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

Percentage Accurate: 88.2% → 99.5%

Time: 7.5s

Alternatives: 10

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-262} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-262) (not (<= t_0 0.0))) t_0 (- (- z) (/ (* x z) y)))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-262) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z - ((x * z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-2d-262)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = -z - ((x * z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-262) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z - ((x * z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -2e-262) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = -z - ((x * z) / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -2e-262) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) - Float64(Float64(x * z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -2e-262) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = -z - ((x * z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -2e-262], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[((-z) - N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -2.00000000000000002e-262 or -0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.9%

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

   if -2.00000000000000002e-262 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 12.9%

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

   3. Taylor expanded in y around inf 12.9%

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

      1. neg-mul-1 12.9%

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

      2. distribute-neg-frac2 12.9%

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

   5. Simplified 12.9%

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

   6. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. associate-/l* 80.4%

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

   8. Simplified 80.4%

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

   9. Taylor expanded in x around 0 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-262} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ t_1 := 1 - \frac{y}{z}\\ t_2 := \frac{x}{t\_1}\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+38}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-54}:\\ \;\;\;\;\left(-z\right) - x \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-200}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 18000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+41}:\\ \;\;\;\;\frac{y}{t\_1}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))) (t_1 (- 1.0 (/ y z))) (t_2 (/ x t_1)))
   (if (<= y -1.4e+38)
     t_0
     (if (<= y -5.8e-10)
       (+ x y)
       (if (<= y -2.45e-54)
         (- (- z) (* x (/ z y)))
         (if (<= y -4.7e-200)
           (+ x y)
           (if (<= y 18000000000.0)
             t_2
             (if (<= y 1.4e+41) (/ y t_1) (if (<= y 1.45e+56) t_2 t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double t_1 = 1.0 - (y / z);
	double t_2 = x / t_1;
	double tmp;
	if (y <= -1.4e+38) {
		tmp = t_0;
	} else if (y <= -5.8e-10) {
		tmp = x + y;
	} else if (y <= -2.45e-54) {
		tmp = -z - (x * (z / y));
	} else if (y <= -4.7e-200) {
		tmp = x + y;
	} else if (y <= 18000000000.0) {
		tmp = t_2;
	} else if (y <= 1.4e+41) {
		tmp = y / t_1;
	} else if (y <= 1.45e+56) {
		tmp = t_2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = z * ((-1.0d0) - (x / y))
    t_1 = 1.0d0 - (y / z)
    t_2 = x / t_1
    if (y <= (-1.4d+38)) then
        tmp = t_0
    else if (y <= (-5.8d-10)) then
        tmp = x + y
    else if (y <= (-2.45d-54)) then
        tmp = -z - (x * (z / y))
    else if (y <= (-4.7d-200)) then
        tmp = x + y
    else if (y <= 18000000000.0d0) then
        tmp = t_2
    else if (y <= 1.4d+41) then
        tmp = y / t_1
    else if (y <= 1.45d+56) then
        tmp = t_2
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double t_1 = 1.0 - (y / z);
	double t_2 = x / t_1;
	double tmp;
	if (y <= -1.4e+38) {
		tmp = t_0;
	} else if (y <= -5.8e-10) {
		tmp = x + y;
	} else if (y <= -2.45e-54) {
		tmp = -z - (x * (z / y));
	} else if (y <= -4.7e-200) {
		tmp = x + y;
	} else if (y <= 18000000000.0) {
		tmp = t_2;
	} else if (y <= 1.4e+41) {
		tmp = y / t_1;
	} else if (y <= 1.45e+56) {
		tmp = t_2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	t_1 = 1.0 - (y / z)
	t_2 = x / t_1
	tmp = 0
	if y <= -1.4e+38:
		tmp = t_0
	elif y <= -5.8e-10:
		tmp = x + y
	elif y <= -2.45e-54:
		tmp = -z - (x * (z / y))
	elif y <= -4.7e-200:
		tmp = x + y
	elif y <= 18000000000.0:
		tmp = t_2
	elif y <= 1.4e+41:
		tmp = y / t_1
	elif y <= 1.45e+56:
		tmp = t_2
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-1.0 - Float64(x / y)))
	t_1 = Float64(1.0 - Float64(y / z))
	t_2 = Float64(x / t_1)
	tmp = 0.0
	if (y <= -1.4e+38)
		tmp = t_0;
	elseif (y <= -5.8e-10)
		tmp = Float64(x + y);
	elseif (y <= -2.45e-54)
		tmp = Float64(Float64(-z) - Float64(x * Float64(z / y)));
	elseif (y <= -4.7e-200)
		tmp = Float64(x + y);
	elseif (y <= 18000000000.0)
		tmp = t_2;
	elseif (y <= 1.4e+41)
		tmp = Float64(y / t_1);
	elseif (y <= 1.45e+56)
		tmp = t_2;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-1.0 - (x / y));
	t_1 = 1.0 - (y / z);
	t_2 = x / t_1;
	tmp = 0.0;
	if (y <= -1.4e+38)
		tmp = t_0;
	elseif (y <= -5.8e-10)
		tmp = x + y;
	elseif (y <= -2.45e-54)
		tmp = -z - (x * (z / y));
	elseif (y <= -4.7e-200)
		tmp = x + y;
	elseif (y <= 18000000000.0)
		tmp = t_2;
	elseif (y <= 1.4e+41)
		tmp = y / t_1;
	elseif (y <= 1.45e+56)
		tmp = t_2;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / t$95$1), $MachinePrecision]}, If[LessEqual[y, -1.4e+38], t$95$0, If[LessEqual[y, -5.8e-10], N[(x + y), $MachinePrecision], If[LessEqual[y, -2.45e-54], N[((-z) - N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.7e-200], N[(x + y), $MachinePrecision], If[LessEqual[y, 18000000000.0], t$95$2, If[LessEqual[y, 1.4e+41], N[(y / t$95$1), $MachinePrecision], If[LessEqual[y, 1.45e+56], t$95$2, t$95$0]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.4e38 or 1.45000000000000004e56 < y

