. neg-mul-1 76.8%

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

      5. distribute-neg-in 76.8%

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

      6. unsub-neg 76.8%

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

   5. Simplified 76.8%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-25} \lor \neg \left(z \leq 4.5 \cdot 10^{-14}\right):\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(\left(-x\right) - y\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-25} \lor \neg \left(z \leq 2.2 \cdot 10^{-17}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(\left(-x\right) - y\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.8e-25) (not (<= z 2.2e-17)))
   (+ x y)
   (/ (* z (- (- x) y)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.8e-25) || !(z <= 2.2e-17)) {
		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 <= (-5.8d-25)) .or. (.not. (z <= 2.2d-17))) 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 <= -5.8e-25) || !(z <= 2.2e-17)) {
		tmp = x + y;
	} else {
		tmp = (z * (-x - y)) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.8e-25) or not (z <= 2.2e-17):
		tmp = x + y
	else:
		tmp = (z * (-x - y)) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.8e-25) || !(z <= 2.2e-17))
		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 <= -5.8e-25) || ~((z <= 2.2e-17)))
		tmp = x + y;
	else
		tmp = (z * (-x - y)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.8e-25], N[Not[LessEqual[z, 2.2e-17]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(N[(z * N[((-x) - y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8000000000000001e-25 or 2.2e-17 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 78.1%

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

      1. +-commutative 78.1%

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

   5. Simplified 78.1%

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

   if -5.8000000000000001e-25 < z < 2.2e-17

   1. Initial program 77.6%

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

   3. Taylor expanded in z around 0 76.8%

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

      1. associate-*r/ 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*r* 76.8%

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

      4. neg-mul-1 76.8%

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

      5. distribute-neg-in 76.8%

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

      6. unsub-neg 76.8%

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

   5. Simplified 76.8%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-25} \lor \neg \left(z \leq 2.2 \cdot 10^{-17}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(\left(-x\right) - y\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-80} \lor \neg \left(y \leq 2.5 \cdot 10^{-25}\right):\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.5e-80) (not (<= y 2.5e-25)))
   (* z (/ (- (- x) y) y))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e-80) || !(y <= 2.5e-25)) {
		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 ((y <= (-6.5d-80)) .or. (.not. (y <= 2.5d-25))) 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 ((y <= -6.5e-80) || !(y <= 2.5e-25)) {
		tmp = z * ((-x - y) / y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.5e-80) or not (y <= 2.5e-25):
		tmp = z * ((-x - y) / y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.5e-80) || !(y <= 2.5e-25))
		tmp = Float64(z * Float64(Float64(Float64(-x) - y) / y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.5e-80) || ~((y <= 2.5e-25)))
		tmp = z * ((-x - y) / y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.5e-80], N[Not[LessEqual[y, 2.5e-25]], $MachinePrecision]], N[(z * N[(N[((-x) - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.49999999999999984e-80 or 2.49999999999999981e-25 < y

   1. Initial program 80.8%

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

   3. Taylor expanded in z around 0 64.1%

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

      1. mul-1-neg 64.1%

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

      2. associate-/l* 73.4%

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

      3. distribute-rgt-neg-in 73.4%

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

      4. distribute-neg-frac2 73.4%

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

      5. +-commutative 73.4%

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

   5. Simplified 73.4%

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

   if -6.49999999999999984e-80 < y < 2.49999999999999981e-25

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 82.1%

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

      1. +-commutative 82.1%

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

   5. Simplified 82.1%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-80} \lor \neg \left(y \leq 2.5 \cdot 10^{-25}\right):\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{z - y}\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{-63} \lor \neg \left(x \leq 3.5 \cdot 10^{-123}\right):\\ \;\;\;\;x \cdot t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ z (- z y))))
   (if (or (<= x -2.8e-63) (not (<= x 3.5e-123))) (* x t_0) (* y t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z / (z - y);
	double tmp;
	if ((x <= -2.8e-63) || !(x <= 3.5e-123)) {
		tmp = x * t_0;
	} else {
		tmp = y * t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z / (z - y)
    if ((x <= (-2.8d-63)) .or. (.not. (x <= 3.5d-123))) then
        tmp = x * t_0
    else
        tmp = y * t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z / (z - y);
	double tmp;
	if ((x <= -2.8e-63) || !(x <= 3.5e-123)) {
		tmp = x * t_0;
	} else {
		tmp = y * t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z / (z - y)
	tmp = 0
	if (x <= -2.8e-63) or not (x <= 3.5e-123):
		tmp = x * t_0
	else:
		tmp = y * t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z / Float64(z - y))
	tmp = 0.0
	if ((x <= -2.8e-63) || !(x <= 3.5e-123))
		tmp = Float64(x * t_0);
	else
		tmp = Float64(y * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z / (z - y);
	tmp = 0.0;
	if ((x <= -2.8e-63) || ~((x <= 3.5e-123)))
		tmp = x * t_0;
	else
		tmp = y * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -2.8e-63], N[Not[LessEqual[x, 3.5e-123]], $MachinePrecision]], N[(x * t$95$0), $MachinePrecision], N[(y * t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8000000000000002e-63 or 3.4999999999999999e-123 < x

