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

Percentage Accurate: 88.7% → 98.8%

Time: 5.6s

Alternatives: 10

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.7% 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: 98.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-223} \lor \neg \left(t\_0 \leq 5 \cdot 10^{-292}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{z \cdot \left(x + z\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -5e-223) (not (<= t_0 5e-292)))
     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 <= -5e-223) || !(t_0 <= 5e-292)) {
		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 <= (-5d-223)) .or. (.not. (t_0 <= 5d-292))) 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 <= -5e-223) || !(t_0 <= 5e-292)) {
		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 <= -5e-223) or not (t_0 <= 5e-292):
		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 <= -5e-223) || !(t_0 <= 5e-292))
		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 <= -5e-223) || ~((t_0 <= 5e-292)))
		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, -5e-223], N[Not[LessEqual[t$95$0, 5e-292]], $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 #s(literal 1 binary64) (/.f64 y z))) < -5.00000000000000024e-223 or 4.99999999999999981e-292 < (/.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 -5.00000000000000024e-223 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 4.99999999999999981e-292

   1. Initial program 17.1%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. div-sub 100.0%

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

      4. remove-double-neg 100.0%

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

      5. mul-1-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. distribute-lft-out-- 100.0%

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

      8. mul-1-neg 100.0%

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

      9. distribute-neg-frac 100.0%

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

      10. unsub-neg 100.0%

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

      11. mul-1-neg 100.0%

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

      12. cancel-sign-sub-inv 100.0%

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

      13. metadata-eval 100.0%

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

      14. *-lft-identity 100.0%

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

      15. +-commutative 100.0%

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

      16. unpow2 100.0%

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

      17. distribute-rgt-out 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-223} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 5 \cdot 10^{-292}\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{z \cdot \left(x + z\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-223} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -5e-223) (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-223) || !(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-223)) .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-223) || !(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-223) 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-223) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(Float64(x + y) / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -5e-223) || ~((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-223], 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))) < -5.00000000000000024e-223 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 -5.00000000000000024e-223 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 0.0

   1. Initial program 14.7%

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

   3. Taylor expanded in z around 0 99.2%

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

      1. mul-1-neg 99.2%

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

      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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-223} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - \frac{y}{z}}\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{-31}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-192}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-86}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 520000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+32}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 (/ y z)))))
   (if (<= x -3.6e-31)
     t_0
     (if (<= x 3e-192)
       (+ x y)
       (if (<= x 9.2e-86)
         (- z)
         (if (<= x 520000000000.0) (+ x y) (if (<= x 9.5e+32) (- z) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double tmp;
	if (x <= -3.6e-31) {
		tmp = t_0;
	} else if (x <= 3e-192) {
		tmp = x + y;
	} else if (x <= 9.2e-86) {
		tmp = -z;
	} else if (x <= 520000000000.0) {
		tmp = x + y;
	} else if (x <= 9.5e+32) {
		tmp = -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 = x / (1.0d0 - (y / z))
    if (x <= (-3.6d-31)) then
        tmp = t_0
    else if (x <= 3d-192) then
        tmp = x + y
    else if (x <= 9.2d-86) then
        tmp = -z
    else if (x <= 520000000000.0d0) then
        tmp = x + y
    else if (x <= 9.5d+32) then
        tmp = -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 = x / (1.0 - (y / z));
	double tmp;
	if (x <= -3.6e-31) {
		tmp = t_0;
	} else if (x <= 3e-192) {
		tmp = x + y;
	} else if (x <= 9.2e-86) {
		tmp = -z;
	} else if (x <= 520000000000.0) {
		tmp = x + y;
	} else if (x <= 9.5e+32) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (1.0 - (y / z))
	tmp = 0
	if x <= -3.6e-31:
		tmp = t_0
	elif x <= 3e-192:
		tmp = x + y
	elif x <= 9.2e-86:
		tmp = -z
	elif x <= 520000000000.0:
		tmp = x + y
	elif x <= 9.5e+32:
		tmp = -z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (x <= -3.6e-31)
		tmp = t_0;
	elseif (x <= 3e-192)
		tmp = Float64(x + y);
	elseif (x <= 9.2e-86)
		tmp = Float64(-z);
	elseif (x <= 520000000000.0)
		tmp = Float64(x + y);
	elseif (x <= 9.5e+32)
		tmp = Float64(-z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (1.0 - (y / z));
	tmp = 0.0;
	if (x <= -3.6e-31)
		tmp = t_0;
	elseif (x <= 3e-192)
		tmp = x + y;
	elseif (x <= 9.2e-86)
		tmp = -z;
	elseif (x <= 520000000000.0)
		tmp = x + y;
	elseif (x <= 9.5e+32)
		tmp = -z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.6e-31], t$95$0, If[LessEqual[x, 3e-192], N[(x + y), $MachinePrecision], If[LessEqual[x, 9.2e-86], (-z), If[LessEqual[x, 520000000000.0], N[(x + y), $MachinePrecision], If[LessEqual[x, 9.5e+32], (-z), t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.60000000000000004e-31 or 9.50000000000000006e32 < x

