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

Percentage Accurate: 88.2% → 99.3%

Time: 8.0s

Alternatives: 11

Speedup: 0.5×

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: 88.2% 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: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{-249} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-249) (not (<= t_0 0.0))) t_0 (/ (- z) (/ y (+ 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 <= -2e-249) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-2d-249)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = -z / (y / (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 <= -2e-249) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -2e-249) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = -z / (y / (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 <= -2e-249) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) / Float64(y / 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 <= -2e-249) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = -z / (y / (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, -2e-249], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -2.00000000000000011e-249 or 0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.8%

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

   if -2.00000000000000011e-249 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 0.0

   1. Initial program 11.2%

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

   3. Taylor expanded in z around 0 97.3%

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

      1. mul-1-neg 97.3%

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

      2. associate-/l* 100.0%

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

      3. distribute-neg-frac 100.0%

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

      4. +-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-249} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 75.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{\frac{1}{y} - \frac{1}{z}}\\ t_1 := \frac{x}{1 - \frac{y}{z}}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+90}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -29000000:\\ \;\;\;\;\frac{z \cdot \left(-\left(x + y\right)\right)}{y}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-19}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-239}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2400000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+90} \lor \neg \left(y \leq 1.95 \cdot 10^{+237}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ 1.0 (- (/ 1.0 y) (/ 1.0 z)))) (t_1 (/ x (- 1.0 (/ y z)))))
   (if (<= y -2.2e+90)
     t_0
     (if (<= y -29000000.0)
       (/ (* z (- (+ x y))) y)
       (if (<= y -2.9e-19)
         (+ x y)
         (if (<= y -4.3e-98)
           t_1
           (if (<= y -5.8e-239)
             (+ x y)
             (if (<= y 2400000.0)
               t_1
               (if (or (<= y 2.6e+90) (not (<= y 1.95e+237)))
                 t_0
                 (/ (- z) (/ y (+ x y))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 / ((1.0 / y) - (1.0 / z));
	double t_1 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -2.2e+90) {
		tmp = t_0;
	} else if (y <= -29000000.0) {
		tmp = (z * -(x + y)) / y;
	} else if (y <= -2.9e-19) {
		tmp = x + y;
	} else if (y <= -4.3e-98) {
		tmp = t_1;
	} else if (y <= -5.8e-239) {
		tmp = x + y;
	} else if (y <= 2400000.0) {
		tmp = t_1;
	} else if ((y <= 2.6e+90) || !(y <= 1.95e+237)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 / ((1.0d0 / y) - (1.0d0 / z))
    t_1 = x / (1.0d0 - (y / z))
    if (y <= (-2.2d+90)) then
        tmp = t_0
    else if (y <= (-29000000.0d0)) then
        tmp = (z * -(x + y)) / y
    else if (y <= (-2.9d-19)) then
        tmp = x + y
    else if (y <= (-4.3d-98)) then
        tmp = t_1
    else if (y <= (-5.8d-239)) then
        tmp = x + y
    else if (y <= 2400000.0d0) then
        tmp = t_1
    else if ((y <= 2.6d+90) .or. (.not. (y <= 1.95d+237))) then
        tmp = t_0
    else
        tmp = -z / (y / (x + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 / ((1.0 / y) - (1.0 / z));
	double t_1 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -2.2e+90) {
		tmp = t_0;
	} else if (y <= -29000000.0) {
		tmp = (z * -(x + y)) / y;
	} else if (y <= -2.9e-19) {
		tmp = x + y;
	} else if (y <= -4.3e-98) {
		tmp = t_1;
	} else if (y <= -5.8e-239) {
		tmp = x + y;
	} else if (y <= 2400000.0) {
		tmp = t_1;
	} else if ((y <= 2.6e+90) || !(y <= 1.95e+237)) {
		tmp = t_0;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 / ((1.0 / y) - (1.0 / z))
	t_1 = x / (1.0 - (y / z))
	tmp = 0
	if y <= -2.2e+90:
		tmp = t_0
	elif y <= -29000000.0:
		tmp = (z * -(x + y)) / y
	elif y <= -2.9e-19:
		tmp = x + y
	elif y <= -4.3e-98:
		tmp = t_1
	elif y <= -5.8e-239:
		tmp = x + y
	elif y <= 2400000.0:
		tmp = t_1
	elif (y <= 2.6e+90) or not (y <= 1.95e+237):
		tmp = t_0
	else:
		tmp = -z / (y / (x + y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 / Float64(Float64(1.0 / y) - Float64(1.0 / z)))
	t_1 = Float64(x / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (y <= -2.2e+90)
		tmp = t_0;
	elseif (y <= -29000000.0)
		tmp = Float64(Float64(z * Float64(-Float64(x + y))) / y);
	elseif (y <= -2.9e-19)
		tmp = Float64(x + y);
	elseif (y <= -4.3e-98)
		tmp = t_1;
	elseif (y <= -5.8e-239)
		tmp = Float64(x + y);
	elseif (y <= 2400000.0)
		tmp = t_1;
	elseif ((y <= 2.6e+90) || !(y <= 1.95e+237))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) / Float64(y / Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 / ((1.0 / y) - (1.0 / z));
	t_1 = x / (1.0 - (y / z));
	tmp = 0.0;
	if (y <= -2.2e+90)
		tmp = t_0;
	elseif (y <= -29000000.0)
		tmp = (z * -(x + y)) / y;
	elseif (y <= -2.9e-19)
		tmp = x + y;
	elseif (y <= -4.3e-98)
		tmp = t_1;
	elseif (y <= -5.8e-239)
		tmp = x + y;
	elseif (y <= 2400000.0)
		tmp = t_1;
	elseif ((y <= 2.6e+90) || ~((y <= 1.95e+237)))
		tmp = t_0;
	else
		tmp = -z / (y / (x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 / N[(N[(1.0 / y), $MachinePrecision] - N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+90], t$95$0, If[LessEqual[y, -29000000.0], N[(N[(z * (-N[(x + y), $MachinePrecision])), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -2.9e-19], N[(x + y), $MachinePrecision], If[LessEqual[y, -4.3e-98], t$95$1, If[LessEqual[y, -5.8e-239], N[(x + y), $MachinePrecision], If[LessEqual[y, 2400000.0], t$95$1, If[Or[LessEqual[y, 2.6e+90], N[Not[LessEqual[y, 1.95e+237]], $MachinePrecision]], t$95$0, N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.1999999999999999e90 or 2.4e6 < y < 2.5999999999999998e90 or 1.9500000000000001e237 < y

