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

Percentage Accurate: 87.9% → 99.1%

Time: 6.0s

Alternatives: 11

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 87.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{-281} \lor \neg \left(t_0 \leq 5 \cdot 10^{-241}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -5e-281) (not (<= t_0 5e-241)))
     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 <= -5e-281) || !(t_0 <= 5e-241)) {
		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 <= (-5d-281)) .or. (.not. (t_0 <= 5d-241))) 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 <= -5e-281) || !(t_0 <= 5e-241)) {
		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 <= -5e-281) or not (t_0 <= 5e-241):
		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 <= -5e-281) || !(t_0 <= 5e-241))
		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 <= -5e-281) || ~((t_0 <= 5e-241)))
		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, -5e-281], N[Not[LessEqual[t$95$0, 5e-241]], $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))) < -4.9999999999999998e-281 or 4.9999999999999998e-241 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

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

   if -4.9999999999999998e-281 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 4.9999999999999998e-241

   1. Initial program 19.3%

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

   3. Taylor expanded in z around 0 92.3%

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

      1. mul-1-neg 92.3%

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

      2. associate-/l* 99.9%

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

      3. distribute-neg-frac 99.9%

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

      4. +-commutative 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-281} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 5 \cdot 10^{-241}\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 66.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{x}{t_0}\\ \mathbf{if}\;y \leq -4.9 \cdot 10^{+129}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{+91}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+74}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -5.9 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-21}:\\ \;\;\;\;\frac{y}{t_0}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+173}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ x t_0)))
   (if (<= y -4.9e+129)
     (- z)
     (if (<= y -4.3e+112)
       t_1
       (if (<= y -1.42e+91)
         (- z)
         (if (<= y -3.5e+74)
           (* (- z) (/ x y))
           (if (<= y -5.9e+62)
             t_1
             (if (<= y -1.05e-21)
               (/ y t_0)
               (if (<= y 1.2e+173) (+ x y) (- z))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = x / t_0;
	double tmp;
	if (y <= -4.9e+129) {
		tmp = -z;
	} else if (y <= -4.3e+112) {
		tmp = t_1;
	} else if (y <= -1.42e+91) {
		tmp = -z;
	} else if (y <= -3.5e+74) {
		tmp = -z * (x / y);
	} else if (y <= -5.9e+62) {
		tmp = t_1;
	} else if (y <= -1.05e-21) {
		tmp = y / t_0;
	} else if (y <= 1.2e+173) {
		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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = x / t_0
    if (y <= (-4.9d+129)) then
        tmp = -z
    else if (y <= (-4.3d+112)) then
        tmp = t_1
    else if (y <= (-1.42d+91)) then
        tmp = -z
    else if (y <= (-3.5d+74)) then
        tmp = -z * (x / y)
    else if (y <= (-5.9d+62)) then
        tmp = t_1
    else if (y <= (-1.05d-21)) then
        tmp = y / t_0
    else if (y <= 1.2d+173) 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 = 1.0 - (y / z);
	double t_1 = x / t_0;
	double tmp;
	if (y <= -4.9e+129) {
		tmp = -z;
	} else if (y <= -4.3e+112) {
		tmp = t_1;
	} else if (y <= -1.42e+91) {
		tmp = -z;
	} else if (y <= -3.5e+74) {
		tmp = -z * (x / y);
	} else if (y <= -5.9e+62) {
		tmp = t_1;
	} else if (y <= -1.05e-21) {
		tmp = y / t_0;
	} else if (y <= 1.2e+173) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = x / t_0
	tmp = 0
	if y <= -4.9e+129:
		tmp = -z
	elif y <= -4.3e+112:
		tmp = t_1
	elif y <= -1.42e+91:
		tmp = -z
	elif y <= -3.5e+74:
		tmp = -z * (x / y)
	elif y <= -5.9e+62:
		tmp = t_1
	elif y <= -1.05e-21:
		tmp = y / t_0
	elif y <= 1.2e+173:
		tmp = x + y
	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)
	tmp = 0.0
	if (y <= -4.9e+129)
		tmp = Float64(-z);
	elseif (y <= -4.3e+112)
		tmp = t_1;
	elseif (y <= -1.42e+91)
		tmp = Float64(-z);
	elseif (y <= -3.5e+74)
		tmp = Float64(Float64(-z) * Float64(x / y));
	elseif (y <= -5.9e+62)
		tmp = t_1;
	elseif (y <= -1.05e-21)
		tmp = Float64(y / t_0);
	elseif (y <= 1.2e+173)
		tmp = Float64(x + y);
	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;
	tmp = 0.0;
	if (y <= -4.9e+129)
		tmp = -z;
	elseif (y <= -4.3e+112)
		tmp = t_1;
	elseif (y <= -1.42e+91)
		tmp = -z;
	elseif (y <= -3.5e+74)
		tmp = -z * (x / y);
	elseif (y <= -5.9e+62)
		tmp = t_1;
	elseif (y <= -1.05e-21)
		tmp = y / t_0;
	elseif (y <= 1.2e+173)
		tmp = x + y;
	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]}, If[LessEqual[y, -4.9e+129], (-z), If[LessEqual[y, -4.3e+112], t$95$1, If[LessEqual[y, -1.42e+91], (-z), If[LessEqual[y, -3.5e+74], N[((-z) * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.9e+62], t$95$1, If[LessEqual[y, -1.05e-21], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, 1.2e+173], N[(x + y), $MachinePrecision], (-z)]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.9e129 or -4.29999999999999983e112 < y < -1.41999999999999995e91 or 1.2e173 < y

