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

Percentage Accurate: 88.2% → 99.8%

Time: 6.2s

Alternatives: 10

Speedup: 0.3×

• could not determine a ground truth

  1. x = 1.1170867005291165e-241
  2. y = 1.0229131818298259e-241
  3. z = -2.0565049842392974e-22

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: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-291} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-291) (not (<= t_0 0.0))) 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-291) || !(t_0 <= 0.0)) {
		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-291)) .or. (.not. (t_0 <= 0.0d0))) 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-291) || !(t_0 <= 0.0)) {
		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-291) or not (t_0 <= 0.0):
		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-291) || !(t_0 <= 0.0))
		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-291) || ~((t_0 <= 0.0)))
		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-291], N[Not[LessEqual[t$95$0, 0.0]], $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 #s(literal 1 binary64) (/.f64 y z))) < -1.99999999999999992e-291 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 -1.99999999999999992e-291 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 5.8%

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

   3. Taylor expanded in y around inf 99.9%

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

   5. Simplified 87.8%

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

   6. Taylor expanded in y around -inf 99.9%

      \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z + {z}^{2}}{y}} \]
   7. Step-by-step derivation

      1. neg-mul-1 99.9%

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

      2. mul-1-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. unpow2 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. associate-/l* 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x around inf 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-291} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 66.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+82}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-57}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-105}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.4e+82)
   (- z)
   (if (<= y -4.5e-57)
     (+ x y)
     (if (<= y -5.4e-105)
       (* x (/ z (- y)))
       (if (<= y 2.55e+76) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e+82) {
		tmp = -z;
	} else if (y <= -4.5e-57) {
		tmp = x + y;
	} else if (y <= -5.4e-105) {
		tmp = x * (z / -y);
	} else if (y <= 2.55e+76) {
		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 <= (-1.4d+82)) then
        tmp = -z
    else if (y <= (-4.5d-57)) then
        tmp = x + y
    else if (y <= (-5.4d-105)) then
        tmp = x * (z / -y)
    else if (y <= 2.55d+76) 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 <= -1.4e+82) {
		tmp = -z;
	} else if (y <= -4.5e-57) {
		tmp = x + y;
	} else if (y <= -5.4e-105) {
		tmp = x * (z / -y);
	} else if (y <= 2.55e+76) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.4e+82:
		tmp = -z
	elif y <= -4.5e-57:
		tmp = x + y
	elif y <= -5.4e-105:
		tmp = x * (z / -y)
	elif y <= 2.55e+76:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.4e+82)
		tmp = Float64(-z);
	elseif (y <= -4.5e-57)
		tmp = Float64(x + y);
	elseif (y <= -5.4e-105)
		tmp = Float64(x * Float64(z / Float64(-y)));
	elseif (y <= 2.55e+76)
		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 <= -1.4e+82)
		tmp = -z;
	elseif (y <= -4.5e-57)
		tmp = x + y;
	elseif (y <= -5.4e-105)
		tmp = x * (z / -y);
	elseif (y <= 2.55e+76)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.4e+82], (-z), If[LessEqual[y, -4.5e-57], N[(x + y), $MachinePrecision], If[LessEqual[y, -5.4e-105], N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.55e+76], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4e82 or 2.5500000000000001e76 < y

   1. Initial program 70.5%

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

   3. Taylor expanded in y around inf 68.6%

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

      1. mul-1-neg 68.6%

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

   5. Simplified 68.6%

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

   if -1.4e82 < y < -4.49999999999999973e-57 or -5.39999999999999985e-105 < y < 2.5500000000000001e76