   1. Initial program 90.2%

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

   3. Taylor expanded in x around inf 77.9%

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

   if -3.60000000000000004e-31 < x < 2.9999999999999999e-192 or 9.19999999999999985e-86 < x < 5.2e11

   1. Initial program 90.9%

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

   3. Taylor expanded in z around inf 64.6%

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

      1. +-commutative 64.6%

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

   5. Simplified 64.6%

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

   if 2.9999999999999999e-192 < x < 9.19999999999999985e-86 or 5.2e11 < x < 9.50000000000000006e32

   1. Initial program 68.7%

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

   3. Taylor expanded in y around inf 74.8%

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

      1. mul-1-neg 74.8%

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

   5. Simplified 74.8%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-192}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-86}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 520000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+32}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{+45}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-24}:\\ \;\;\;\;\frac{z \cdot \left(\left(-y\right) - x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (+ x y) (+ 1.0 (/ y z)))))
   (if (<= z -2.55e+45)
     t_0
     (if (<= z -6.3e-24)
       (/ x (- 1.0 (/ y z)))
       (if (<= z -5e-33)
         (+ x y)
         (if (<= z 5.7e-24) (/ (* z (- (- y) x)) y) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) * (1.0 + (y / z));
	double tmp;
	if (z <= -2.55e+45) {
		tmp = t_0;
	} else if (z <= -6.3e-24) {
		tmp = x / (1.0 - (y / z));
	} else if (z <= -5e-33) {
		tmp = x + y;
	} else if (z <= 5.7e-24) {
		tmp = (z * (-y - x)) / 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 (z <= (-2.55d+45)) then
        tmp = t_0
    else if (z <= (-6.3d-24)) then
        tmp = x / (1.0d0 - (y / z))
    else if (z <= (-5d-33)) then
        tmp = x + y
    else if (z <= 5.7d-24) then
        tmp = (z * (-y - x)) / 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 (z <= -2.55e+45) {
		tmp = t_0;
	} else if (z <= -6.3e-24) {
		tmp = x / (1.0 - (y / z));
	} else if (z <= -5e-33) {
		tmp = x + y;
	} else if (z <= 5.7e-24) {
		tmp = (z * (-y - x)) / y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) * (1.0 + (y / z))
	tmp = 0
	if z <= -2.55e+45:
		tmp = t_0
	elif z <= -6.3e-24:
		tmp = x / (1.0 - (y / z))
	elif z <= -5e-33:
		tmp = x + y
	elif z <= 5.7e-24:
		tmp = (z * (-y - x)) / 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 (z <= -2.55e+45)
		tmp = t_0;
	elseif (z <= -6.3e-24)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (z <= -5e-33)
		tmp = Float64(x + y);
	elseif (z <= 5.7e-24)
		tmp = Float64(Float64(z * Float64(Float64(-y) - x)) / 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 (z <= -2.55e+45)
		tmp = t_0;
	elseif (z <= -6.3e-24)
		tmp = x / (1.0 - (y / z));
	elseif (z <= -5e-33)
		tmp = x + y;
	elseif (z <= 5.7e-24)
		tmp = (z * (-y - x)) / 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[z, -2.55e+45], t$95$0, If[LessEqual[z, -6.3e-24], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5e-33], N[(x + y), $MachinePrecision], If[LessEqual[z, 5.7e-24], N[(N[(z * N[((-y) - x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.5499999999999999e45 or 5.70000000000000002e-24 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 67.2%

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

      1. associate-+r+ 67.2%

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

      2. *-rgt-identity 67.2%

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

      3. *-commutative 67.2%

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

      4. associate-/l* 81.4%

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

      5. distribute-lft-in 81.4%

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

      6. +-commutative 81.4%

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

   5. Simplified 81.4%

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

   if -2.5499999999999999e45 < z < -6.29999999999999979e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.7%

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

   if -6.29999999999999979e-24 < z < -5.00000000000000028e-33

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -5.00000000000000028e-33 < z < 5.70000000000000002e-24