   1. Initial program 78.7%

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

      1. clear-num 78.6%

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

      2. associate-/r/ 78.6%

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

   4. Applied egg-rr 78.6%

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

      1. associate-/r/ 78.6%

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

      2. +-commutative 78.6%

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

   6. Applied egg-rr 78.6%

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

   7. Taylor expanded in z around 0 75.4%

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

   8. Taylor expanded in x around 0 87.7%

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

   if -2.1999999999999999e90 < y < -2.9e7

   1. Initial program 94.7%

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

   3. Taylor expanded in z around 0 74.4%

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

   if -2.9e7 < y < -2.9e-19 or -4.29999999999999988e-98 < y < -5.8000000000000004e-239

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 88.3%

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

      1. +-commutative 88.3%

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

   5. Simplified 88.3%

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

   if -2.9e-19 < y < -4.29999999999999988e-98 or -5.8000000000000004e-239 < y < 2.4e6

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 80.7%

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

   if 2.5999999999999998e90 < y < 1.9500000000000001e237

   1. Initial program 69.1%

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

   3. Taylor expanded in z around 0 87.4%

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

      1. mul-1-neg 87.4%

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

      2. associate-/l* 93.8%

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

      3. distribute-neg-frac 93.8%

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

      4. +-commutative 93.8%

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

   5. Simplified 93.8%

      \[\leadsto \color{blue}{\frac{-z}{\frac{y}{y + x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+90}:\\ \;\;\;\;\frac{1}{\frac{1}{y} - \frac{1}{z}}\\ \mathbf{elif}\;y \leq -29000000:\\ \;\;\;\;\frac{z \cdot \left(-\left(x + y\right)\right)}{y}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-19}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-239}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2400000:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+90} \lor \neg \left(y \leq 1.95 \cdot 10^{+237}\right):\\ \;\;\;\;\frac{1}{\frac{1}{y} - \frac{1}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{x}{t_0}\\ t_2 := \frac{y}{t_0}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+191}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.00186:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-238}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1150000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+92}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ x t_0)) (t_2 (/ y t_0)))
   (if (<= y -4.2e+191)
     (- z)
     (if (<= y -1e+82)
       t_2
       (if (<= y -5.3e+72)
         t_1
         (if (<= y -0.00186)
           t_2
           (if (<= y -3.8e-96)
             t_1
             (if (<= y -1.95e-238)
               (+ x y)