   1. Initial program 54.7%

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

   3. Taylor expanded in y around inf 79.3%

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

      1. mul-1-neg 79.3%

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

   5. Simplified 79.3%

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

   if -4.9e129 < y < -4.29999999999999983e112 or -3.50000000000000014e74 < y < -5.9000000000000003e62

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 87.4%

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

   if -1.41999999999999995e91 < y < -3.50000000000000014e74

   1. Initial program 52.3%

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

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

      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%

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

      1. clear-num 100.0%

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

      2. associate-/r/ 99.2%

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

   7. Applied egg-rr 99.2%

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

   8. Taylor expanded in y around 0 99.2%

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

      1. mul-1-neg 99.2%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

      4. distribute-lft-neg-in 100.0%

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

   10. Simplified 100.0%

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

   if -5.9000000000000003e62 < y < -1.05000000000000006e-21

   1. Initial program 95.4%

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

   3. Taylor expanded in x around 0 69.3%

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

   if -1.05000000000000006e-21 < y < 1.2e173

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf 75.9%

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

      1. +-commutative 75.9%

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

   5. Simplified 75.9%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+129}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{+112}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{+91}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+74}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -5.9 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-21}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+173}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+129}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+115}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+87}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+81}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-23}:\\ \;\;\;\;\frac{z}{y} \cdot \left(\left(-x\right) - y\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+173}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.9e+129)
   (- z)
   (if (<= y -3.6e+115)
     (/ x (- 1.0 (/ y z)))
     (if (<= y -1.6e+87)
       (- z)
       (if (<= y -4.5e+81)
         (* (- z) (/ x y))
         (if (<= y -2.1e-23)
           (* (/ z y) (- (- x) y))
           (if (<= y 6.5e+173) (+ x y) (- z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.9e+129) {
		tmp = -z;
	} else if (y <= -3.6e+115) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= -1.6e+87) {
		tmp = -z;
	} else if (y <= -4.5e+81) {
		tmp = -z * (x / y);
	} else if (y <= -2.1e-23) {
		tmp = (z / y) * (-x - y);
	} else if (y <= 6.5e+173) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4.9d+129)) then
        tmp = -z
    else if (y <= (-3.6d+115)) then
        tmp = x / (1.0d0 - (y / z))
    else if (y <= (-1.6d+87)) then
        tmp = -z
    else if (y <= (-4.5d+81)) then
        tmp = -z * (x / y)
    else if (y <= (-2.1d-23)) then
        tmp = (z / y) * (-x - y)
    else if (y <= 6.5d+173) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.9e+129) {
		tmp = -z;
	} else if (y <= -3.6e+115) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= -1.6e+87) {
		tmp = -z;
	} else if (y <= -4.5e+81) {
		tmp = -z * (x / y);
	} else if (y <= -2.1e-23) {
		tmp = (z / y) * (-x - y);
	} else if (y <= 6.5e+173) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.9e+129:
		tmp = -z
	elif y <= -3.6e+115:
		tmp = x / (1.0 - (y / z))
	elif y <= -1.6e+87:
		tmp = -z
	elif y <= -4.5e+81:
		tmp = -z * (x / y)
	elif y <= -2.1e-23:
		tmp = (z / y) * (-x - y)
	elif y <= 6.5e+173:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.9e+129)
		tmp = Float64(-z);
	elseif (y <= -3.6e+115)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (y <= -1.6e+87)
		tmp = Float64(-z);
	elseif (y <= -4.5e+81)
		tmp = Float64(Float64(-z) * Float64(x / y));
	elseif (y <= -2.1e-23)
		tmp = Float64(Float64(z / y) * Float64(Float64(-x) - y));
	elseif (y <= 6.5e+173)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.9e+129)
		tmp = -z;
	elseif (y <= -3.6e+115)
		tmp = x / (1.0 - (y / z));
	elseif (y <= -1.6e+87)
		tmp = -z;
	elseif (y <= -4.5e+81)
		tmp = -z * (x / y);
	elseif (y <= -2.1e-23)
		tmp = (z / y) * (-x - y);
	elseif (y <= 6.5e+173)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.9e+129], (-z), If[LessEqual[y, -3.6e+115], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.6e+87], (-z), If[LessEqual[y, -4.5e+81], N[((-z) * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.1e-23], N[(N[(z / y), $MachinePrecision] * N[((-x) - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+173], N[(x + y), $MachinePrecision], (-z)]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.9e129 or -3.6000000000000001e115 < y < -1.6e87 or 6.4999999999999997e173 < y