   1. Initial program 77.0%

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

   3. Taylor expanded in y around inf 60.9%

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

      1. neg-mul-1 60.9%

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

      2. distribute-neg-frac2 60.9%

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

   5. Simplified 60.9%

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

   6. Taylor expanded in x around 0 79.0%

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

      1. mul-1-neg 79.0%

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

      2. unsub-neg 79.0%

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

      3. mul-1-neg 79.0%

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

      4. associate-/l* 78.8%

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

   8. Simplified 78.8%

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

   9. Taylor expanded in x around 0 79.0%

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

   10. Taylor expanded in z around 0 83.8%

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

       1. mul-1-neg 83.8%

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

       2. distribute-rgt-neg-in 83.8%

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

       3. distribute-neg-in 83.8%

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

       4. metadata-eval 83.8%

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

       5. mul-1-neg 83.8%

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

       6. mul-1-neg 83.8%

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

       7. unsub-neg 83.8%

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

   12. Simplified 83.8%

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

   if -1.4e38 < y < -5.79999999999999962e-10 or -2.4500000000000001e-54 < y < -4.7000000000000001e-200

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 75.0%

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

      1. +-commutative 75.0%

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

   5. Simplified 75.0%

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

   if -5.79999999999999962e-10 < y < -2.4500000000000001e-54

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 81.1%

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

      1. neg-mul-1 81.1%

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

      2. distribute-neg-frac2 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in x around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. unsub-neg 81.0%