               (if (<= y 1150000.0) t_1 (if (<= y 2.25e+92) t_2 (- z)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = x / t_0;
	double t_2 = y / t_0;
	double tmp;
	if (y <= -4.2e+191) {
		tmp = -z;
	} else if (y <= -1e+82) {
		tmp = t_2;
	} else if (y <= -5.3e+72) {
		tmp = t_1;
	} else if (y <= -0.00186) {
		tmp = t_2;
	} else if (y <= -3.8e-96) {
		tmp = t_1;
	} else if (y <= -1.95e-238) {
		tmp = x + y;
	} else if (y <= 1150000.0) {
		tmp = t_1;
	} else if (y <= 2.25e+92) {
		tmp = t_2;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = x / t_0
    t_2 = y / t_0
    if (y <= (-4.2d+191)) then
        tmp = -z
    else if (y <= (-1d+82)) then
        tmp = t_2
    else if (y <= (-5.3d+72)) then
        tmp = t_1
    else if (y <= (-0.00186d0)) then
        tmp = t_2
    else if (y <= (-3.8d-96)) then
        tmp = t_1
    else if (y <= (-1.95d-238)) then
        tmp = x + y
    else if (y <= 1150000.0d0) then
        tmp = t_1
    else if (y <= 2.25d+92) then
        tmp = t_2
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = x / t_0;
	double t_2 = y / t_0;
	double tmp;
	if (y <= -4.2e+191) {
		tmp = -z;
	} else if (y <= -1e+82) {
		tmp = t_2;
	} else if (y <= -5.3e+72) {
		tmp = t_1;
	} else if (y <= -0.00186) {
		tmp = t_2;
	} else if (y <= -3.8e-96) {
		tmp = t_1;
	} else if (y <= -1.95e-238) {
		tmp = x + y;
	} else if (y <= 1150000.0) {
		tmp = t_1;
	} else if (y <= 2.25e+92) {
		tmp = t_2;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = x / t_0
	t_2 = y / t_0
	tmp = 0
	if y <= -4.2e+191:
		tmp = -z
	elif y <= -1e+82:
		tmp = t_2
	elif y <= -5.3e+72:
		tmp = t_1
	elif y <= -0.00186:
		tmp = t_2
	elif y <= -3.8e-96:
		tmp = t_1
	elif y <= -1.95e-238:
		tmp = x + y
	elif y <= 1150000.0:
		tmp = t_1
	elif y <= 2.25e+92:
		tmp = t_2
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(x / t_0)
	t_2 = Float64(y / t_0)
	tmp = 0.0
	if (y <= -4.2e+191)
		tmp = Float64(-z);
	elseif (y <= -1e+82)
		tmp = t_2;
	elseif (y <= -5.3e+72)
		tmp = t_1;
	elseif (y <= -0.00186)
		tmp = t_2;
	elseif (y <= -3.8e-96)
		tmp = t_1;
	elseif (y <= -1.95e-238)
		tmp = Float64(x + y);
	elseif (y <= 1150000.0)
		tmp = t_1;
	elseif (y <= 2.25e+92)
		tmp = t_2;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = x / t_0;
	t_2 = y / t_0;
	tmp = 0.0;
	if (y <= -4.2e+191)
		tmp = -z;
	elseif (y <= -1e+82)
		tmp = t_2;
	elseif (y <= -5.3e+72)
		tmp = t_1;
	elseif (y <= -0.00186)
		tmp = t_2;
	elseif (y <= -3.8e-96)
		tmp = t_1;
	elseif (y <= -1.95e-238)
		tmp = x + y;
	elseif (y <= 1150000.0)
		tmp = t_1;
	elseif (y <= 2.25e+92)
		tmp = t_2;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(y / t$95$0), $MachinePrecision]}, If[LessEqual[y, -4.2e+191], (-z), If[LessEqual[y, -1e+82], t$95$2, If[LessEqual[y, -5.3e+72], t$95$1, If[LessEqual[y, -0.00186], t$95$2, If[LessEqual[y, -3.8e-96], t$95$1, If[LessEqual[y, -1.95e-238], N[(x + y), $MachinePrecision], If[LessEqual[y, 1150000.0], t$95$1, If[LessEqual[y, 2.25e+92], t$95$2, (-z)]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.2000000000000001e191 or 2.25e92 < y

   1. Initial program 65.9%

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

   3. Taylor expanded in y around inf 84.7%

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

      1. mul-1-neg 84.7%

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

   5. Simplified 84.7%

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

   if -4.2000000000000001e191 < y < -9.9999999999999996e81 or -5.3000000000000003e72 < y < -0.0018600000000000001 or 1.15e6 < y < 2.25e92

