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

Percentage Accurate: 87.8% → 99.1%

Time: 6.2s

Alternatives: 11

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 87.8% 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: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-232} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z\right) - \frac{z}{\frac{y}{x}}\right) - \frac{z \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-232) (not (<= t_0 0.0)))
     t_0
     (- (- (- z) (/ z (/ y x))) (/ (* z z) y)))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-232) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = (-z - (z / (y / x))) - ((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) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-1d-232)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = (-z - (z / (y / x))) - ((z * z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-232) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = (-z - (z / (y / x))) - ((z * z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -1e-232) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = (-z - (z / (y / x))) - ((z * z) / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -1e-232) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(-z) - Float64(z / Float64(y / x))) - Float64(Float64(z * z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -1e-232) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = (-z - (z / (y / x))) - ((z * z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -1e-232], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(N[((-z) - N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -1.00000000000000002e-232 or -0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

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

   if -1.00000000000000002e-232 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -0.0

   1. Initial program 25.7%

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

      1. clear-num 25.7%

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

      2. associate-/r/ 25.7%

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

   3. Applied egg-rr 25.7%

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

   4. Taylor expanded in y around inf 99.1%

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{z \cdot x}{y}\right) - \frac{{z}^{2}}{y}} \]
   5. Step-by-step derivation

      1. distribute-lft-out 99.1%

         \[\leadsto \color{blue}{-1 \cdot \left(z + \frac{z \cdot x}{y}\right)} - \frac{{z}^{2}}{y} \]

      2. associate-/l* 99.9%

         \[\leadsto -1 \cdot \left(z + \color{blue}{\frac{z}{\frac{y}{x}}}\right) - \frac{{z}^{2}}{y} \]

      3. unpow2 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-232} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z\right) - \frac{z}{\frac{y}{x}}\right) - \frac{z \cdot z}{y}\\ \end{array} \]

Alternative 2: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{-252} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{z \cdot \left(x + z\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-252) (not (<= t_0 0.0)))
     t_0
     (- (- z) (/ (* z (+ x z)) y)))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-252) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z - ((z * (x + z)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-2d-252)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = -z - ((z * (x + z)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-252) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z - ((z * (x + z)) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -2e-252) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = -z - ((z * (x + z)) / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -2e-252) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) - Float64(Float64(z * Float64(x + z)) / 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-252) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = -z - ((z * (x + z)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -2e-252], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[((-z) - N[(N[(z * N[(x + z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -1.99999999999999989e-252 or -0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

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

   if -1.99999999999999989e-252 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -0.0

   1. Initial program 20.1%

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

   2. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{z \cdot x}{y}\right) - \frac{{z}^{2}}{y}} \]
   3. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{z \cdot x}{y}\right) + \left(-\frac{{z}^{2}}{y}\right)} \]

      2. mul-1-neg 100.0%

         \[\leadsto \left(-1 \cdot z + \color{blue}{\left(-\frac{z \cdot x}{y}\right)}\right) + \left(-\frac{{z}^{2}}{y}\right) \]

      3. unsub-neg 100.0%

         \[\leadsto \color{blue}{\left(-1 \cdot z - \frac{z \cdot x}{y}\right)} + \left(-\frac{{z}^{2}}{y}\right) \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{-1 \cdot z - \left(\frac{z \cdot x}{y} - \left(-\frac{{z}^{2}}{y}\right)\right)} \]

      5. mul-1-neg 100.0%

         \[\leadsto \color{blue}{\left(-z\right)} - \left(\frac{z \cdot x}{y} - \left(-\frac{{z}^{2}}{y}\right)\right) \]

      6. distribute-frac-neg 100.0%

         \[\leadsto \left(-z\right) - \left(\frac{z \cdot x}{y} - \color{blue}{\frac{-{z}^{2}}{y}}\right) \]

      7. mul-1-neg 100.0%

         \[\leadsto \left(-z\right) - \left(\frac{z \cdot x}{y} - \frac{\color{blue}{-1 \cdot {z}^{2}}}{y}\right) \]

      8. div-sub 100.0%

         \[\leadsto \left(-z\right) - \color{blue}{\frac{z \cdot x - -1 \cdot {z}^{2}}{y}} \]