   1. Initial program 54.7%

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

   3. Taylor expanded in y around inf 79.3%

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

      1. mul-1-neg 79.3%

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

   5. Simplified 79.3%

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

   if -4.9e129 < y < -3.6000000000000001e115

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 83.2%

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

   if -1.6e87 < y < -4.50000000000000017e81

   1. Initial program 52.3%

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

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

      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%

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

      1. clear-num 100.0%

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

      2. associate-/r/ 99.2%

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

   7. Applied egg-rr 99.2%

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

   8. Taylor expanded in y around 0 99.2%

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

      1. mul-1-neg 99.2%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

      4. distribute-lft-neg-in 100.0%

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

   10. Simplified 100.0%

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

   if -4.50000000000000017e81 < y < -2.1000000000000001e-23

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0 78.5%

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

      1. mul-1-neg 78.5%

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

      2. associate-/l* 78.5%

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

      3. associate-/r/ 74.6%

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

      4. distribute-rgt-neg-in 74.6%

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

      5. +-commutative 74.6%

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

      6. distribute-neg-in 74.6%

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

      7. sub-neg 74.6%

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

   5. Simplified 74.6%

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

   if -2.1000000000000001e-23 < y < 6.4999999999999997e173

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf 75.9%

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

      1. +-commutative 75.9%

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

   5. Simplified 75.9%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+129}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+115}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+87}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+81}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-23}:\\ \;\;\;\;\frac{z}{y} \cdot \left(\left(-x\right) - y\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+173}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+129}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+122}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+87}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+73}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+39} \lor \neg \left(y \leq -1.55 \cdot 10^{-22}\right) \land y \leq 1.16 \cdot 10^{+173}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.2e+129)
   (- z)
   (if (<= y -4.5e+122)
     (/ x (- 1.0 (/ y z)))
     (if (<= y -1.85e+87)
       (- z)
       (if (<= y -1.6e+73)
         (* (- z) (/ x y))
         (if (or (<= y -7e+39) (and (not (<= y -1.55e-22)) (<= y 1.16e+173)))
           (+ x y)
           (- z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.2e+129) {
		tmp = -z;
	} else if (y <= -4.5e+122) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= -1.85e+87) {