   1. Initial program 95.0%

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

   3. Taylor expanded in x around 0 73.0%

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

   if -9.9999999999999996e81 < y < -5.3000000000000003e72 or -0.0018600000000000001 < y < -3.8000000000000001e-96 or -1.9499999999999999e-238 < y < 1.15e6

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 80.9%

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

   if -3.8000000000000001e-96 < y < -1.9499999999999999e-238

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 88.8%

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

      1. +-commutative 88.8%

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

   5. Simplified 88.8%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+191}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+82}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -0.00186:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-96}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-238}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1150000:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+92}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{y}{t_0}\\ t_2 := \frac{x}{t_0}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+192}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -48000000:\\ \;\;\;\;\left(x + y\right) \cdot \left(-\frac{z}{y}\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-19}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-238}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 440000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ y t_0)) (t_2 (/ x t_0)))
   (if (<= y -3.8e+192)
     (- z)
     (if (<= y -6e+87)
       t_1
       (if (<= y -48000000.0)
         (* (+ x y) (- (/ z y)))
         (if (<= y -2.3e-19)
           (+ x y)
           (if (<= y -4.6e-96)
             t_2
             (if (<= y -5e-238)
               (+ x y)
               (if (<= y 440000.0) t_2 (if (<= y 4.6e+92) t_1 (- z)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = y / t_0;
	double t_2 = x / t_0;
	double tmp;
	if (y <= -3.8e+192) {
		tmp = -z;
	} else if (y <= -6e+87) {
		tmp = t_1;
	} else if (y <= -48000000.0) {
		tmp = (x + y) * -(z / y);
	} else if (y <= -2.3e-19) {
		tmp = x + y;
	} else if (y <= -4.6e-96) {
		tmp = t_2;
	} else if (y <= -5e-238) {
		tmp = x + y;
	} else if (y <= 440000.0) {
		tmp = t_2;
	} else if (y <= 4.6e+92) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = y / t_0
    t_2 = x / t_0
    if (y <= (-3.8d+192)) then
        tmp = -z
    else if (y <= (-6d+87)) then
        tmp = t_1
    else if (y <= (-48000000.0d0)) then
        tmp = (x + y) * -(z / y)
    else if (y <= (-2.3d-19)) then
        tmp = x + y
    else if (y <= (-4.6d-96)) then
        tmp = t_2
    else if (y <= (-5d-238)) then
        tmp = x + y
    else if (y <= 440000.0d0) then
        tmp = t_2
    else if (y <= 4.6d+92) then
        tmp = t_1
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = y / t_0;
	double t_2 = x / t_0;
	double tmp;
	if (y <= -3.8e+192) {
		tmp = -z;
	} else if (y <= -6e+87) {
		tmp = t_1;
	} else if (y <= -48000000.0) {
		tmp = (x + y) * -(z / y);
	} else if (y <= -2.3e-19) {
		tmp = x + y;
	} else if (y <= -4.6e-96) {
		tmp = t_2;
	} else if (y <= -5e-238) {
		tmp = x + y;
	} else if (y <= 440000.0) {
		tmp = t_2;
	} else if (y <= 4.6e+92) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = y / t_0
	t_2 = x / t_0
	tmp = 0
	if y <= -3.8e+192:
		tmp = -z
	elif y <= -6e+87:
		tmp = t_1
	elif y <= -48000000.0:
		tmp = (x + y) * -(z / y)
	elif y <= -2.3e-19:
		tmp = x + y
	elif y <= -4.6e-96:
		tmp = t_2
	elif y <= -5e-238:
		tmp = x + y
	elif y <= 440000.0:
		tmp = t_2
	elif y <= 4.6e+92:
		tmp = t_1
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(y / t_0)
	t_2 = Float64(x / t_0)
	tmp = 0.0
	if (y <= -3.8e+192)
		tmp = Float64(-z);
	elseif (y <= -6e+87)
		tmp = t_1;
	elseif (y <= -48000000.0)
		tmp = Float64(Float64(x + y) * Float64(-Float64(z / y)));
	elseif (y <= -2.3e-19)
		tmp = Float64(x + y);
	elseif (y <= -4.6e-96)
		tmp = t_2;
	elseif (y <= -5e-238)
		tmp = Float64(x + y);
	elseif (y <= 440000.0)
		tmp = t_2;
	elseif (y <= 4.6e+92)
		tmp = t_1;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = y / t_0;
	t_2 = x / t_0;
	tmp = 0.0;
	if (y <= -3.8e+192)
		tmp = -z;
	elseif (y <= -6e+87)
		tmp = t_1;
	elseif (y <= -48000000.0)
		tmp = (x + y) * -(z / y);
	elseif (y <= -2.3e-19)
		tmp = x + y;
	elseif (y <= -4.6e-96)
		tmp = t_2;
	elseif (y <= -5e-238)
		tmp = x + y;
	elseif (y <= 440000.0)
		tmp = t_2;
	elseif (y <= 4.6e+92)
		tmp = t_1;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y / t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(x / t$95$0), $MachinePrecision]}, If[LessEqual[y, -3.8e+192], (-z), If[LessEqual[y, -6e+87], t$95$1, If[LessEqual[y, -48000000.0], N[(N[(x + y), $MachinePrecision] * (-N[(z / y), $MachinePrecision])), $MachinePrecision], If[LessEqual[y, -2.3e-19], N[(x + y), $MachinePrecision], If[LessEqual[y, -4.6e-96], t$95$2, If[LessEqual[y, -5e-238], N[(x + y), $MachinePrecision], If[LessEqual[y, 440000.0], t$95$2, If[LessEqual[y, 4.6e+92], t$95$1, (-z)]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.7999999999999999e192 or 4.59999999999999997e92 < y