      9. sub-neg 100.0%

         \[\leadsto \left(-z\right) - \frac{\color{blue}{z \cdot x + \left(--1 \cdot {z}^{2}\right)}}{y} \]

      10. mul-1-neg 100.0%

          \[\leadsto \left(-z\right) - \frac{z \cdot x + \left(-\color{blue}{\left(-{z}^{2}\right)}\right)}{y} \]

      11. remove-double-neg 100.0%

          \[\leadsto \left(-z\right) - \frac{z \cdot x + \color{blue}{{z}^{2}}}{y} \]

      12. unpow2 100.0%

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

      13. distribute-lft-out 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-252} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{z \cdot \left(x + z\right)}{y}\\ \end{array} \]

Alternative 3: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-232} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-232) (not (<= t_0 0.0))) t_0 (* z (- -1.0 (/ x y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-232) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * (-1.0 - (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) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-1d-232)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = z * ((-1.0d0) - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-232) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -1e-232) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = z * (-1.0 - (x / y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -1e-232) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -1e-232) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = z * (-1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -1e-232], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -1.00000000000000002e-232 or -0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

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

   if -1.00000000000000002e-232 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -0.0

   1. Initial program 25.7%

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

   2. Taylor expanded in z around 0 89.4%

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

      1. associate-*r/ 89.4%

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

      2. +-commutative 89.4%

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

      3. *-commutative 89.4%

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

      4. associate-*r* 89.4%

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

      5. mul-1-neg 89.4%

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

      6. +-commutative 89.4%

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

   4. Simplified 89.4%

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

   5. Taylor expanded in y around 0 99.1%

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

      1. distribute-lft-out 99.1%

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

      2. associate-*r/ 99.9%

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

      3. *-commutative 99.9%

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

      4. distribute-rgt1-in 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-*r* 99.8%

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

      7. neg-mul-1 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. metadata-eval 99.8%

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

      10. unsub-neg 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-232} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 4: 72.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := z \cdot \left(-1 - \frac{x}{y}\right)\\ t_2 := \frac{x}{t_0}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.07 \cdot 10^{-19}:\\ \;\;\;\;\frac{y}{t_0}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-197}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (* z (- -1.0 (/ x y)))) (t_2 (/ x t_0)))
   (if (<= y -1.6e+130)
     t_1
     (if (<= y -1.07e-19)
       (/ y t_0)
       (if (<= y -3.5e-101)
         t_2
         (if (<= y -4.7e-197) (+ x y) (if (<= y 6.5e+108) t_2 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = z * (-1.0 - (x / y));
	double t_2 = x / t_0;
	double tmp;
	if (y <= -1.6e+130) {
		tmp = t_1;
	} else if (y <= -1.07e-19) {
		tmp = y / t_0;
	} else if (y <= -3.5e-101) {
		tmp = t_2;
	} else if (y <= -4.7e-197) {
		tmp = x + y;
	} else if (y <= 6.5e+108) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = z * ((-1.0d0) - (x / y))
    t_2 = x / t_0
    if (y <= (-1.6d+130)) then
        tmp = t_1
    else if (y <= (-1.07d-19)) then
        tmp = y / t_0
    else if (y <= (-3.5d-101)) then
        tmp = t_2
    else if (y <= (-4.7d-197)) then
        tmp = x + y
    else if (y <= 6.5d+108) then
        tmp = t_2
    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 * (-1.0 - (x / y));
	double t_2 = x / t_0;
	double tmp;
	if (y <= -1.6e+130) {
		tmp = t_1;
	} else if (y <= -1.07e-19) {
		tmp = y / t_0;
	} else if (y <= -3.5e-101) {
		tmp = t_2;
	} else if (y <= -4.7e-197) {
		tmp = x + y;
	} else if (y <= 6.5e+108) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = z * (-1.0 - (x / y))
	t_2 = x / t_0
	tmp = 0
	if y <= -1.6e+130:
		tmp = t_1
	elif y <= -1.07e-19:
		tmp = y / t_0
	elif y <= -3.5e-101:
		tmp = t_2
	elif y <= -4.7e-197:
		tmp = x + y
	elif y <= 6.5e+108:
		tmp = t_2
	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(-1.0 - Float64(x / y)))
	t_2 = Float64(x / t_0)
	tmp = 0.0
	if (y <= -1.6e+130)
		tmp = t_1;
	elseif (y <= -1.07e-19)
		tmp = Float64(y / t_0);
	elseif (y <= -3.5e-101)
		tmp = t_2;
	elseif (y <= -4.7e-197)
		tmp = Float64(x + y);
	elseif (y <= 6.5e+108)
		tmp = t_2;
	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 * (-1.0 - (x / y));
	t_2 = x / t_0;
	tmp = 0.0;
	if (y <= -1.6e+130)
		tmp = t_1;
	elseif (y <= -1.07e-19)
		tmp = y / t_0;
	elseif (y <= -3.5e-101)
		tmp = t_2;
	elseif (y <= -4.7e-197)
		tmp = x + y;
	elseif (y <= 6.5e+108)
		tmp = t_2;
	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[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / t$95$0), $MachinePrecision]}, If[LessEqual[y, -1.6e+130], t$95$1, If[LessEqual[y, -1.07e-19], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, -3.5e-101], t$95$2, If[LessEqual[y, -4.7e-197], N[(x + y), $MachinePrecision], If[LessEqual[y, 6.5e+108], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6e130 or 6.4999999999999996e108 < y