   1. Initial program 89.2%

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

   3. Taylor expanded in x around inf 73.3%

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

      1. div-inv 73.3%

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

      2. *-commutative 73.3%

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

      3. *-inverses 73.3%

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

      4. div-sub 73.3%

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

      5. clear-num 73.4%

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

   5. Applied egg-rr 73.4%

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

   if -2.8000000000000002e-63 < x < 3.4999999999999999e-123

   1. Initial program 88.3%

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

   3. Taylor expanded in z around 0 88.3%

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

   4. Taylor expanded in x around 0 76.8%

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

      1. associate-/l* 76.8%

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

   6. Simplified 76.8%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-63} \lor \neg \left(x \leq 3.5 \cdot 10^{-123}\right):\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{-64} \lor \neg \left(x \leq 4.9 \cdot 10^{-92}\right):\\ \;\;\;\;z \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.22e-64) (not (<= x 4.9e-92)))
   (* z (/ x (- z y)))
   (* y (/ z (- z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.22e-64) || !(x <= 4.9e-92)) {
		tmp = z * (x / (z - y));
	} else {
		tmp = y * (z / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.22d-64)) .or. (.not. (x <= 4.9d-92))) then
        tmp = z * (x / (z - y))
    else
        tmp = y * (z / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.22e-64) || !(x <= 4.9e-92)) {
		tmp = z * (x / (z - y));
	} else {
		tmp = y * (z / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.22e-64) or not (x <= 4.9e-92):
		tmp = z * (x / (z - y))
	else:
		tmp = y * (z / (z - y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.22e-64) || !(x <= 4.9e-92))
		tmp = Float64(z * Float64(x / Float64(z - y)));
	else
		tmp = Float64(y * Float64(z / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.22e-64) || ~((x <= 4.9e-92)))
		tmp = z * (x / (z - y));
	else
		tmp = y * (z / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.22e-64], N[Not[LessEqual[x, 4.9e-92]], $MachinePrecision]], N[(z * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.22000000000000003e-64 or 4.9e-92 < x

   1. Initial program 89.9%

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

   3. Taylor expanded in x around inf 74.5%

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

      1. div-inv 74.5%

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

      2. *-commutative 74.5%

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

      3. *-inverses 74.5%

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

      4. div-sub 74.5%

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

      5. clear-num 74.6%

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

   5. Applied egg-rr 74.6%

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

   6. Taylor expanded in x around 0 58.0%

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

      1. *-commutative 58.0%

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

      2. associate-/l* 68.0%

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

   8. Simplified 68.0%

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

   if -1.22000000000000003e-64 < x < 4.9e-92

   1. Initial program 87.3%

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

   3. Taylor expanded in z around 0 87.3%

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

   4. Taylor expanded in x around 0 74.6%

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

      1. associate-/l* 74.6%

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

   6. Simplified 74.6%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{-64} \lor \neg \left(x \leq 4.9 \cdot 10^{-92}\right):\\ \;\;\;\;z \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{z - y}\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-123}:\\ \;\;\;\;y \cdot t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ z (- z y))))
   (if (<= x -1.9e-63)
     (/ x (- 1.0 (/ y z)))
     (if (<= x 3.1e-123) (* y t_0) (* x t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z / (z - y);
	double tmp;
	if (x <= -1.9e-63) {
		tmp = x / (1.0 - (y / z));
	} else if (x <= 3.1e-123) {
		tmp = y * t_0;
	} else {
		tmp = x * 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 = z / (z - y)
    if (x <= (-1.9d-63)) then
        tmp = x / (1.0d0 - (y / z))
    else if (x <= 3.1d-123) then
        tmp = y * t_0
    else
        tmp = x * t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z / (z - y);
	double tmp;
	if (x <= -1.9e-63) {
		tmp = x / (1.0 - (y / z));
	} else if (x <= 3.1e-123) {
		tmp = y * t_0;
	} else {
		tmp = x * t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z / (z - y)
	tmp = 0
	if x <= -1.9e-63:
		tmp = x / (1.0 - (y / z))
	elif x <= 3.1e-123:
		tmp = y * t_0
	else:
		tmp = x * t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z / Float64(z - y))
	tmp = 0.0
	if (x <= -1.9e-63)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (x <= 3.1e-123)
		tmp = Float64(y * t_0);
	else
		tmp = Float64(x * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z / (z - y);
	tmp = 0.0;
	if (x <= -1.9e-63)
		tmp = x / (1.0 - (y / z));
	elseif (x <= 3.1e-123)
		tmp = y * t_0;
	else
		tmp = x * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.9e-63], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e-123], N[(y * t$95$0), $MachinePrecision], N[(x * t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.90000000000000009e-63