   1. Initial program 71.7%

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

   3. Taylor expanded in z around 0 81.7%

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

      1. mul-1-neg 81.7%

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

      2. +-commutative 81.7%

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

   5. Simplified 81.7%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+45}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-24}:\\ \;\;\;\;\frac{z \cdot \left(\left(-y\right) - x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.35 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-33} \lor \neg \left(z \leq 9 \cdot 10^{-5}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(\left(-y\right) - x\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9.5e+38)
   (+ x y)
   (if (<= z -3.35e-25)
     (/ x (- 1.0 (/ y z)))
     (if (or (<= z -3.6e-33) (not (<= z 9e-5)))
       (+ x y)
       (/ (* z (- (- y) x)) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.5e+38) {
		tmp = x + y;
	} else if (z <= -3.35e-25) {
		tmp = x / (1.0 - (y / z));
	} else if ((z <= -3.6e-33) || !(z <= 9e-5)) {
		tmp = x + y;
	} else {
		tmp = (z * (-y - 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 <= (-9.5d+38)) then
        tmp = x + y
    else if (z <= (-3.35d-25)) then
        tmp = x / (1.0d0 - (y / z))
    else if ((z <= (-3.6d-33)) .or. (.not. (z <= 9d-5))) then
        tmp = x + y
    else
        tmp = (z * (-y - x)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.5e+38) {
		tmp = x + y;
	} else if (z <= -3.35e-25) {
		tmp = x / (1.0 - (y / z));
	} else if ((z <= -3.6e-33) || !(z <= 9e-5)) {
		tmp = x + y;
	} else {
		tmp = (z * (-y - x)) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9.5e+38:
		tmp = x + y
	elif z <= -3.35e-25:
		tmp = x / (1.0 - (y / z))
	elif (z <= -3.6e-33) or not (z <= 9e-5):
		tmp = x + y
	else:
		tmp = (z * (-y - x)) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9.5e+38)
		tmp = Float64(x + y);
	elseif (z <= -3.35e-25)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif ((z <= -3.6e-33) || !(z <= 9e-5))
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(z * Float64(Float64(-y) - x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9.5e+38)
		tmp = x + y;
	elseif (z <= -3.35e-25)
		tmp = x / (1.0 - (y / z));
	elseif ((z <= -3.6e-33) || ~((z <= 9e-5)))
		tmp = x + y;
	else
		tmp = (z * (-y - x)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9.5e+38], N[(x + y), $MachinePrecision], If[LessEqual[z, -3.35e-25], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3.6e-33], N[Not[LessEqual[z, 9e-5]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(N[(z * N[((-y) - x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.4999999999999995e38 or -3.35000000000000016e-25 < z < -3.60000000000000034e-33 or 9.00000000000000057e-5 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 82.3%

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

      1. +-commutative 82.3%

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

   5. Simplified 82.3%

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

   if -9.4999999999999995e38 < z < -3.35000000000000016e-25

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.7%

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

   if -3.60000000000000034e-33 < z < 9.00000000000000057e-5

   1. Initial program 72.2%

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

   3. Taylor expanded in z around 0 81.1%

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

      1. mul-1-neg 81.1%

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

      2. +-commutative 81.1%

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

   5. Simplified 81.1%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.35 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-33} \lor \neg \left(z \leq 9 \cdot 10^{-5}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(\left(-y\right) - x\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+75}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+16}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -52000 \lor \neg \left(y \leq 3 \cdot 10^{+94}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.8e+75)
   (- z)
   (if (<= y -1.05e+16)
     y
     (if (or (<= y -52000.0) (not (<= y 3e+94))) (- z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.8e+75) {
		tmp = -z;
	} else if (y <= -1.05e+16) {
		tmp = y;
	} else if ((y <= -52000.0) || !(y <= 3e+94)) {
		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 <= (-6.8d+75)) then
        tmp = -z
    else if (y <= (-1.05d+16)) then
        tmp = y
    else if ((y <= (-52000.0d0)) .or. (.not. (y <= 3d+94))) 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 <= -6.8e+75) {
		tmp = -z;
	} else if (y <= -1.05e+16) {
		tmp = y;
	} else if ((y <= -52000.0) || !(y <= 3e+94)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.8e+75:
		tmp = -z
	elif y <= -1.05e+16:
		tmp = y
	elif (y <= -52000.0) or not (y <= 3e+94):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.8e+75)
		tmp = Float64(-z);
	elseif (y <= -1.05e+16)
		tmp = y;
	elseif ((y <= -52000.0) || !(y <= 3e+94))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.8e+75)
		tmp = -z;
	elseif (y <= -1.05e+16)
		tmp = y;
	elseif ((y <= -52000.0) || ~((y <= 3e+94)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.8e+75], (-z), If[LessEqual[y, -1.05e+16], y, If[Or[LessEqual[y, -52000.0], N[Not[LessEqual[y, 3e+94]], $MachinePrecision]], (-z), x]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.80000000000000022e75 or -1.05e16 < y < -52000 or 3.0000000000000001e94 < y

