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

Percentage Accurate: 88.3% → 98.8%

Time: 6.5s

Alternatives: 8

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{-266} \lor \neg \left(t_0 \leq 2 \cdot 10^{-215}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-266) (not (<= t_0 2e-215)))
     t_0
     (- (- z) (* z (/ 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-266) || !(t_0 <= 2e-215)) {
		tmp = t_0;
	} else {
		tmp = -z - (z * (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-266)) .or. (.not. (t_0 <= 2d-215))) then
        tmp = t_0
    else
        tmp = -z - (z * (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-266) || !(t_0 <= 2e-215)) {
		tmp = t_0;
	} else {
		tmp = -z - (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -2e-266) or not (t_0 <= 2e-215):
		tmp = t_0
	else:
		tmp = -z - (z * (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-266) || !(t_0 <= 2e-215))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) - Float64(z * 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-266) || ~((t_0 <= 2e-215)))
		tmp = t_0;
	else
		tmp = -z - (z * (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-266], N[Not[LessEqual[t$95$0, 2e-215]], $MachinePrecision]], t$95$0, N[((-z) - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -2e-266 or 2.00000000000000008e-215 < (/.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 -2e-266 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 2.00000000000000008e-215

   1. Initial program 18.6%

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

      1. clear-num 18.6%

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

      2. associate-/r/ 18.6%

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

   4. Applied egg-rr 18.6%

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

   5. Taylor expanded in z around 0 91.1%

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

      1. mul-1-neg 91.1%

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

      2. associate-/l* 99.7%

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

      3. +-commutative 99.7%

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

      4. associate-/r/ 21.9%

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

      5. distribute-rgt-in 21.9%

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

      6. distribute-neg-in 21.9%

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

      7. *-commutative 21.9%

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

      8. associate-*l/ 75.5%

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

      9. associate-/l* 84.3%

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

      10. *-inverses 84.3%

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

      11. /-rgt-identity 84.3%

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

      12. unsub-neg 84.3%

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

      13. associate-*r/ 99.2%

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

      14. unsub-neg 99.2%

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

      15. mul-1-neg 99.2%

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

      16. +-commutative 99.2%

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

      17. unsub-neg 99.2%

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

      18. mul-1-neg 99.2%

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

      19. associate-/l* 82.8%

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

      20. distribute-neg-frac 82.8%

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

   7. Simplified 82.8%

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

      1. frac-2neg 82.8%

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

      2. associate-/r/ 99.9%

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

      3. frac-2neg 99.9%

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

   9. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-266} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 2 \cdot 10^{-215}\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{x}{t_0}\\ t_2 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -540000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{y}{t_0}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+14}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ x t_0)) (t_2 (* z (- -1.0 (/ x y)))))
   (if (<= y -5e+46)
     t_2
     (if (<= y -540000000000.0)
       t_1
       (if (<= y -7.5e-34)
         (/ y t_0)
         (if (<= y -1.05e-163) t_1 (if (<= y 1.95e+14) (+ x y) t_2)))))))

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 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -5e+46) {
		tmp = t_2;
	} else if (y <= -540000000000.0) {
		tmp = t_1;
	} else if (y <= -7.5e-34) {
		tmp = y / t_0;
	} else if (y <= -1.05e-163) {
		tmp = t_1;
	} else if (y <= 1.95e+14) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	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 = z * ((-1.0d0) - (x / y))
    if (y <= (-5d+46)) then
        tmp = t_2
    else if (y <= (-540000000000.0d0)) then
        tmp = t_1
    else if (y <= (-7.5d-34)) then
        tmp = y / t_0
    else if (y <= (-1.05d-163)) then
        tmp = t_1
    else if (y <= 1.95d+14) then
        tmp = x + y
    else
        tmp = t_2
    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 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -5e+46) {
		tmp = t_2;
	} else if (y <= -540000000000.0) {
		tmp = t_1;
	} else if (y <= -7.5e-34) {
		tmp = y / t_0;
	} else if (y <= -1.05e-163) {
		tmp = t_1;
	} else if (y <= 1.95e+14) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = x / t_0
	t_2 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -5e+46:
		tmp = t_2
	elif y <= -540000000000.0:
		tmp = t_1
	elif y <= -7.5e-34:
		tmp = y / t_0
	elif y <= -1.05e-163:
		tmp = t_1
	elif y <= 1.95e+14:
		tmp = x + y
	else:
		tmp = t_2
	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(z * Float64(-1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -5e+46)
		tmp = t_2;
	elseif (y <= -540000000000.0)
		tmp = t_1;
	elseif (y <= -7.5e-34)
		tmp = Float64(y / t_0);
	elseif (y <= -1.05e-163)
		tmp = t_1;
	elseif (y <= 1.95e+14)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	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 = z * (-1.0 - (x / y));
	tmp = 0.0;
	if (y <= -5e+46)
		tmp = t_2;
	elseif (y <= -540000000000.0)
		tmp = t_1;
	elseif (y <= -7.5e-34)
		tmp = y / t_0;
	elseif (y <= -1.05e-163)
		tmp = t_1;
	elseif (y <= 1.95e+14)
		tmp = x + y;
	else
		tmp = t_2;
	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[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+46], t$95$2, If[LessEqual[y, -540000000000.0], t$95$1, If[LessEqual[y, -7.5e-34], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, -1.05e-163], t$95$1, If[LessEqual[y, 1.95e+14], N[(x + y), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.0000000000000002e46 or 1.95e14 < y