		tmp = -z;
	} else if (y <= -1.6e+73) {
		tmp = -z * (x / y);
	} else if ((y <= -7e+39) || (!(y <= -1.55e-22) && (y <= 1.16e+173))) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.2d+129)) then
        tmp = -z
    else if (y <= (-4.5d+122)) then
        tmp = x / (1.0d0 - (y / z))
    else if (y <= (-1.85d+87)) then
        tmp = -z
    else if (y <= (-1.6d+73)) then
        tmp = -z * (x / y)
    else if ((y <= (-7d+39)) .or. (.not. (y <= (-1.55d-22))) .and. (y <= 1.16d+173)) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.2e+129) {
		tmp = -z;
	} else if (y <= -4.5e+122) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= -1.85e+87) {
		tmp = -z;
	} else if (y <= -1.6e+73) {
		tmp = -z * (x / y);
	} else if ((y <= -7e+39) || (!(y <= -1.55e-22) && (y <= 1.16e+173))) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.2e+129:
		tmp = -z
	elif y <= -4.5e+122:
		tmp = x / (1.0 - (y / z))
	elif y <= -1.85e+87:
		tmp = -z
	elif y <= -1.6e+73:
		tmp = -z * (x / y)
	elif (y <= -7e+39) or (not (y <= -1.55e-22) and (y <= 1.16e+173)):
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.2e+129)
		tmp = Float64(-z);
	elseif (y <= -4.5e+122)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (y <= -1.85e+87)
		tmp = Float64(-z);
	elseif (y <= -1.6e+73)
		tmp = Float64(Float64(-z) * Float64(x / y));
	elseif ((y <= -7e+39) || (!(y <= -1.55e-22) && (y <= 1.16e+173)))
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.2e+129)
		tmp = -z;
	elseif (y <= -4.5e+122)
		tmp = x / (1.0 - (y / z));
	elseif (y <= -1.85e+87)
		tmp = -z;
	elseif (y <= -1.6e+73)
		tmp = -z * (x / y);
	elseif ((y <= -7e+39) || (~((y <= -1.55e-22)) && (y <= 1.16e+173)))
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.2e+129], (-z), If[LessEqual[y, -4.5e+122], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.85e+87], (-z), If[LessEqual[y, -1.6e+73], N[((-z) * N[(x / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -7e+39], And[N[Not[LessEqual[y, -1.55e-22]], $MachinePrecision], LessEqual[y, 1.16e+173]]], N[(x + y), $MachinePrecision], (-z)]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.20000000000000024e129 or -4.49999999999999997e122 < y < -1.85000000000000001e87 or -7.0000000000000003e39 < y < -1.55000000000000006e-22 or 1.16e173 < y

   1. Initial program 62.9%

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

   3. Taylor expanded in y around inf 77.6%

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

      1. mul-1-neg 77.6%

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

   5. Simplified 77.6%

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

   if -5.20000000000000024e129 < y < -4.49999999999999997e122

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 83.2%

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

   if -1.85000000000000001e87 < y < -1.59999999999999991e73

   1. Initial program 52.3%

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

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

      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%

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

      1. clear-num 100.0%

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

      2. associate-/r/ 99.2%

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

   7. Applied egg-rr 99.2%

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

   8. Taylor expanded in y around 0 99.2%

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

      1. mul-1-neg 99.2%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

      4. distribute-lft-neg-in 100.0%

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

   10. Simplified 100.0%

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

   if -1.59999999999999991e73 < y < -7.0000000000000003e39 or -1.55000000000000006e-22 < y < 1.16e173