   1. Initial program 72.1%

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

   3. Taylor expanded in y around inf 65.3%

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

      1. mul-1-neg 65.3%

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

   5. Simplified 65.3%

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

   if -6.80000000000000022e75 < y < -1.05e16

   1. Initial program 93.3%

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

   3. Taylor expanded in x around 0 51.8%

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

   4. Taylor expanded in y around 0 43.5%

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

   if -52000 < y < 3.0000000000000001e94

   1. Initial program 98.6%

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

   3. Taylor expanded in y around 0 55.8%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+75}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+16}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -52000 \lor \neg \left(y \leq 3 \cdot 10^{+94}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{-34} \lor \neg \left(x \leq 3.65 \cdot 10^{-72}\right):\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (or (<= x -3.3e-34) (not (<= x 3.65e-72))) (/ x t_0) (/ y t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if ((x <= -3.3e-34) || !(x <= 3.65e-72)) {
		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 = 1.0d0 - (y / z)
    if ((x <= (-3.3d-34)) .or. (.not. (x <= 3.65d-72))) 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 = 1.0 - (y / z);
	double tmp;
	if ((x <= -3.3e-34) || !(x <= 3.65e-72)) {
		tmp = x / t_0;
	} else {
		tmp = y / t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if (x <= -3.3e-34) or not (x <= 3.65e-72):
		tmp = x / t_0
	else:
		tmp = y / t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if ((x <= -3.3e-34) || !(x <= 3.65e-72))
		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 = 1.0 - (y / z);
	tmp = 0.0;
	if ((x <= -3.3e-34) || ~((x <= 3.65e-72)))
		tmp = x / t_0;
	else
		tmp = y / t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -3.3e-34], N[Not[LessEqual[x, 3.65e-72]], $MachinePrecision]], N[(x / t$95$0), $MachinePrecision], N[(y / t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.29999999999999983e-34 or 3.65000000000000001e-72 < x

   1. Initial program 88.7%

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

   3. Taylor expanded in x around inf 74.0%

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

   if -3.29999999999999983e-34 < x < 3.65000000000000001e-72

   1. Initial program 87.3%

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

   3. Taylor expanded in x around 0 72.5%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-34} \lor \neg \left(x \leq 3.65 \cdot 10^{-72}\right):\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-34} \lor \neg \left(z \leq 1.3 \cdot 10^{-24}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4e-34) (not (<= z 1.3e-24))) (+ x y) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4e-34) || !(z <= 1.3e-24)) {
		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 ((z <= (-4d-34)) .or. (.not. (z <= 1.3d-24))) 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 ((z <= -4e-34) || !(z <= 1.3e-24)) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4e-34) or not (z <= 1.3e-24):
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4e-34) || !(z <= 1.3e-24))
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4e-34) || ~((z <= 1.3e-24)))
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4e-34], N[Not[LessEqual[z, 1.3e-24]], $MachinePrecision]], N[(x + y), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if z < -3.99999999999999971e-34 or 1.3e-24 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 78.2%

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

      1. +-commutative 78.2%

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

   5. Simplified 78.2%

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

   if -3.99999999999999971e-34 < z < 1.3e-24

   1. Initial program 71.7%

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

   3. Taylor expanded in y around inf 52.2%

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

      1. mul-1-neg 52.2%

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

   5. Simplified 52.2%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-34} \lor \neg \left(z \leq 1.3 \cdot 10^{-24}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 40.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{-152}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-72}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.08e-152) x (if (<= x 5e-72) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.08e-152) {
		tmp = x;
	} else if (x <= 5e-72) {
		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 <= (-1.08d-152)) then
        tmp = x
    else if (x <= 5d-72) 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 <= -1.08e-152) {
		tmp = x;
	} else if (x <= 5e-72) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.08e-152:
		tmp = x
	elif x <= 5e-72:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.08e-152)
		tmp = x;
	elseif (x <= 5e-72)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.08e-152)
		tmp = x;
	elseif (x <= 5e-72)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.08e-152], x, If[LessEqual[x, 5e-72], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.08000000000000004e-152 or 4.9999999999999996e-72 < x

   1. Initial program 87.8%

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

   3. Taylor expanded in y around 0 45.8%

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

   if -1.08000000000000004e-152 < x < 4.9999999999999996e-72

   1. Initial program 89.3%

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

   3. Taylor expanded in x around 0 80.0%

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

   4. Taylor expanded in y around 0 52.7%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{-152}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-72}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 88.2%

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

3. Taylor expanded in y around 0 36.0%

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

4. Final simplification 36.0%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 93.8% 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 2024076 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

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

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