   1. Initial program 76.3%

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

      1. clear-num 76.1%

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

      2. associate-/r/ 76.1%

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

   4. Applied egg-rr 76.1%

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

   5. Taylor expanded in z around 0 63.2%

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

      1. mul-1-neg 63.2%

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

      2. associate-/l* 77.9%

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

      3. +-commutative 77.9%

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

      4. associate-/r/ 55.3%

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

      5. distribute-rgt-in 55.4%

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

      6. distribute-neg-in 55.4%

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

      7. *-commutative 55.4%

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

      8. associate-*l/ 59.4%

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

      9. associate-/l* 73.5%

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

      10. *-inverses 73.5%

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

      11. /-rgt-identity 73.5%

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

      12. unsub-neg 73.5%

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

      13. associate-*r/ 73.1%

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

      14. unsub-neg 73.1%

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

      15. mul-1-neg 73.1%

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

      16. +-commutative 73.1%

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

      17. unsub-neg 73.1%

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

      18. mul-1-neg 73.1%

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

      19. associate-/l* 73.1%

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

      20. distribute-neg-frac 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in x around 0 73.1%

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

      1. neg-mul-1 73.1%

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

      2. mul-1-neg 73.1%

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

      3. associate-*l/ 78.0%

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

      4. distribute-lft-neg-in 78.0%

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

      5. cancel-sign-sub-inv 78.0%

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

      6. neg-mul-1 78.0%

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

      7. distribute-rgt-out-- 78.0%

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

   10. Simplified 78.0%

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

   if -5.0000000000000002e46 < y < -5.4e11 or -7.5000000000000004e-34 < y < -1.04999999999999999e-163

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 84.2%

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

   if -5.4e11 < y < -7.5000000000000004e-34

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 85.9%

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

   if -1.04999999999999999e-163 < y < 1.95e14

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 86.2%

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

      1. +-commutative 86.2%

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

   5. Simplified 86.2%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+46}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -540000000000:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+14}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+51}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+85}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+130}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.36e+51)
   (- z)
   (if (<= y 2.7e+28)
     (+ x y)
     (if (<= y 9e+85) (/ (- z) (/ y x)) (if (<= y 8e+130) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.36e+51) {
		tmp = -z;
	} else if (y <= 2.7e+28) {
		tmp = x + y;
	} else if (y <= 9e+85) {
		tmp = -z / (y / x);
	} else if (y <= 8e+130) {
		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 <= (-1.36d+51)) then
        tmp = -z
    else if (y <= 2.7d+28) then
        tmp = x + y
    else if (y <= 9d+85) then
        tmp = -z / (y / x)
    else if (y <= 8d+130) 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 <= -1.36e+51) {
		tmp = -z;
	} else if (y <= 2.7e+28) {
		tmp = x + y;
	} else if (y <= 9e+85) {
		tmp = -z / (y / x);
	} else if (y <= 8e+130) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.36e+51:
		tmp = -z
	elif y <= 2.7e+28:
		tmp = x + y
	elif y <= 9e+85:
		tmp = -z / (y / x)
	elif y <= 8e+130:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.36e+51)
		tmp = Float64(-z);
	elseif (y <= 2.7e+28)
		tmp = Float64(x + y);
	elseif (y <= 9e+85)
		tmp = Float64(Float64(-z) / Float64(y / x));
	elseif (y <= 8e+130)
		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 <= -1.36e+51)
		tmp = -z;
	elseif (y <= 2.7e+28)
		tmp = x + y;
	elseif (y <= 9e+85)
		tmp = -z / (y / x);
	elseif (y <= 8e+130)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.36e+51], (-z), If[LessEqual[y, 2.7e+28], N[(x + y), $MachinePrecision], If[LessEqual[y, 9e+85], N[((-z) / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+130], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3599999999999999e51 or 8.0000000000000005e130 < y