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf 75.9%

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

      1. +-commutative 75.9%

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

   5. Simplified 75.9%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+129}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+122}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+87}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+73}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+39} \lor \neg \left(y \leq -1.55 \cdot 10^{-22}\right) \land y \leq 1.16 \cdot 10^{+173}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-24} \lor \neg \left(y \leq 1.16 \cdot 10^{+173}\right):\\ \;\;\;\;\left(-z\right) - x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.1e-24) (not (<= y 1.16e+173)))
   (- (- z) (* x (/ z y)))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.1e-24) || !(y <= 1.16e+173)) {
		tmp = -z - (x * (z / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-4.1d-24)) .or. (.not. (y <= 1.16d+173))) then
        tmp = -z - (x * (z / y))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.1e-24) || !(y <= 1.16e+173)) {
		tmp = -z - (x * (z / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.1e-24) or not (y <= 1.16e+173):
		tmp = -z - (x * (z / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.1e-24) || !(y <= 1.16e+173))
		tmp = Float64(Float64(-z) - Float64(x * Float64(z / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.1e-24) || ~((y <= 1.16e+173)))
		tmp = -z - (x * (z / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.1e-24], N[Not[LessEqual[y, 1.16e+173]], $MachinePrecision]], N[((-z) - N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.10000000000000015e-24 or 1.16e173 < y

   1. Initial program 65.9%

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

   3. Taylor expanded in z around 0 70.4%

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

      1. mul-1-neg 70.4%

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

      2. associate-/l* 86.3%

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

      3. distribute-neg-frac 86.3%

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

      4. +-commutative 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in y around 0 79.2%

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

      1. +-commutative 79.2%

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

      2. mul-1-neg 79.2%

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

      3. unsub-neg 79.2%

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

      4. mul-1-neg 79.2%

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

      5. associate-*r/ 79.6%

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

      6. *-commutative 79.6%

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

      7. distribute-rgt-neg-out 79.6%

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

   8. Simplified 79.6%

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

   if -4.10000000000000015e-24 < y < 1.16e173

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf 75.9%

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

      1. +-commutative 75.9%

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

   5. Simplified 75.9%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-24} \lor \neg \left(y \leq 1.16 \cdot 10^{+173}\right):\\ \;\;\;\;\left(-z\right) - x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-24} \lor \neg \left(y \leq 1.16 \cdot 10^{+173}\right):\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.5e-24) (not (<= y 1.16e+173)))
   (/ (- z) (/ y (+ x y)))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.5e-24) || !(y <= 1.16e+173)) {
		tmp = -z / (y / (x + y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-7.5d-24)) .or. (.not. (y <= 1.16d+173))) then
        tmp = -z / (y / (x + y))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.5e-24) || !(y <= 1.16e+173)) {
		tmp = -z / (y / (x + y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.5e-24) or not (y <= 1.16e+173):
		tmp = -z / (y / (x + y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.5e-24) || !(y <= 1.16e+173))
		tmp = Float64(Float64(-z) / Float64(y / Float64(x + y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.5e-24) || ~((y <= 1.16e+173)))
		tmp = -z / (y / (x + y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.5e-24], N[Not[LessEqual[y, 1.16e+173]], $MachinePrecision]], N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.50000000000000007e-24 or 1.16e173 < y