   1. Initial program 70.0%

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

   2. Taylor expanded in z around 0 63.5%

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

      1. associate-*r/ 63.5%

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

      2. +-commutative 63.5%

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

      3. *-commutative 63.5%

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

      4. associate-*r* 63.5%

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

      5. mul-1-neg 63.5%

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

      6. +-commutative 63.5%

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

   4. Simplified 63.5%

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

   5. Taylor expanded in y around 0 73.9%

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

      1. distribute-lft-out 73.9%

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

      2. associate-*r/ 78.3%

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

      3. *-commutative 78.3%

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

      4. distribute-rgt1-in 78.3%

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

      5. +-commutative 78.3%

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

      6. associate-*r* 78.3%

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

      7. neg-mul-1 78.3%

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

      8. distribute-neg-in 78.3%

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

      9. metadata-eval 78.3%

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

      10. unsub-neg 78.3%

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

   7. Simplified 78.3%

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

   if -1.6e130 < y < -1.07000000000000001e-19

   1. Initial program 97.1%

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

   2. Taylor expanded in x around 0 75.6%

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

   if -1.07000000000000001e-19 < y < -3.49999999999999994e-101 or -4.7000000000000001e-197 < y < 6.4999999999999996e108

   1. Initial program 99.1%

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

   2. Taylor expanded in x around inf 81.0%

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

   if -3.49999999999999994e-101 < y < -4.7000000000000001e-197

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 88.7%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+130}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.07 \cdot 10^{-19}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-197}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 5: 72.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := z \cdot \left(-1 - \frac{x}{y}\right)\\ t_2 := \frac{x}{t_0}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-17}:\\ \;\;\;\;\frac{y}{t_0}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-197}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (* z (- -1.0 (/ x y)))) (t_2 (/ x t_0)))
   (if (<= y -5.8e+134)
     t_1
     (if (<= y -2.8e-17)
       (/ y t_0)
       (if (<= y -5.8e-101)
         t_2
         (if (<= y -2.9e-197)
           (* (+ x y) (+ 1.0 (/ y z)))
           (if (<= y 6.5e+108) t_2 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = z * (-1.0 - (x / y));
	double t_2 = x / t_0;
	double tmp;
	if (y <= -5.8e+134) {
		tmp = t_1;
	} else if (y <= -2.8e-17) {
		tmp = y / t_0;
	} else if (y <= -5.8e-101) {
		tmp = t_2;
	} else if (y <= -2.9e-197) {
		tmp = (x + y) * (1.0 + (y / z));
	} else if (y <= 6.5e+108) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = z * ((-1.0d0) - (x / y))
    t_2 = x / t_0
    if (y <= (-5.8d+134)) then
        tmp = t_1
    else if (y <= (-2.8d-17)) then
        tmp = y / t_0
    else if (y <= (-5.8d-101)) then
        tmp = t_2
    else if (y <= (-2.9d-197)) then
        tmp = (x + y) * (1.0d0 + (y / z))
    else if (y <= 6.5d+108) then