   1. Initial program 92.2%

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

   3. Taylor expanded in x around inf 78.4%

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

   if -1.90000000000000009e-63 < x < 3.09999999999999998e-123

   1. Initial program 88.3%

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

   3. Taylor expanded in z around 0 88.3%

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

   4. Taylor expanded in x around 0 76.8%

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

      1. associate-/l* 76.8%

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

   6. Simplified 76.8%

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

   if 3.09999999999999998e-123 < x

   1. Initial program 87.3%

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

   3. Taylor expanded in x around inf 70.0%

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

      1. div-inv 70.0%

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

      2. *-commutative 70.0%

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

      3. *-inverses 70.0%

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

      4. div-sub 70.0%

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

      5. clear-num 70.2%

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

   5. Applied egg-rr 70.2%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-123}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+67} \lor \neg \left(y \leq 2.9 \cdot 10^{+18}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.8e+67) (not (<= y 2.9e+18))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.8e+67) || !(y <= 2.9e+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 <= (-6.8d+67)) .or. (.not. (y <= 2.9d+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 <= -6.8e+67) || !(y <= 2.9e+18)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.8e+67) or not (y <= 2.9e+18):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.8e+67) || !(y <= 2.9e+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 <= -6.8e+67) || ~((y <= 2.9e+18)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.8e+67], N[Not[LessEqual[y, 2.9e+18]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8000000000000003e67 or 2.9e18 < y

   1. Initial program 70.6%

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

   3. Taylor expanded in y around inf 67.6%

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

      1. neg-mul-1 67.6%

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

   5. Simplified 67.6%

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

   if -6.8000000000000003e67 < y < 2.9e18

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 69.6%

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

      1. +-commutative 69.6%

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

   5. Simplified 69.6%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+67} \lor \neg \left(y \leq 2.9 \cdot 10^{+18}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{-45} \lor \neg \left(y \leq 4.2 \cdot 10^{-36}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.36e-45) (not (<= y 4.2e-36))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.36e-45) || !(y <= 4.2e-36)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.36d-45)) .or. (.not. (y <= 4.2d-36))) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.36e-45) || !(y <= 4.2e-36)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.36e-45) or not (y <= 4.2e-36):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.36e-45) || !(y <= 4.2e-36))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.36e-45) || ~((y <= 4.2e-36)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.36e-45], N[Not[LessEqual[y, 4.2e-36]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -1.35999999999999998e-45 or 4.19999999999999982e-36 < y

   1. Initial program 79.7%

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

   3. Taylor expanded in y around inf 54.3%

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

      1. neg-mul-1 54.3%

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

   5. Simplified 54.3%

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

   if -1.35999999999999998e-45 < y < 4.19999999999999982e-36

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 60.9%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{-45} \lor \neg \left(y \leq 4.2 \cdot 10^{-36}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-126}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9e-75) x (if (<= x 4.4e-126) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9e-75) {
		tmp = x;
	} else if (x <= 4.4e-126) {
		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 <= (-9d-75)) then
        tmp = x
    else if (x <= 4.4d-126) 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 <= -9e-75) {
		tmp = x;
	} else if (x <= 4.4e-126) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9e-75:
		tmp = x
	elif x <= 4.4e-126:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9e-75)
		tmp = x;
	elseif (x <= 4.4e-126)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9e-75)
		tmp = x;
	elseif (x <= 4.4e-126)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9e-75], x, If[LessEqual[x, 4.4e-126], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -9.0000000000000006e-75 or 4.40000000000000029e-126 < x

   1. Initial program 89.4%

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

   3. Taylor expanded in y around 0 46.1%

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

   if -9.0000000000000006e-75 < x < 4.40000000000000029e-126

   1. Initial program 87.9%

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

   3. Taylor expanded in z around 0 87.9%

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

   4. Taylor expanded in x around 0 76.0%

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

      1. associate-/l* 76.0%

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

   6. Simplified 76.0%

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

   7. Taylor expanded in y around 0 41.1%

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

Alternative 12: 35.6% 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 88.9%

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

3. Taylor expanded in y around 0 35.2%

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

Developer Target 1: 93.7% 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 2024170 
(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))))