   1. Initial program 73.6%

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

   3. Taylor expanded in y around inf 73.7%

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

      1. mul-1-neg 73.7%

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

   5. Simplified 73.7%

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

   if -1.3599999999999999e51 < y < 2.7000000000000002e28 or 9.00000000000000013e85 < y < 8.0000000000000005e130

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 77.8%

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

      1. +-commutative 77.8%

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

   5. Simplified 77.8%

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

   if 2.7000000000000002e28 < y < 9.00000000000000013e85

   1. Initial program 79.2%

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

   3. Taylor expanded in x around inf 41.5%

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

   4. Taylor expanded in y around inf 47.2%

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

      1. mul-1-neg 47.2%

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

      2. associate-*r/ 41.8%

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

      3. distribute-lft-neg-out 41.8%

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

      4. *-commutative 41.8%

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

   6. Simplified 41.8%

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

   7. Taylor expanded in z around 0 47.2%

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

      1. associate-*r/ 47.2%

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

      2. *-commutative 47.2%

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

      3. neg-mul-1 47.2%

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

      4. distribute-lft-neg-out 47.2%

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

      5. associate-/l* 46.9%

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

   9. Simplified 46.9%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+51}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+85}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+130}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+52}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+85}:\\ \;\;\;\;\frac{x \cdot z}{-y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+129}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.65e+52)
   (- z)
   (if (<= y 2.7e+28)
     (+ x y)
     (if (<= y 8.5e+85) (/ (* x z) (- y)) (if (<= y 6e+129) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.65e+52) {
		tmp = -z;
	} else if (y <= 2.7e+28) {
		tmp = x + y;
	} else if (y <= 8.5e+85) {
		tmp = (x * z) / -y;
	} else if (y <= 6e+129) {
		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 <= (-1.65d+52)) then
        tmp = -z
    else if (y <= 2.7d+28) then
        tmp = x + y
    else if (y <= 8.5d+85) then
        tmp = (x * z) / -y
    else if (y <= 6d+129) 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 <= -1.65e+52) {
		tmp = -z;
	} else if (y <= 2.7e+28) {
		tmp = x + y;
	} else if (y <= 8.5e+85) {
		tmp = (x * z) / -y;
	} else if (y <= 6e+129) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.65e+52:
		tmp = -z
	elif y <= 2.7e+28:
		tmp = x + y
	elif y <= 8.5e+85:
		tmp = (x * z) / -y
	elif y <= 6e+129:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.65e+52)
		tmp = Float64(-z);
	elseif (y <= 2.7e+28)
		tmp = Float64(x + y);
	elseif (y <= 8.5e+85)
		tmp = Float64(Float64(x * z) / Float64(-y));
	elseif (y <= 6e+129)
		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 <= -1.65e+52)
		tmp = -z;
	elseif (y <= 2.7e+28)
		tmp = x + y;
	elseif (y <= 8.5e+85)
		tmp = (x * z) / -y;
	elseif (y <= 6e+129)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.65e+52], (-z), If[LessEqual[y, 2.7e+28], N[(x + y), $MachinePrecision], If[LessEqual[y, 8.5e+85], N[(N[(x * z), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[y, 6e+129], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65e52 or 6.0000000000000006e129 < y

   1. Initial program 73.6%

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

   3. Taylor expanded in y around inf 73.7%

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

      1. mul-1-neg 73.7%

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

   5. Simplified 73.7%

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

   if -1.65e52 < y < 2.7000000000000002e28 or 8.4999999999999994e85 < y < 6.0000000000000006e129