   1. Initial program 65.9%

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

   3. Taylor expanded in y around inf 84.7%

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

      1. mul-1-neg 84.7%

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

   5. Simplified 84.7%

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

   if -3.7999999999999999e192 < y < -5.9999999999999998e87 or 4.4e5 < y < 4.59999999999999997e92

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0 73.5%

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

   if -5.9999999999999998e87 < y < -4.8e7

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. associate-/l* 75.4%

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

      3. associate-/r/ 75.6%

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

      4. distribute-rgt-neg-in 75.6%

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

      5. +-commutative 75.6%

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

      6. distribute-neg-in 75.6%

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

      7. sub-neg 75.6%

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

   5. Simplified 75.6%

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

   if -4.8e7 < y < -2.2999999999999998e-19 or -4.6e-96 < y < -5e-238

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 88.3%

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

      1. +-commutative 88.3%

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

   5. Simplified 88.3%

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

   if -2.2999999999999998e-19 < y < -4.6e-96 or -5e-238 < y < 4.4e5

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 80.7%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+192}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+87}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -48000000:\\ \;\;\;\;\left(x + y\right) \cdot \left(-\frac{z}{y}\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-19}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-96}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-238}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 440000:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+92}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-z}{\frac{y}{x + y}}\\ t_1 := 1 - \frac{y}{z}\\ \mathbf{if}\;y \leq -0.007:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-20}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-79}:\\ \;\;\;\;\left(x + y\right) \cdot \left(-\frac{z}{y}\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-238}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 195000:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+86}:\\ \;\;\;\;\frac{y}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- z) (/ y (+ x y)))) (t_1 (- 1.0 (/ y z))))
   (if (<= y -0.007)
     t_0
     (if (<= y -8e-20)
       (+ x y)
       (if (<= y -2.1e-79)
         (* (+ x y) (- (/ z y)))
         (if (<= y -2.3e-238)
           (+ x y)
           (if (<= y 195000.0)
             (/ x t_1)
             (if (<= y 6.8e+86) (/ y t_1) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = -z / (y / (x + y));
	double t_1 = 1.0 - (y / z);
	double tmp;
	if (y <= -0.007) {
		tmp = t_0;
	} else if (y <= -8e-20) {
		tmp = x + y;
	} else if (y <= -2.1e-79) {
		tmp = (x + y) * -(z / y);
	} else if (y <= -2.3e-238) {
		tmp = x + y;
	} else if (y <= 195000.0) {
		tmp = x / t_1;
	} else if (y <= 6.8e+86) {
		tmp = y / t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = -z / (y / (x + y))
    t_1 = 1.0d0 - (y / z)
    if (y <= (-0.007d0)) then
        tmp = t_0
    else if (y <= (-8d-20)) then
        tmp = x + y
    else if (y <= (-2.1d-79)) then
        tmp = (x + y) * -(z / y)
    else if (y <= (-2.3d-238)) then
        tmp = x + y
    else if (y <= 195000.0d0) then
        tmp = x / t_1
    else if (y <= 6.8d+86) then
        tmp = y / t_1
    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 / (y / (x + y));
	double t_1 = 1.0 - (y / z);
	double tmp;
	if (y <= -0.007) {
		tmp = t_0;
	} else if (y <= -8e-20) {
		tmp = x + y;
	} else if (y <= -2.1e-79) {
		tmp = (x + y) * -(z / y);
	} else if (y <= -2.3e-238) {
		tmp = x + y;
	} else if (y <= 195000.0) {
		tmp = x / t_1;
	} else if (y <= 6.8e+86) {
		tmp = y / t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -z / (y / (x + y))
	t_1 = 1.0 - (y / z)
	tmp = 0
	if y <= -0.007:
		tmp = t_0
	elif y <= -8e-20:
		tmp = x + y
	elif y <= -2.1e-79:
		tmp = (x + y) * -(z / y)
	elif y <= -2.3e-238:
		tmp = x + y
	elif y <= 195000.0:
		tmp = x / t_1
	elif y <= 6.8e+86:
		tmp = y / t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-z) / Float64(y / Float64(x + y)))
	t_1 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if (y <= -0.007)
		tmp = t_0;
	elseif (y <= -8e-20)
		tmp = Float64(x + y);
	elseif (y <= -2.1e-79)
		tmp = Float64(Float64(x + y) * Float64(-Float64(z / y)));
	elseif (y <= -2.3e-238)
		tmp = Float64(x + y);
	elseif (y <= 195000.0)
		tmp = Float64(x / t_1);
	elseif (y <= 6.8e+86)
		tmp = Float64(y / t_1);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -z / (y / (x + y));
	t_1 = 1.0 - (y / z);
	tmp = 0.0;
	if (y <= -0.007)
		tmp = t_0;
	elseif (y <= -8e-20)
		tmp = x + y;
	elseif (y <= -2.1e-79)
		tmp = (x + y) * -(z / y);
	elseif (y <= -2.3e-238)
		tmp = x + y;
	elseif (y <= 195000.0)
		tmp = x / t_1;
	elseif (y <= 6.8e+86)
		tmp = y / t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.007], t$95$0, If[LessEqual[y, -8e-20], N[(x + y), $MachinePrecision], If[LessEqual[y, -2.1e-79], N[(N[(x + y), $MachinePrecision] * (-N[(z / y), $MachinePrecision])), $MachinePrecision], If[LessEqual[y, -2.3e-238], N[(x + y), $MachinePrecision], If[LessEqual[y, 195000.0], N[(x / t$95$1), $MachinePrecision], If[LessEqual[y, 6.8e+86], N[(y / t$95$1), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -0.00700000000000000015 or 6.7999999999999995e86 < y

   1. Initial program 76.6%

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

   3. Taylor expanded in z around 0 64.1%

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

      1. mul-1-neg 64.1%

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

      2. associate-/l* 82.0%

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

      3. distribute-neg-frac 82.0%

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

      4. +-commutative 82.0%

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

   5. Simplified 82.0%

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

   if -0.00700000000000000015 < y < -7.99999999999999956e-20 or -2.0999999999999999e-79 < y < -2.30000000000000005e-238