        tmp = t_2
    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 * (-1.0 - (x / y));
	double t_2 = x / t_0;
	double tmp;
	if (y <= -5.8e+134) {
		tmp = t_1;
	} else if (y <= -2.8e-17) {
		tmp = y / t_0;
	} else if (y <= -5.8e-101) {
		tmp = t_2;
	} else if (y <= -2.9e-197) {
		tmp = (x + y) * (1.0 + (y / z));
	} else if (y <= 6.5e+108) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = z * (-1.0 - (x / y))
	t_2 = x / t_0
	tmp = 0
	if y <= -5.8e+134:
		tmp = t_1
	elif y <= -2.8e-17:
		tmp = y / t_0
	elif y <= -5.8e-101:
		tmp = t_2
	elif y <= -2.9e-197:
		tmp = (x + y) * (1.0 + (y / z))
	elif y <= 6.5e+108:
		tmp = t_2
	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(-1.0 - Float64(x / y)))
	t_2 = Float64(x / t_0)
	tmp = 0.0
	if (y <= -5.8e+134)
		tmp = t_1;
	elseif (y <= -2.8e-17)
		tmp = Float64(y / t_0);
	elseif (y <= -5.8e-101)
		tmp = t_2;
	elseif (y <= -2.9e-197)
		tmp = Float64(Float64(x + y) * Float64(1.0 + Float64(y / z)));
	elseif (y <= 6.5e+108)
		tmp = t_2;
	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 * (-1.0 - (x / y));
	t_2 = x / t_0;
	tmp = 0.0;
	if (y <= -5.8e+134)
		tmp = t_1;
	elseif (y <= -2.8e-17)
		tmp = y / t_0;
	elseif (y <= -5.8e-101)
		tmp = t_2;
	elseif (y <= -2.9e-197)
		tmp = (x + y) * (1.0 + (y / z));
	elseif (y <= 6.5e+108)
		tmp = t_2;
	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[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / t$95$0), $MachinePrecision]}, If[LessEqual[y, -5.8e+134], t$95$1, If[LessEqual[y, -2.8e-17], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, -5.8e-101], t$95$2, If[LessEqual[y, -2.9e-197], N[(N[(x + y), $MachinePrecision] * N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+108], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.80000000000000023e134 or 6.4999999999999996e108 < y

   1. Initial program 70.0%

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

   2. Taylor expanded in z around 0 63.5%

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

      1. associate-*r/ 63.5%

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

      2. +-commutative 63.5%

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

      3. *-commutative 63.5%

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

      4. associate-*r* 63.5%

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

      5. mul-1-neg 63.5%

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

      6. +-commutative 63.5%

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

   4. Simplified 63.5%

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

   5. Taylor expanded in y around 0 73.9%

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

      1. distribute-lft-out 73.9%

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

      2. associate-*r/ 78.3%

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

      3. *-commutative 78.3%

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

      4. distribute-rgt1-in 78.3%

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

      5. +-commutative 78.3%

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

      6. associate-*r* 78.3%

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

      7. neg-mul-1 78.3%

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

      8. distribute-neg-in 78.3%

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

      9. metadata-eval 78.3%

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

      10. unsub-neg 78.3%

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

   7. Simplified 78.3%

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

   if -5.80000000000000023e134 < y < -2.7999999999999999e-17

   1. Initial program 97.1%

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

   2. Taylor expanded in x around 0 75.6%

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

   if -2.7999999999999999e-17 < y < -5.800000000000001e-101 or -2.90000000000000023e-197 < y < 6.4999999999999996e108