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 73.4%

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

      1. +-commutative 73.4%

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

   5. Simplified 73.4%

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

   if -4.49999999999999973e-57 < y < -5.39999999999999985e-105

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 90.7%

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

   4. Taylor expanded in y around inf 81.1%

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

      1. mul-1-neg 81.1%

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

      2. associate-*r/ 80.8%

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

      3. distribute-rgt-neg-in 80.8%

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

      4. distribute-frac-neg2 80.8%

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

   6. Simplified 80.8%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+82}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-57}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-105}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+81}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-57}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{\frac{y}{-z}}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+75}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.8e+81)
   (- z)
   (if (<= y -4.5e-57)
     (+ x y)
     (if (<= y -5.4e-105)
       (/ x (/ y (- z)))
       (if (<= y 4.9e+75) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.8e+81) {
		tmp = -z;
	} else if (y <= -4.5e-57) {
		tmp = x + y;
	} else if (y <= -5.4e-105) {
		tmp = x / (y / -z);
	} else if (y <= 4.9e+75) {
		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 <= (-6.8d+81)) then
        tmp = -z
    else if (y <= (-4.5d-57)) then
        tmp = x + y
    else if (y <= (-5.4d-105)) then
        tmp = x / (y / -z)
    else if (y <= 4.9d+75) 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 <= -6.8e+81) {
		tmp = -z;
	} else if (y <= -4.5e-57) {
		tmp = x + y;
	} else if (y <= -5.4e-105) {
		tmp = x / (y / -z);
	} else if (y <= 4.9e+75) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.8e+81:
		tmp = -z
	elif y <= -4.5e-57:
		tmp = x + y
	elif y <= -5.4e-105:
		tmp = x / (y / -z)
	elif y <= 4.9e+75:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.8e+81)
		tmp = Float64(-z);
	elseif (y <= -4.5e-57)
		tmp = Float64(x + y);
	elseif (y <= -5.4e-105)
		tmp = Float64(x / Float64(y / Float64(-z)));
	elseif (y <= 4.9e+75)
		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 <= -6.8e+81)
		tmp = -z;
	elseif (y <= -4.5e-57)
		tmp = x + y;
	elseif (y <= -5.4e-105)
		tmp = x / (y / -z);
	elseif (y <= 4.9e+75)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.8e+81], (-z), If[LessEqual[y, -4.5e-57], N[(x + y), $MachinePrecision], If[LessEqual[y, -5.4e-105], N[(x / N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.9e+75], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.80000000000000005e81 or 4.9000000000000001e75 < y

   1. Initial program 70.5%

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

   3. Taylor expanded in y around inf 68.6%

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

      1. mul-1-neg 68.6%

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

   5. Simplified 68.6%

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

   if -6.80000000000000005e81 < y < -4.49999999999999973e-57 or -5.39999999999999985e-105 < y < 4.9000000000000001e75

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 73.4%

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

      1. +-commutative 73.4%

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

   5. Simplified 73.4%

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

   if -4.49999999999999973e-57 < y < -5.39999999999999985e-105

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 90.7%

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

   4. Taylor expanded in y around inf 81.1%

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

      1. neg-mul-1 81.1%

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

      2. distribute-neg-frac 81.1%

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

   6. Simplified 81.1%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+81}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-57}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{\frac{y}{-z}}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+75}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+16} \lor \neg \left(z \leq 9.6 \cdot 10^{+37}\right):\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.52e+16) (not (<= z 9.6e+37)))
   (* (+ x y) (+ 1.0 (/ y z)))
   (- (- z) (* z (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.52e+16) || !(z <= 9.6e+37)) {
		tmp = (x + y) * (1.0 + (y / z));
	} 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) :: tmp
    if ((z <= (-1.52d+16)) .or. (.not. (z <= 9.6d+37))) then
        tmp = (x + y) * (1.0d0 + (y / z))
    else
        tmp = -z - (z * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.52e+16) || !(z <= 9.6e+37)) {
		tmp = (x + y) * (1.0 + (y / z));
	} else {
		tmp = -z - (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.52e+16) or not (z <= 9.6e+37):
		tmp = (x + y) * (1.0 + (y / z))
	else:
		tmp = -z - (z * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.52e+16) || !(z <= 9.6e+37))
		tmp = Float64(Float64(x + y) * Float64(1.0 + Float64(y / z)));
	else
		tmp = Float64(Float64(-z) - Float64(z * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.52e+16) || ~((z <= 9.6e+37)))
		tmp = (x + y) * (1.0 + (y / z));
	else
		tmp = -z - (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.52e+16], N[Not[LessEqual[z, 9.6e+37]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] * N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-z) - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.52e16 or 9.5999999999999999e37 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 73.3%