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

      3. mul-1-neg 81.0%

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

      4. associate-/l* 81.0%

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

   8. Simplified 81.0%

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

   if -4.7000000000000001e-200 < y < 1.8e10 or 1.4e41 < y < 1.45000000000000004e56

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 84.5%

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

   if 1.8e10 < y < 1.4e41

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.9%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-54}:\\ \;\;\;\;\left(-z\right) - x \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-200}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 18000000000:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+41}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+56}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ t_1 := 1 - \frac{y}{z}\\ t_2 := \frac{x}{t\_1}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+38}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-7}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-56}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-200}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 34000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{y}{t\_1}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))) (t_1 (- 1.0 (/ y z))) (t_2 (/ x t_1)))
   (if (<= y -1.3e+38)
     t_0
     (if (<= y -3.5e-7)
       (+ x y)
       (if (<= y -2.8e-56)
         t_0
         (if (<= y -1.6e-200)
           (+ x y)
           (if (<= y 34000000000.0)
             t_2
             (if (<= y 1.2e+40) (/ y t_1) (if (<= y 1.85e+56) t_2 t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double t_1 = 1.0 - (y / z);
	double t_2 = x / t_1;
	double tmp;
	if (y <= -1.3e+38) {
		tmp = t_0;
	} else if (y <= -3.5e-7) {
		tmp = x + y;
	} else if (y <= -2.8e-56) {
		tmp = t_0;
	} else if (y <= -1.6e-200) {
		tmp = x + y;
	} else if (y <= 34000000000.0) {
		tmp = t_2;
	} else if (y <= 1.2e+40) {
		tmp = y / t_1;
	} else if (y <= 1.85e+56) {
		tmp = t_2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = z * ((-1.0d0) - (x / y))
    t_1 = 1.0d0 - (y / z)
    t_2 = x / t_1
    if (y <= (-1.3d+38)) then
        tmp = t_0
    else if (y <= (-3.5d-7)) then
        tmp = x + y
    else if (y <= (-2.8d-56)) then
        tmp = t_0
    else if (y <= (-1.6d-200)) then
        tmp = x + y
    else if (y <= 34000000000.0d0) then
        tmp = t_2
    else if (y <= 1.2d+40) then
        tmp = y / t_1
    else if (y <= 1.85d+56) then
        tmp = t_2
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double t_1 = 1.0 - (y / z);
	double t_2 = x / t_1;
	double tmp;
	if (y <= -1.3e+38) {
		tmp = t_0;
	} else if (y <= -3.5e-7) {
		tmp = x + y;
	} else if (y <= -2.8e-56) {
		tmp = t_0;
	} else if (y <= -1.6e-200) {
		tmp = x + y;
	} else if (y <= 34000000000.0) {
		tmp = t_2;
	} else if (y <= 1.2e+40) {
		tmp = y / t_1;
	} else if (y <= 1.85e+56) {
		tmp = t_2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	t_1 = 1.0 - (y / z)
	t_2 = x / t_1
	tmp = 0
	if y <= -1.3e+38:
		tmp = t_0
	elif y <= -3.5e-7:
		tmp = x + y
	elif y <= -2.8e-56:
		tmp = t_0
	elif y <= -1.6e-200:
		tmp = x + y
	elif y <= 34000000000.0:
		tmp = t_2
	elif y <= 1.2e+40:
		tmp = y / t_1
	elif y <= 1.85e+56:
		tmp = t_2
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-1.0 - Float64(x / y)))
	t_1 = Float64(1.0 - Float64(y / z))
	t_2 = Float64(x / t_1)
	tmp = 0.0
	if (y <= -1.3e+38)
		tmp = t_0;
	elseif (y <= -3.5e-7)
		tmp = Float64(x + y);
	elseif (y <= -2.8e-56)
		tmp = t_0;
	elseif (y <= -1.6e-200)
		tmp = Float64(x + y);
	elseif (y <= 34000000000.0)
		tmp = t_2;
	elseif (y <= 1.2e+40)
		tmp = Float64(y / t_1);
	elseif (y <= 1.85e+56)
		tmp = t_2;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-1.0 - (x / y));
	t_1 = 1.0 - (y / z);
	t_2 = x / t_1;
	tmp = 0.0;
	if (y <= -1.3e+38)
		tmp = t_0;
	elseif (y <= -3.5e-7)
		tmp = x + y;
	elseif (y <= -2.8e-56)
		tmp = t_0;
	elseif (y <= -1.6e-200)
		tmp = x + y;
	elseif (y <= 34000000000.0)
		tmp = t_2;
	elseif (y <= 1.2e+40)
		tmp = y / t_1;
	elseif (y <= 1.85e+56)
		tmp = t_2;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / t$95$1), $MachinePrecision]}, If[LessEqual[y, -1.3e+38], t$95$0, If[LessEqual[y, -3.5e-7], N[(x + y), $MachinePrecision], If[LessEqual[y, -2.8e-56], t$95$0, If[LessEqual[y, -1.6e-200], N[(x + y), $MachinePrecision], If[LessEqual[y, 34000000000.0], t$95$2, If[LessEqual[y, 1.2e+40], N[(y / t$95$1), $MachinePrecision], If[LessEqual[y, 1.85e+56], t$95$2, t$95$0]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3e38 or -3.49999999999999984e-7 < y < -2.79999999999999993e-56 or 1.84999999999999998e56 < y