   1. Initial program 65.9%

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

   3. Taylor expanded in z around 0 70.4%

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

      1. mul-1-neg 70.4%

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

      2. associate-/l* 86.3%

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

      3. distribute-neg-frac 86.3%

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

      4. +-commutative 86.3%

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

   5. Simplified 86.3%

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

   if -7.50000000000000007e-24 < y < 1.16e173

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf 75.9%

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

      1. +-commutative 75.9%

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

   5. Simplified 75.9%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-24} \lor \neg \left(y \leq 1.16 \cdot 10^{+173}\right):\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+192}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+39}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-21} \lor \neg \left(y \leq 1.16 \cdot 10^{+173}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.9e+192)
   (- z)
   (if (<= y -5.5e+39)
     (* (- z) (/ x y))
     (if (or (<= y -1.1e-21) (not (<= y 1.16e+173))) (- z) (+ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e+192) {
		tmp = -z;
	} else if (y <= -5.5e+39) {
		tmp = -z * (x / y);
	} else if ((y <= -1.1e-21) || !(y <= 1.16e+173)) {
		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 <= (-1.9d+192)) then
        tmp = -z
    else if (y <= (-5.5d+39)) then
        tmp = -z * (x / y)
    else if ((y <= (-1.1d-21)) .or. (.not. (y <= 1.16d+173))) 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 <= -1.9e+192) {
		tmp = -z;
	} else if (y <= -5.5e+39) {
		tmp = -z * (x / y);
	} else if ((y <= -1.1e-21) || !(y <= 1.16e+173)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.9e+192:
		tmp = -z
	elif y <= -5.5e+39:
		tmp = -z * (x / y)
	elif (y <= -1.1e-21) or not (y <= 1.16e+173):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.9e+192)
		tmp = Float64(-z);
	elseif (y <= -5.5e+39)
		tmp = Float64(Float64(-z) * Float64(x / y));
	elseif ((y <= -1.1e-21) || !(y <= 1.16e+173))
		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 <= -1.9e+192)
		tmp = -z;
	elseif (y <= -5.5e+39)
		tmp = -z * (x / y);
	elseif ((y <= -1.1e-21) || ~((y <= 1.16e+173)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.9e+192], (-z), If[LessEqual[y, -5.5e+39], N[((-z) * N[(x / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.1e-21], N[Not[LessEqual[y, 1.16e+173]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9e192 or -5.4999999999999997e39 < y < -1.1e-21 or 1.16e173 < y

   1. Initial program 65.7%

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

   3. Taylor expanded in y around inf 82.8%

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

      1. mul-1-neg 82.8%

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

   5. Simplified 82.8%

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

   if -1.9e192 < y < -5.4999999999999997e39

   1. Initial program 66.4%

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

   3. Taylor expanded in z around 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. associate-/l* 74.1%

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

      3. distribute-neg-frac 74.1%

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

      4. +-commutative 74.1%

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

   5. Simplified 74.1%

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

      1. clear-num 74.1%

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

      2. associate-/r/ 74.0%

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

   7. Applied egg-rr 74.0%

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

   8. Taylor expanded in y around 0 44.3%

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

      1. mul-1-neg 44.3%

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

      2. associate-*l/ 47.6%

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

      3. *-commutative 47.6%

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

      4. distribute-lft-neg-in 47.6%

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

   10. Simplified 47.6%

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

   if -1.1e-21 < y < 1.16e173

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf 75.9%

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

      1. +-commutative 75.9%

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

   5. Simplified 75.9%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+192}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+39}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-21} \lor \neg \left(y \leq 1.16 \cdot 10^{+173}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-22}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.82 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+173}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.5e-22)
   (- z)
   (if (<= y 1.82e-9) x (if (<= y 1.16e+173) y (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.5e-22) {
		tmp = -z;
	} else if (y <= 1.82e-9) {
		tmp = x;
	} else if (y <= 1.16e+173) {
		tmp = y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-9.5d-22)) then
        tmp = -z
    else if (y <= 1.82d-9) then
        tmp = x
    else if (y <= 1.16d+173) then
        tmp = y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.5e-22) {
		tmp = -z;
	} else if (y <= 1.82e-9) {
		tmp = x;
	} else if (y <= 1.16e+173) {
		tmp = y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.5e-22:
		tmp = -z
	elif y <= 1.82e-9:
		tmp = x
	elif y <= 1.16e+173:
		tmp = y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.5e-22)
		tmp = Float64(-z);
	elseif (y <= 1.82e-9)
		tmp = x;
	elseif (y <= 1.16e+173)
		tmp = y;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.5e-22)
		tmp = -z;
	elseif (y <= 1.82e-9)
		tmp = x;
	elseif (y <= 1.16e+173)
		tmp = y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.5e-22], (-z), If[LessEqual[y, 1.82e-9], x, If[LessEqual[y, 1.16e+173], y, (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.4999999999999994e-22 or 1.16e173 < y