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 77.8%

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

      1. +-commutative 77.8%

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

   5. Simplified 77.8%

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

   if 2.7000000000000002e28 < y < 8.4999999999999994e85

   1. Initial program 79.2%

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

   3. Taylor expanded in x around inf 41.5%

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

   4. Taylor expanded in y around inf 47.2%

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

      1. mul-1-neg 47.2%

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

      2. associate-*r/ 41.8%

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

      3. distribute-lft-neg-out 41.8%

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

      4. *-commutative 41.8%

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

   6. Simplified 41.8%

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

      1. add-sqr-sqrt 29.6%

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

      2. sqrt-unprod 20.4%

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

      3. sqr-neg 20.4%

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

      4. sqrt-unprod 1.3%

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

      5. add-sqr-sqrt 3.9%

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

      6. associate-*l/ 3.8%

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

      7. associate-*r/ 3.8%

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

      8. frac-2neg 3.8%

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

      9. associate-*r/ 3.8%

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

      10. add-sqr-sqrt 2.5%

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

      11. sqrt-unprod 8.9%

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

      12. sqr-neg 8.9%

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

      13. sqrt-unprod 11.9%

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

      14. add-sqr-sqrt 47.2%

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

   8. Applied egg-rr 47.2%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+52}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+85}:\\ \;\;\;\;\frac{x \cdot z}{-y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+129}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+48} \lor \neg \left(y \leq 1.38 \cdot 10^{+14}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4e+48) (not (<= y 1.38e+14))) (* z (- -1.0 (/ x y))) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e+48) || !(y <= 1.38e+14)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-4d+48)) .or. (.not. (y <= 1.38d+14))) then
        tmp = z * ((-1.0d0) - (x / y))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e+48) || !(y <= 1.38e+14)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4e+48) or not (y <= 1.38e+14):
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4e+48) || !(y <= 1.38e+14))
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4e+48) || ~((y <= 1.38e+14)))
		tmp = z * (-1.0 - (x / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4e+48], N[Not[LessEqual[y, 1.38e+14]], $MachinePrecision]], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.00000000000000018e48 or 1.38e14 < y

   1. Initial program 76.1%

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

      1. clear-num 75.9%

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

      2. associate-/r/ 75.9%

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

   4. Applied egg-rr 75.9%

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

   5. Taylor expanded in z around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. associate-/l* 78.6%

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

      3. +-commutative 78.6%

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

      4. associate-/r/ 55.8%

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

      5. distribute-rgt-in 55.8%

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

      6. distribute-neg-in 55.8%

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

      7. *-commutative 55.8%

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

      8. associate-*l/ 59.9%

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

      9. associate-/l* 74.1%

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

      10. *-inverses 74.1%

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

      11. /-rgt-identity 74.1%

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

      12. unsub-neg 74.1%

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

      13. associate-*r/ 73.7%

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

      14. unsub-neg 73.7%

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

      15. mul-1-neg 73.7%

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

      16. +-commutative 73.7%

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

      17. unsub-neg 73.7%

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

      18. mul-1-neg 73.7%

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

      19. associate-/l* 73.7%

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

      20. distribute-neg-frac 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in x around 0 73.7%

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

      1. neg-mul-1 73.7%

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

      2. mul-1-neg 73.7%

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

      3. associate-*l/ 78.7%

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

      4. distribute-lft-neg-in 78.7%

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

      5. cancel-sign-sub-inv 78.7%

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

      6. neg-mul-1 78.7%

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

      7. distribute-rgt-out-- 78.7%

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

   10. Simplified 78.7%

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

   if -4.00000000000000018e48 < y < 1.38e14

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 80.5%

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

      1. +-commutative 80.5%

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

   5. Simplified 80.5%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+48} \lor \neg \left(y \leq 1.38 \cdot 10^{+14}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+51} \lor \neg \left(y \leq 1.3 \cdot 10^{+133}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.5e+51) (not (<= y 1.3e+133))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e+51) || !(y <= 1.3e+133)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-6.5d+51)) .or. (.not. (y <= 1.3d+133))) then
        tmp = -z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e+51) || !(y <= 1.3e+133)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.5e+51) or not (y <= 1.3e+133):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.5e+51) || !(y <= 1.3e+133))
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.5e+51) || ~((y <= 1.3e+133)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.5e+51], N[Not[LessEqual[y, 1.3e+133]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e51 or 1.2999999999999999e133 < y

   1. Initial program 73.6%

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

   3. Taylor expanded in y around inf 73.7%

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

      1. mul-1-neg 73.7%

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

   5. Simplified 73.7%

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

   if -6.5e51 < y < 1.2999999999999999e133

   1. Initial program 96.3%

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

   3. Taylor expanded in z around inf 72.6%

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

      1. +-commutative 72.6%

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

   5. Simplified 72.6%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+51} \lor \neg \left(y \leq 1.3 \cdot 10^{+133}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+46} \lor \neg \left(y \leq 1.36 \cdot 10^{+14}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.45e+46) (not (<= y 1.36e+14))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.45e+46) || !(y <= 1.36e+14)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.45d+46)) .or. (.not. (y <= 1.36d+14))) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.45e+46) || !(y <= 1.36e+14)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.45e+46) or not (y <= 1.36e+14):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.45e+46) || !(y <= 1.36e+14))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.45e+46) || ~((y <= 1.36e+14)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.45e+46], N[Not[LessEqual[y, 1.36e+14]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -1.4500000000000001e46 or 1.36e14 < y

   1. Initial program 76.3%

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

   3. Taylor expanded in y around inf 59.1%

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

      1. mul-1-neg 59.1%

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

   5. Simplified 59.1%

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

   if -1.4500000000000001e46 < y < 1.36e14

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 63.9%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+46} \lor \neg \left(y \leq 1.36 \cdot 10^{+14}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 36.5% 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 90.0%

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

3. Taylor expanded in y around 0 41.0%

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

4. Final simplification 41.0%

   \[\leadsto x \]
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 2024013 
(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))))