   1. Initial program 79.1%

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

   3. Taylor expanded in y around inf 62.8%

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

      1. neg-mul-1 62.8%

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

      2. distribute-neg-frac2 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in x around 0 79.1%

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

      1. mul-1-neg 79.1%

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

      2. unsub-neg 79.1%

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

      3. mul-1-neg 79.1%

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

      4. associate-/l* 79.0%

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

   8. Simplified 79.0%

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

   9. Taylor expanded in x around 0 79.1%

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

   10. Taylor expanded in z around 0 83.6%

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

       1. mul-1-neg 83.6%

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

       2. distribute-rgt-neg-in 83.6%

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

       3. distribute-neg-in 83.6%

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

       4. metadata-eval 83.6%

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

       5. mul-1-neg 83.6%

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

       6. mul-1-neg 83.6%

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

       7. unsub-neg 83.6%

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

   12. Simplified 83.6%

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

   if -1.3e38 < y < -3.49999999999999984e-7 or -2.79999999999999993e-56 < y < -1.59999999999999991e-200

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 75.0%

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

      1. +-commutative 75.0%

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

   5. Simplified 75.0%

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

   if -1.59999999999999991e-200 < y < 3.4e10 or 1.2e40 < y < 1.84999999999999998e56

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 84.5%

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

   if 3.4e10 < y < 1.2e40

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.9%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{y}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-7}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-56}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-200}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 34000000000:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+56}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-9}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-200}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+56}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))))
   (if (<= y -2.5e+38)
     t_0
     (if (<= y -1e-9)
       (+ x y)
       (if (<= y -4.5e-54)
         t_0
         (if (<= y -2.6e-200)
           (+ x y)
           (if (<= y 8e+56) (/ x (- 1.0 (/ y z))) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -2.5e+38) {
		tmp = t_0;
	} else if (y <= -1e-9) {
		tmp = x + y;
	} else if (y <= -4.5e-54) {
		tmp = t_0;
	} else if (y <= -2.6e-200) {
		tmp = x + y;
	} else if (y <= 8e+56) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * ((-1.0d0) - (x / y))
    if (y <= (-2.5d+38)) then
        tmp = t_0
    else if (y <= (-1d-9)) then
        tmp = x + y
    else if (y <= (-4.5d-54)) then
        tmp = t_0
    else if (y <= (-2.6d-200)) then
        tmp = x + y
    else if (y <= 8d+56) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -2.5e+38) {
		tmp = t_0;
	} else if (y <= -1e-9) {
		tmp = x + y;
	} else if (y <= -4.5e-54) {
		tmp = t_0;
	} else if (y <= -2.6e-200) {
		tmp = x + y;
	} else if (y <= 8e+56) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -2.5e+38:
		tmp = t_0
	elif y <= -1e-9:
		tmp = x + y
	elif y <= -4.5e-54:
		tmp = t_0
	elif y <= -2.6e-200:
		tmp = x + y
	elif y <= 8e+56:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -2.5e+38)
		tmp = t_0;
	elseif (y <= -1e-9)
		tmp = Float64(x + y);
	elseif (y <= -4.5e-54)
		tmp = t_0;
	elseif (y <= -2.6e-200)
		tmp = Float64(x + y);
	elseif (y <= 8e+56)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-1.0 - (x / y));
	tmp = 0.0;
	if (y <= -2.5e+38)
		tmp = t_0;
	elseif (y <= -1e-9)
		tmp = x + y;
	elseif (y <= -4.5e-54)
		tmp = t_0;
	elseif (y <= -2.6e-200)
		tmp = x + y;
	elseif (y <= 8e+56)
		tmp = x / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e+38], t$95$0, If[LessEqual[y, -1e-9], N[(x + y), $MachinePrecision], If[LessEqual[y, -4.5e-54], t$95$0, If[LessEqual[y, -2.6e-200], N[(x + y), $MachinePrecision], If[LessEqual[y, 8e+56], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.49999999999999985e38 or -1.00000000000000006e-9 < y < -4.4999999999999998e-54 or 8.00000000000000074e56 < y