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 87.9%

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

      1. +-commutative 87.9%

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

   5. Simplified 87.9%

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

   if -7.99999999999999956e-20 < y < -2.0999999999999999e-79

   1. Initial program 99.5%

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

   3. Taylor expanded in z around 0 71.3%

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

      1. mul-1-neg 71.3%

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

      2. associate-/l* 61.4%

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

      3. associate-/r/ 71.3%

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

      4. distribute-rgt-neg-in 71.3%

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

      5. +-commutative 71.3%

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

      6. distribute-neg-in 71.3%

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

      7. sub-neg 71.3%

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

   5. Simplified 71.3%

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

   if -2.30000000000000005e-238 < y < 195000

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 81.5%

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

   if 195000 < y < 6.7999999999999995e86

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 81.2%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{y}{z}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.007:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-20}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-79}:\\ \;\;\;\;\left(x + y\right) \cdot \left(-\frac{z}{y}\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-238}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 195000:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+86}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - \frac{y}{z}}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+153}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+84}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{-98}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-239}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-13}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+86}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 (/ y z)))))
   (if (<= y -1.05e+153)
     (- z)
     (if (<= y -3.4e+84)
       (+ x y)
       (if (<= y -5.7e-98)
         t_0
         (if (<= y -5.8e-239)
           (+ x y)
           (if (<= y 8e-13) t_0 (if (<= y 4.2e+86) (+ x y) (- z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -1.05e+153) {
		tmp = -z;
	} else if (y <= -3.4e+84) {
		tmp = x + y;
	} else if (y <= -5.7e-98) {
		tmp = t_0;
	} else if (y <= -5.8e-239) {
		tmp = x + y;
	} else if (y <= 8e-13) {
		tmp = t_0;
	} else if (y <= 4.2e+86) {
		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) :: t_0
    real(8) :: tmp
    t_0 = x / (1.0d0 - (y / z))
    if (y <= (-1.05d+153)) then
        tmp = -z
    else if (y <= (-3.4d+84)) then
        tmp = x + y
    else if (y <= (-5.7d-98)) then
        tmp = t_0
    else if (y <= (-5.8d-239)) then
        tmp = x + y
    else if (y <= 8d-13) then
        tmp = t_0
    else if (y <= 4.2d+86) 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 t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -1.05e+153) {
		tmp = -z;
	} else if (y <= -3.4e+84) {
		tmp = x + y;
	} else if (y <= -5.7e-98) {
		tmp = t_0;
	} else if (y <= -5.8e-239) {
		tmp = x + y;
	} else if (y <= 8e-13) {
		tmp = t_0;
	} else if (y <= 4.2e+86) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (1.0 - (y / z))
	tmp = 0
	if y <= -1.05e+153:
		tmp = -z
	elif y <= -3.4e+84:
		tmp = x + y
	elif y <= -5.7e-98:
		tmp = t_0
	elif y <= -5.8e-239:
		tmp = x + y
	elif y <= 8e-13:
		tmp = t_0
	elif y <= 4.2e+86:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (y <= -1.05e+153)
		tmp = Float64(-z);
	elseif (y <= -3.4e+84)
		tmp = Float64(x + y);
	elseif (y <= -5.7e-98)
		tmp = t_0;
	elseif (y <= -5.8e-239)
		tmp = Float64(x + y);
	elseif (y <= 8e-13)
		tmp = t_0;
	elseif (y <= 4.2e+86)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (1.0 - (y / z));
	tmp = 0.0;
	if (y <= -1.05e+153)
		tmp = -z;
	elseif (y <= -3.4e+84)
		tmp = x + y;
	elseif (y <= -5.7e-98)
		tmp = t_0;
	elseif (y <= -5.8e-239)
		tmp = x + y;
	elseif (y <= 8e-13)
		tmp = t_0;
	elseif (y <= 4.2e+86)
		tmp = x + y;
	else
		tmp = -z;
	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[y, -1.05e+153], (-z), If[LessEqual[y, -3.4e+84], N[(x + y), $MachinePrecision], If[LessEqual[y, -5.7e-98], t$95$0, If[LessEqual[y, -5.8e-239], N[(x + y), $MachinePrecision], If[LessEqual[y, 8e-13], t$95$0, If[LessEqual[y, 4.2e+86], N[(x + y), $MachinePrecision], (-z)]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05000000000000008e153 or 4.1999999999999998e86 < y

   1. Initial program 70.1%

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

   3. Taylor expanded in y around inf 81.7%

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

      1. mul-1-neg 81.7%

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

   5. Simplified 81.7%

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

   if -1.05000000000000008e153 < y < -3.3999999999999998e84 or -5.6999999999999998e-98 < y < -5.8000000000000004e-239 or 8.0000000000000002e-13 < y < 4.1999999999999998e86

   1. Initial program 95.5%

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

   3. Taylor expanded in z around inf 73.0%

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

      1. +-commutative 73.0%

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

   5. Simplified 73.0%

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

   if -3.3999999999999998e84 < y < -5.6999999999999998e-98 or -5.8000000000000004e-239 < y < 8.0000000000000002e-13

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 74.3%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+153}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+84}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-239}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+86}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+153} \lor \neg \left(y \leq -4.6 \cdot 10^{+71} \lor \neg \left(y \leq -1.4 \cdot 10^{+23}\right) \land y \leq 7.5 \cdot 10^{+89}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.05e+153)
         (not (or (<= y -4.6e+71) (and (not (<= y -1.4e+23)) (<= y 7.5e+89)))))
   (- z)
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.05e+153) || !((y <= -4.6e+71) || (!(y <= -1.4e+23) && (y <= 7.5e+89)))) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.05d+153)) .or. (.not. (y <= (-4.6d+71)) .or. (.not. (y <= (-1.4d+23))) .and. (y <= 7.5d+89))) then
        tmp = -z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.05e+153) || !((y <= -4.6e+71) || (!(y <= -1.4e+23) && (y <= 7.5e+89)))) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.05e+153) or not ((y <= -4.6e+71) or (not (y <= -1.4e+23) and (y <= 7.5e+89))):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.05e+153) || !((y <= -4.6e+71) || (!(y <= -1.4e+23) && (y <= 7.5e+89))))
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.05e+153) || ~(((y <= -4.6e+71) || (~((y <= -1.4e+23)) && (y <= 7.5e+89)))))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.05e+153], N[Not[Or[LessEqual[y, -4.6e+71], And[N[Not[LessEqual[y, -1.4e+23]], $MachinePrecision], LessEqual[y, 7.5e+89]]]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05000000000000008e153 or -4.6000000000000005e71 < y < -1.4e23 or 7.49999999999999947e89 < y