   1. Initial program 99.1%

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

   2. Taylor expanded in x around inf 81.0%

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

   if -5.800000000000001e-101 < y < -2.90000000000000023e-197

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 88.8%

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

      1. associate-/l* 85.9%

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

      2. +-commutative 85.9%

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

      3. associate-/r/ 88.8%

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

      4. +-commutative 88.8%

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

      5. *-lft-identity 88.8%

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

      6. distribute-rgt-in 88.8%

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

      7. +-commutative 88.8%

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

      8. +-commutative 88.8%

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

   4. Simplified 88.8%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+134}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-17}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-197}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 6: 72.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+47}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-197}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))))
   (if (<= y -4.8e+47)
     t_0
     (if (<= y -1.05e-197)
       (+ x y)
       (if (<= y 6.5e+108) (/ x (- 1.0 (/ y z))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -4.8e+47) {
		tmp = t_0;
	} else if (y <= -1.05e-197) {
		tmp = x + y;
	} else if (y <= 6.5e+108) {
		tmp = x / (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 = z * ((-1.0d0) - (x / y))
    if (y <= (-4.8d+47)) then
        tmp = t_0
    else if (y <= (-1.05d-197)) then
        tmp = x + y
    else if (y <= 6.5d+108) then
        tmp = x / (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 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -4.8e+47) {
		tmp = t_0;
	} else if (y <= -1.05e-197) {
		tmp = x + y;
	} else if (y <= 6.5e+108) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -4.8e+47:
		tmp = t_0
	elif y <= -1.05e-197:
		tmp = x + y
	elif y <= 6.5e+108:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -4.8e+47)
		tmp = t_0;
	elseif (y <= -1.05e-197)
		tmp = Float64(x + y);
	elseif (y <= 6.5e+108)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-1.0 - (x / y));
	tmp = 0.0;
	if (y <= -4.8e+47)
		tmp = t_0;
	elseif (y <= -1.05e-197)
		tmp = x + y;
	elseif (y <= 6.5e+108)
		tmp = x / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+47], t$95$0, If[LessEqual[y, -1.05e-197], N[(x + y), $MachinePrecision], If[LessEqual[y, 6.5e+108], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.80000000000000037e47 or 6.4999999999999996e108 < y

   1. Initial program 75.4%

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

   2. Taylor expanded in z around 0 63.4%

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

      1. associate-*r/ 63.4%

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

      2. +-commutative 63.4%

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

      3. *-commutative 63.4%

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

      4. associate-*r* 63.4%

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

      5. mul-1-neg 63.4%

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

      6. +-commutative 63.4%

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

   4. Simplified 63.4%

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

   5. Taylor expanded in y around 0 71.5%

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

      1. distribute-lft-out 71.5%

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

      2. associate-*r/ 75.0%

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

      3. *-commutative 75.0%

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

      4. distribute-rgt1-in 74.9%

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

      5. +-commutative 74.9%

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

      6. associate-*r* 74.9%

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

      7. neg-mul-1 74.9%

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

      8. distribute-neg-in 74.9%

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

      9. metadata-eval 74.9%

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

      10. unsub-neg 74.9%

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

   7. Simplified 74.9%

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

   if -4.80000000000000037e47 < y < -1.05e-197

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 78.4%

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

   if -1.05e-197 < y < 6.4999999999999996e108

   1. Initial program 99.0%

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

   2. Taylor expanded in x around inf 82.4%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+47}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-197}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 7: 73.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{-19}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.05e-19)
   (+ x y)
   (if (<= z 5.1e-17) (* z (- -1.0 (/ x y))) (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.05e-19) {
		tmp = x + y;
	} else if (z <= 5.1e-17) {
		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 (z <= (-3.05d-19)) then
        tmp = x + y
    else if (z <= 5.1d-17) 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 (z <= -3.05e-19) {
		tmp = x + y;
	} else if (z <= 5.1e-17) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.05e-19:
		tmp = x + y
	elif z <= 5.1e-17:
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.05e-19)
		tmp = Float64(x + y);
	elseif (z <= 5.1e-17)
		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 (z <= -3.05e-19)
		tmp = x + y;
	elseif (z <= 5.1e-17)
		tmp = z * (-1.0 - (x / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.05e-19], N[(x + y), $MachinePrecision], If[LessEqual[z, 5.1e-17], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0500000000000001e-19 or 5.1000000000000003e-17 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 81.1%