   1. Initial program 79.1%

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

   3. Taylor expanded in y around inf 62.8%

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

      1. neg-mul-1 62.8%

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

      2. distribute-neg-frac2 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in x around 0 79.1%

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

      1. mul-1-neg 79.1%

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

      2. unsub-neg 79.1%

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

      3. mul-1-neg 79.1%

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

      4. associate-/l* 79.0%

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

   8. Simplified 79.0%

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

   9. Taylor expanded in x around 0 79.1%

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

   10. Taylor expanded in z around 0 83.6%

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

       1. mul-1-neg 83.6%

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

       2. distribute-rgt-neg-in 83.6%

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

       3. distribute-neg-in 83.6%

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

       4. metadata-eval 83.6%

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

       5. mul-1-neg 83.6%

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

       6. mul-1-neg 83.6%

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

       7. unsub-neg 83.6%

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

   12. Simplified 83.6%

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

   if -2.49999999999999985e38 < y < -1.00000000000000006e-9 or -4.4999999999999998e-54 < y < -2.5999999999999999e-200

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 75.0%

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

      1. +-commutative 75.0%

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

   5. Simplified 75.0%

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

   if -2.5999999999999999e-200 < y < 8.00000000000000074e56

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 80.1%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-9}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-54}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-200}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+56}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+37} \lor \neg \left(y \leq -1.25 \cdot 10^{-8} \lor \neg \left(y \leq -9.5 \cdot 10^{-55}\right) \land y \leq 8 \cdot 10^{+39}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5e+37)
         (not (or (<= y -1.25e-8) (and (not (<= y -9.5e-55)) (<= y 8e+39)))))
   (* z (- -1.0 (/ x y)))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5e+37) || !((y <= -1.25e-8) || (!(y <= -9.5e-55) && (y <= 8e+39)))) {
		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 <= (-5d+37)) .or. (.not. (y <= (-1.25d-8)) .or. (.not. (y <= (-9.5d-55))) .and. (y <= 8d+39))) 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 <= -5e+37) || !((y <= -1.25e-8) || (!(y <= -9.5e-55) && (y <= 8e+39)))) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5e+37) or not ((y <= -1.25e-8) or (not (y <= -9.5e-55) and (y <= 8e+39))):
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5e+37) || !((y <= -1.25e-8) || (!(y <= -9.5e-55) && (y <= 8e+39))))
		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 <= -5e+37) || ~(((y <= -1.25e-8) || (~((y <= -9.5e-55)) && (y <= 8e+39)))))
		tmp = z * (-1.0 - (x / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5e+37], N[Not[Or[LessEqual[y, -1.25e-8], And[N[Not[LessEqual[y, -9.5e-55]], $MachinePrecision], LessEqual[y, 8e+39]]]], $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 < -4.99999999999999989e37 or -1.2499999999999999e-8 < y < -9.5000000000000006e-55 or 7.99999999999999952e39 < y