   1. Initial program 72.3%

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

   3. Taylor expanded in y around inf 81.9%

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

      1. mul-1-neg 81.9%

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

   5. Simplified 81.9%

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

   if -1.05000000000000008e153 < y < -4.6000000000000005e71 or -1.4e23 < y < 7.49999999999999947e89

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 67.4%

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

      1. +-commutative 67.4%

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

   5. Simplified 67.4%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+153} \lor \neg \left(y \leq -4.6 \cdot 10^{+71} \lor \neg \left(y \leq -1.4 \cdot 10^{+23}\right) \land y \leq 7.5 \cdot 10^{+89}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.4%

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

   1. clear-num 88.2%

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

   2. associate-/r/ 88.3%

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

4. Applied egg-rr 88.3%

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

   1. associate-/r/ 88.2%

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

   2. +-commutative 88.2%

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

6. Applied egg-rr 88.2%

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

7. Taylor expanded in z around 0 87.5%

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

   1. clear-num 87.5%

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

   2. inv-pow 87.5%

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

   3. +-commutative 87.5%

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

   4. *-commutative 87.5%

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

   5. associate-/l* 88.2%

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

9. Applied egg-rr 88.2%

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

    1. unpow-1 88.2%

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

    2. associate-/r/ 97.0%

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

    3. *-commutative 97.0%

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

    4. +-commutative 97.0%

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

11. Simplified 97.0%

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

12. Final simplification 97.0%

    \[\leadsto \frac{1}{\frac{-1}{z \cdot \frac{x + y}{y}} + \frac{1}{x + y}} \]
13. Add Preprocessing

Alternative 9: 58.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00055 \lor \neg \left(y \leq 380000\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00055) (not (<= y 380000.0))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00055) || !(y <= 380000.0)) {
		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 <= (-0.00055d0)) .or. (.not. (y <= 380000.0d0))) 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 <= -0.00055) || !(y <= 380000.0)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.00055) or not (y <= 380000.0):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00055) || !(y <= 380000.0))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.00055) || ~((y <= 380000.0)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00055], N[Not[LessEqual[y, 380000.0]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -5.50000000000000033e-4 or 3.8e5 < y

   1. Initial program 79.2%

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

   3. Taylor expanded in y around inf 64.5%

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

      1. mul-1-neg 64.5%

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

   5. Simplified 64.5%

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

   if -5.50000000000000033e-4 < y < 3.8e5

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 56.7%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00055 \lor \neg \left(y \leq 380000\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 40.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-176}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.5e-126) x (if (<= x 7.8e-176) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.5e-126) {
		tmp = x;
	} else if (x <= 7.8e-176) {
		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 <= (-1.5d-126)) then
        tmp = x
    else if (x <= 7.8d-176) 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 <= -1.5e-126) {
		tmp = x;
	} else if (x <= 7.8e-176) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.5e-126:
		tmp = x
	elif x <= 7.8e-176:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.5e-126)
		tmp = x;
	elseif (x <= 7.8e-176)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.5e-126)
		tmp = x;
	elseif (x <= 7.8e-176)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.5e-126], x, If[LessEqual[x, 7.8e-176], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5000000000000001e-126 or 7.7999999999999994e-176 < x

   1. Initial program 89.2%

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

   3. Taylor expanded in y around 0 38.0%

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

   if -1.5000000000000001e-126 < x < 7.7999999999999994e-176

   1. Initial program 86.3%

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

   3. Taylor expanded in x around 0 77.1%

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

   4. Taylor expanded in y around 0 42.4%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-176}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 34.7% 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 88.4%

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

3. Taylor expanded in y around 0 30.6%

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

4. Final simplification 30.6%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 93.6% 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 2024019 
(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))))