   1. Initial program 65.9%

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

   3. Taylor expanded in y around inf 67.9%

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

      1. mul-1-neg 67.9%

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

   5. Simplified 67.9%

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

   if -9.4999999999999994e-22 < y < 1.8199999999999999e-9

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 65.5%

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

   if 1.8199999999999999e-9 < y < 1.16e173

   1. Initial program 88.3%

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

   3. Taylor expanded in x around 0 67.1%

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

   4. Taylor expanded in y around 0 48.3%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-22}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.82 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+173}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-21} \lor \neg \left(y \leq 1.16 \cdot 10^{+173}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.1e-21) (not (<= y 1.16e+173))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.1e-21) || !(y <= 1.16e+173)) {
		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 <= (-1.1d-21)) .or. (.not. (y <= 1.16d+173))) 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 <= -1.1e-21) || !(y <= 1.16e+173)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.1e-21) or not (y <= 1.16e+173):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.1e-21) || !(y <= 1.16e+173))
		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 <= -1.1e-21) || ~((y <= 1.16e+173)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.1e-21], N[Not[LessEqual[y, 1.16e+173]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e-21 or 1.16e173 < y

   1. Initial program 65.9%

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

   3. Taylor expanded in y around inf 67.9%

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

      1. mul-1-neg 67.9%

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

   5. Simplified 67.9%

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

   if -1.1e-21 < y < 1.16e173

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf 75.9%

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

      1. +-commutative 75.9%

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

   5. Simplified 75.9%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-21} \lor \neg \left(y \leq 1.16 \cdot 10^{+173}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{+25}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.38e+25) y (if (<= y 5e-8) x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.38e+25) {
		tmp = y;
	} else if (y <= 5e-8) {
		tmp = x;
	} else {
		tmp = 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 <= (-1.38d+25)) then
        tmp = y
    else if (y <= 5d-8) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.38e+25) {
		tmp = y;
	} else if (y <= 5e-8) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.38e+25:
		tmp = y
	elif y <= 5e-8:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.38e+25)
		tmp = y;
	elseif (y <= 5e-8)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.38e+25)
		tmp = y;
	elseif (y <= 5e-8)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.38e+25], y, If[LessEqual[y, 5e-8], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3800000000000001e25 or 4.9999999999999998e-8 < y

   1. Initial program 67.7%

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

   3. Taylor expanded in x around 0 53.0%

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

   4. Taylor expanded in y around 0 20.8%

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

   if -1.3800000000000001e25 < y < 4.9999999999999998e-8

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 60.2%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{+25}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 34.8% 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 84.2%

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

3. Taylor expanded in y around 0 34.8%

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

4. Final simplification 34.8%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 93.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y + x}{-y} \cdot z\\ \mathbf{if}\;y < -3.7429310762689856 \cdot 10^{+171}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y < 3.5534662456086734 \cdot 10^{+168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ (+ y x) (- y)) z)))
   (if (< y -3.7429310762689856e+171)
     t_0
     (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y + x) / -y) * z
    if (y < (-3.7429310762689856d+171)) then
        tmp = t_0
    else if (y < 3.5534662456086734d+168) then
        tmp = (x + y) / (1.0d0 - (y / z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y + x) / -y) * z
	tmp = 0
	if y < -3.7429310762689856e+171:
		tmp = t_0
	elif y < 3.5534662456086734e+168:
		tmp = (x + y) / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y + x) / Float64(-y)) * z)
	tmp = 0.0
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y + x) / -y) * z;
	tmp = 0.0;
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = (x + y) / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y + x), $MachinePrecision] / (-y)), $MachinePrecision] * z), $MachinePrecision]}, If[Less[y, -3.7429310762689856e+171], t$95$0, If[Less[y, 3.5534662456086734e+168], N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024010 
(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))))