   1. Initial program 80.7%

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

   3. Taylor expanded in y around inf 62.9%

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

      1. neg-mul-1 62.9%

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

      2. distribute-neg-frac2 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in x around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. unsub-neg 77.6%

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

      3. mul-1-neg 77.6%

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

      4. associate-/l* 77.9%

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

   8. Simplified 77.9%

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

   9. Taylor expanded in x around 0 77.6%

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

   10. Taylor expanded in z around 0 82.1%

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

       1. mul-1-neg 82.1%

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

       2. distribute-rgt-neg-in 82.1%

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

       3. distribute-neg-in 82.1%

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

       4. metadata-eval 82.1%

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

       5. mul-1-neg 82.1%

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

       6. mul-1-neg 82.1%

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

       7. unsub-neg 82.1%

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

   12. Simplified 82.1%

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

   if -4.99999999999999989e37 < y < -1.2499999999999999e-8 or -9.5000000000000006e-55 < y < 7.99999999999999952e39

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 76.1%

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

      1. +-commutative 76.1%

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

   5. Simplified 76.1%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+37} \lor \neg \left(y \leq -1.25 \cdot 10^{-8} \lor \neg \left(y \leq -9.5 \cdot 10^{-55}\right) \land y \leq 8 \cdot 10^{+39}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+47}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-10}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-54} \lor \neg \left(y \leq 1.55 \cdot 10^{+56}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.8e+47)
   (- z)
   (if (<= y -3.9e-10)
     y
     (if (or (<= y -2.1e-54) (not (<= y 1.55e+56))) (- z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e+47) {
		tmp = -z;
	} else if (y <= -3.9e-10) {
		tmp = y;
	} else if ((y <= -2.1e-54) || !(y <= 1.55e+56)) {
		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 <= (-2.8d+47)) then
        tmp = -z
    else if (y <= (-3.9d-10)) then
        tmp = y
    else if ((y <= (-2.1d-54)) .or. (.not. (y <= 1.55d+56))) 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 <= -2.8e+47) {
		tmp = -z;
	} else if (y <= -3.9e-10) {
		tmp = y;
	} else if ((y <= -2.1e-54) || !(y <= 1.55e+56)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.8e+47:
		tmp = -z
	elif y <= -3.9e-10:
		tmp = y
	elif (y <= -2.1e-54) or not (y <= 1.55e+56):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.8e+47)
		tmp = Float64(-z);
	elseif (y <= -3.9e-10)
		tmp = y;
	elseif ((y <= -2.1e-54) || !(y <= 1.55e+56))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.8e+47)
		tmp = -z;
	elseif (y <= -3.9e-10)
		tmp = y;
	elseif ((y <= -2.1e-54) || ~((y <= 1.55e+56)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.8e+47], (-z), If[LessEqual[y, -3.9e-10], y, If[Or[LessEqual[y, -2.1e-54], N[Not[LessEqual[y, 1.55e+56]], $MachinePrecision]], (-z), x]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.79999999999999988e47 or -3.9e-10 < y < -2.1e-54 or 1.55000000000000002e56 < y

   1. Initial program 78.7%

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

   3. Taylor expanded in y around inf 66.1%

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

      1. neg-mul-1 66.1%

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

   5. Simplified 66.1%

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

   if -2.79999999999999988e47 < y < -3.9e-10

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 80.8%

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

      1. +-commutative 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in y around inf 52.0%