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

      1. associate-+r+ 73.3%

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

      2. *-rgt-identity 73.3%

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

      3. *-commutative 73.3%

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

      4. associate-/l* 84.3%

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

      5. distribute-lft-in 84.3%

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

      6. +-commutative 84.3%

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

   5. Simplified 84.3%

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

   if -1.52e16 < z < 9.5999999999999999e37

   1. Initial program 78.7%

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

   3. Taylor expanded in y around inf 76.9%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in y around -inf 78.4%

      \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z + {z}^{2}}{y}} \]
   7. Step-by-step derivation

      1. neg-mul-1 78.4%

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

      2. mul-1-neg 78.4%

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

      3. unsub-neg 78.4%

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

      4. unpow2 78.4%

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

      5. distribute-rgt-in 78.4%

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

      6. associate-/l* 75.3%

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

   8. Simplified 75.3%

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

   9. Taylor expanded in x around inf 75.3%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+16} \lor \neg \left(z \leq 9.6 \cdot 10^{+37}\right):\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+16} \lor \neg \left(z \leq 2.9 \cdot 10^{+37}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.65e+16) (not (<= z 2.9e+37)))
   (+ x y)
   (- (- z) (* z (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.65e+16) || !(z <= 2.9e+37)) {
		tmp = x + y;
	} 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) :: tmp
    if ((z <= (-2.65d+16)) .or. (.not. (z <= 2.9d+37))) then
        tmp = x + y
    else
        tmp = -z - (z * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.65e+16) || !(z <= 2.9e+37)) {
		tmp = x + y;
	} else {
		tmp = -z - (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.65e+16) or not (z <= 2.9e+37):
		tmp = x + y
	else:
		tmp = -z - (z * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.65e+16) || !(z <= 2.9e+37))
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(-z) - Float64(z * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.65e+16) || ~((z <= 2.9e+37)))
		tmp = x + y;
	else
		tmp = -z - (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.65e+16], N[Not[LessEqual[z, 2.9e+37]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[((-z) - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.65e16 or 2.89999999999999978e37 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 84.2%

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

      1. +-commutative 84.2%

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

   5. Simplified 84.2%

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

   if -2.65e16 < z < 2.89999999999999978e37

   1. Initial program 78.7%

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

   3. Taylor expanded in y around inf 76.9%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in y around -inf 78.4%

      \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z + {z}^{2}}{y}} \]
   7. Step-by-step derivation

      1. neg-mul-1 78.4%

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

      2. mul-1-neg 78.4%

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

      3. unsub-neg 78.4%

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

      4. unpow2 78.4%

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

      5. distribute-rgt-in 78.4%

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

      6. associate-/l* 75.3%

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

   8. Simplified 75.3%

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

   9. Taylor expanded in x around inf 75.3%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+16} \lor \neg \left(z \leq 2.9 \cdot 10^{+37}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+16} \lor \neg \left(z \leq 1.35 \cdot 10^{+37}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.5e+16) (not (<= z 1.35e+37)))
   (+ x y)
   (* z (- -1.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e+16) || !(z <= 1.35e+37)) {
		tmp = x + y;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2.5d+16)) .or. (.not. (z <= 1.35d+37))) then
        tmp = x + y
    else
        tmp = z * ((-1.0d0) - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e+16) || !(z <= 1.35e+37)) {
		tmp = x + y;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.5e+16) or not (z <= 1.35e+37):
		tmp = x + y
	else:
		tmp = z * (-1.0 - (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.5e+16) || !(z <= 1.35e+37))
		tmp = Float64(x + y);
	else
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.5e+16) || ~((z <= 1.35e+37)))
		tmp = x + y;
	else
		tmp = z * (-1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.5e+16], N[Not[LessEqual[z, 1.35e+37]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5e16 or 1.34999999999999993e37 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 84.2%

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

      1. +-commutative 84.2%

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

   5. Simplified 84.2%

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

   if -2.5e16 < z < 1.34999999999999993e37

   1. Initial program 78.7%

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

   3. Taylor expanded in y around inf 76.9%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in y around -inf 78.4%

      \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z + {z}^{2}}{y}} \]
   7. Step-by-step derivation