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

   if -3.0500000000000001e-19 < z < 5.1000000000000003e-17

   1. Initial program 80.5%

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

   2. Taylor expanded in z around 0 65.7%

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

      1. associate-*r/ 65.7%

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

      2. +-commutative 65.7%

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

      3. *-commutative 65.7%

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

      4. associate-*r* 65.7%

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

      5. mul-1-neg 65.7%

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

      6. +-commutative 65.7%

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

   4. Simplified 65.7%

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

   5. Taylor expanded in y around 0 68.3%

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

      1. distribute-lft-out 68.3%

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

      2. associate-*r/ 66.5%

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

      3. *-commutative 66.5%

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

      4. distribute-rgt1-in 66.5%

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

      5. +-commutative 66.5%

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

      6. associate-*r* 66.5%

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

      7. neg-mul-1 66.5%

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

      8. distribute-neg-in 66.5%

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

      9. metadata-eval 66.5%

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

      10. unsub-neg 66.5%

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

   7. Simplified 66.5%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{-19}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8: 67.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+120}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.5e+49) (- z) (if (<= y 6.8e+120) (+ x y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.5e+49) {
		tmp = -z;
	} else if (y <= 6.8e+120) {
		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 <= (-8.5d+49)) then
        tmp = -z
    else if (y <= 6.8d+120) 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 <= -8.5e+49) {
		tmp = -z;
	} else if (y <= 6.8e+120) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.5e+49:
		tmp = -z
	elif y <= 6.8e+120:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.5e+49)
		tmp = Float64(-z);
	elseif (y <= 6.8e+120)
		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 <= -8.5e+49)
		tmp = -z;
	elseif (y <= 6.8e+120)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.5e+49], (-z), If[LessEqual[y, 6.8e+120], N[(x + y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -8.4999999999999996e49 or 6.79999999999999998e120 < y

   1. Initial program 75.1%

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

   2. Taylor expanded in y around inf 65.9%

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

      1. mul-1-neg 65.9%

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

   4. Simplified 65.9%

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

   if -8.4999999999999996e49 < y < 6.79999999999999998e120

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf 74.7%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+120}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 9: 56.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-19}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6e-19) (- z) (if (<= y 6.5e+108) x (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e-19) {
		tmp = -z;
	} else if (y <= 6.5e+108) {
		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 <= (-6d-19)) then
        tmp = -z
    else if (y <= 6.5d+108) 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 <= -6e-19) {
		tmp = -z;
	} else if (y <= 6.5e+108) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6e-19:
		tmp = -z
	elif y <= 6.5e+108:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6e-19)
		tmp = Float64(-z);
	elseif (y <= 6.5e+108)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6e-19)
		tmp = -z;
	elseif (y <= 6.5e+108)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6e-19], (-z), If[LessEqual[y, 6.5e+108], x, (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -5.99999999999999985e-19 or 6.4999999999999996e108 < y

   1. Initial program 79.3%

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

   2. Taylor expanded in y around inf 59.9%

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

      1. mul-1-neg 59.9%

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

   4. Simplified 59.9%

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

   if -5.99999999999999985e-19 < y < 6.4999999999999996e108

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0 56.5%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-19}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 10: 40.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-171}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.5e-76) x (if (<= x 1.8e-171) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.5e-76) {
		tmp = x;
	} else if (x <= 1.8e-171) {
		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 <= (-4.5d-76)) then
        tmp = x
    else if (x <= 1.8d-171) 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 <= -4.5e-76) {
		tmp = x;
	} else if (x <= 1.8e-171) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.5e-76:
		tmp = x
	elif x <= 1.8e-171:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.5e-76)
		tmp = x;
	elseif (x <= 1.8e-171)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.5e-76)
		tmp = x;
	elseif (x <= 1.8e-171)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.5e-76], x, If[LessEqual[x, 1.8e-171], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5000000000000001e-76 or 1.80000000000000002e-171 < x

   1. Initial program 92.8%

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

   2. Taylor expanded in y around 0 48.4%

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

   if -4.5000000000000001e-76 < x < 1.80000000000000002e-171

   1. Initial program 89.5%

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

   2. Taylor expanded in x around 0 74.0%

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

   3. Taylor expanded in y around 0 49.9%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-171}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 34.1% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 91.8%

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

2. Taylor expanded in y around 0 38.6%

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

3. Final simplification 38.6%

   \[\leadsto x \]

Developer target: 93.7% accurate, 0.7× 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 2023185 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :herbie-target
  (if (< y -3.7429310762689856e+171) (* (/ (+ y x) (- y)) z) (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) (* (/ (+ y x) (- y)) z)))

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