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

   if -2.1e-54 < y < 1.55000000000000002e56

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 58.8%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+47}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-10}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-54} \lor \neg \left(y \leq 1.55 \cdot 10^{+56}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3200 \lor \neg \left(z \leq 2500000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3200.0) (not (<= z 2500000000.0)))
   (+ x y)
   (- (- z) (/ (* x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3200.0) || !(z <= 2500000000.0)) {
		tmp = x + y;
	} else {
		tmp = -z - ((x * z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3200.0d0)) .or. (.not. (z <= 2500000000.0d0))) then
        tmp = x + y
    else
        tmp = -z - ((x * z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3200.0) || !(z <= 2500000000.0)) {
		tmp = x + y;
	} else {
		tmp = -z - ((x * z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3200.0) or not (z <= 2500000000.0):
		tmp = x + y
	else:
		tmp = -z - ((x * z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3200.0) || !(z <= 2500000000.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(-z) - Float64(Float64(x * z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3200.0) || ~((z <= 2500000000.0)))
		tmp = x + y;
	else
		tmp = -z - ((x * z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3200.0], N[Not[LessEqual[z, 2500000000.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[((-z) - N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3200 or 2.5e9 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 75.3%

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

      1. +-commutative 75.3%

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

   5. Simplified 75.3%

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

   if -3200 < z < 2.5e9

   1. Initial program 81.9%

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

   3. Taylor expanded in y around inf 58.6%

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

      1. neg-mul-1 58.6%

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

      2. distribute-neg-frac2 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in x around 0 75.3%

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

      1. mul-1-neg 75.3%

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

      2. unsub-neg 75.3%

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

      3. mul-1-neg 75.3%

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

      4. associate-/l* 72.6%

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

   8. Simplified 72.6%

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

   9. Taylor expanded in x around 0 75.3%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3200 \lor \neg \left(z \leq 2500000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+91} \lor \neg \left(y \leq 1.45 \cdot 10^{+82}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8.8e+91) (not (<= y 1.45e+82))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.8e+91) || !(y <= 1.45e+82)) {
		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 <= (-8.8d+91)) .or. (.not. (y <= 1.45d+82))) 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 <= -8.8e+91) || !(y <= 1.45e+82)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8.8e+91) or not (y <= 1.45e+82):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8.8e+91) || !(y <= 1.45e+82))
		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 <= -8.8e+91) || ~((y <= 1.45e+82)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8.8e+91], N[Not[LessEqual[y, 1.45e+82]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.79999999999999998e91 or 1.4500000000000001e82 < y

   1. Initial program 72.4%

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

   3. Taylor expanded in y around inf 75.7%

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

      1. neg-mul-1 75.7%

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

   5. Simplified 75.7%

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

   if -8.79999999999999998e91 < y < 1.4500000000000001e82

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 67.2%

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

      1. +-commutative 67.2%

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

   5. Simplified 67.2%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+91} \lor \neg \left(y \leq 1.45 \cdot 10^{+82}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 39.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-123}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9.2e-9) x (if (<= x 7e-123) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.2e-9) {
		tmp = x;
	} else if (x <= 7e-123) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-9.2d-9)) then
        tmp = x
    else if (x <= 7d-123) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.2e-9) {
		tmp = x;
	} else if (x <= 7e-123) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9.2e-9:
		tmp = x
	elif x <= 7e-123:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9.2e-9)
		tmp = x;
	elseif (x <= 7e-123)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9.2e-9)
		tmp = x;
	elseif (x <= 7e-123)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9.2e-9], x, If[LessEqual[x, 7e-123], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -9.1999999999999997e-9 or 6.9999999999999997e-123 < x

   1. Initial program 90.3%

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

   3. Taylor expanded in y around 0 46.4%

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

   if -9.1999999999999997e-9 < x < 6.9999999999999997e-123

   1. Initial program 92.5%

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

   3. Taylor expanded in z around inf 51.1%

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

      1. +-commutative 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in y around inf 39.5%

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

Alternative 10: 35.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 91.1%

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

3. Taylor expanded in y around 0 35.7%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 93.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y + x}{-y} \cdot z\\ \mathbf{if}\;y < -3.7429310762689856 \cdot 10^{+171}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y < 3.5534662456086734 \cdot 10^{+168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

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

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