      1. neg-mul-1 78.4%

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

      2. mul-1-neg 78.4%

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

      3. unsub-neg 78.4%

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

      4. unpow2 78.4%

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

      5. distribute-rgt-in 78.4%

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

      6. associate-/l* 75.3%

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

   8. Simplified 75.3%

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

   9. Taylor expanded in z around 0 75.3%

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

       1. mul-1-neg 75.3%

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

       2. distribute-rgt-neg-in 75.3%

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

       3. distribute-neg-in 75.3%

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

       4. metadata-eval 75.3%

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

       5. sub-neg 75.3%

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

   11. Simplified 75.3%

       \[\leadsto \color{blue}{z \cdot \left(-1 - \frac{x}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+16} \lor \neg \left(z \leq 1.35 \cdot 10^{+37}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+81} \lor \neg \left(y \leq 2.1 \cdot 10^{+77}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.7e+81) (not (<= y 2.1e+77))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.7e+81) || !(y <= 2.1e+77)) {
		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 <= (-2.7d+81)) .or. (.not. (y <= 2.1d+77))) 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 <= -2.7e+81) || !(y <= 2.1e+77)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.7e+81) or not (y <= 2.1e+77):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.7e+81) || !(y <= 2.1e+77))
		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 <= -2.7e+81) || ~((y <= 2.1e+77)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.7e+81], N[Not[LessEqual[y, 2.1e+77]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6999999999999999e81 or 2.0999999999999999e77 < y

   1. Initial program 70.5%

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

   3. Taylor expanded in y around inf 68.6%

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

      1. mul-1-neg 68.6%

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

   5. Simplified 68.6%

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

   if -2.6999999999999999e81 < y < 2.0999999999999999e77

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 70.3%

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

      1. +-commutative 70.3%

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

   5. Simplified 70.3%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+81} \lor \neg \left(y \leq 2.1 \cdot 10^{+77}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-18} \lor \neg \left(y \leq 3.2 \cdot 10^{-50}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6e-18) (not (<= y 3.2e-50))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6e-18) || !(y <= 3.2e-50)) {
		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 <= (-6d-18)) .or. (.not. (y <= 3.2d-50))) 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 <= -6e-18) || !(y <= 3.2e-50)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6e-18) or not (y <= 3.2e-50):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6e-18) || !(y <= 3.2e-50))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6e-18) || ~((y <= 3.2e-50)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6e-18], N[Not[LessEqual[y, 3.2e-50]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -5.99999999999999966e-18 or 3.2e-50 < y

   1. Initial program 81.0%

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

   3. Taylor expanded in y around inf 54.7%

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

      1. mul-1-neg 54.7%

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

   5. Simplified 54.7%

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

   if -5.99999999999999966e-18 < y < 3.2e-50

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 65.1%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-18} \lor \neg \left(y \leq 3.2 \cdot 10^{-50}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 41.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-174}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9.5e-77) x (if (<= x 1.4e-174) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.5e-77) {
		tmp = x;
	} else if (x <= 1.4e-174) {
		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 <= (-9.5d-77)) then
        tmp = x
    else if (x <= 1.4d-174) 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 <= -9.5e-77) {
		tmp = x;
	} else if (x <= 1.4e-174) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9.5e-77:
		tmp = x
	elif x <= 1.4e-174:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9.5e-77)
		tmp = x;
	elseif (x <= 1.4e-174)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9.5e-77)
		tmp = x;
	elseif (x <= 1.4e-174)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9.5e-77], x, If[LessEqual[x, 1.4e-174], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5000000000000005e-77 or 1.39999999999999999e-174 < x

   1. Initial program 91.1%

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

   3. Taylor expanded in y around 0 40.6%

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

   if -9.5000000000000005e-77 < x < 1.39999999999999999e-174

   1. Initial program 83.1%

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

   3. Taylor expanded in x around 0 67.1%

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

   4. Taylor expanded in y around 0 40.1%

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

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-174}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 35.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 88.5%

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

3. Taylor expanded in y around 0 33.1%

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

4. Final simplification 33.1%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 93.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024079 
(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))))