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

Percentage Accurate: 88.2% → 99.5%

Time: 10.3s

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

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

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (<= t_0 -2e-262)
     t_0
     (if (<= t_0 0.0) (- (- 0.0 z) (/ (* z x) y)) t_0))))

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) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (0.0 - z) - ((z * x) / y);
	} 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 = (x + y) / (1.0d0 - (y / z))
    if (t_0 <= (-2d-262)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = (0.0d0 - z) - ((z * x) / y)
    else
        tmp = t_0
    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) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (0.0 - z) - ((z * x) / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if t_0 <= -2e-262:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = (0.0 - z) - ((z * x) / y)
	else:
		tmp = t_0
	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)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(0.0 - z) - Float64(Float64(z * x) / y));
	else
		tmp = t_0;
	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)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = (0.0 - z) - ((z * x) / y);
	else
		tmp = t_0;
	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[LessEqual[t$95$0, -2e-262], t$95$0, If[LessEqual[t$95$0, 0.0], N[(N[(0.0 - z), $MachinePrecision] - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 73.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot \left(1 + \frac{x}{z}\right)\\ t_1 := z \cdot \left(-1 - \frac{x}{y}\right)\\ t_2 := 1 - \frac{y}{z}\\ t_3 := \frac{x}{t\_2}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-9}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-200}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+41}:\\ \;\;\;\;\frac{y}{t\_2}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+56}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y (+ 1.0 (/ x z)))))
        (t_1 (* z (- -1.0 (/ x y))))
        (t_2 (- 1.0 (/ y z)))
        (t_3 (/ x t_2)))
   (if (<= y -3.6e+38)
     t_1
     (if (<= y -2.15e-9)
       t_0
       (if (<= y -4.5e-54)
         t_1
         (if (<= y -1.85e-200)
           t_0
           (if (<= y 4000000000.0)
             t_3
             (if (<= y 1.45e+41) (/ y t_2) (if (<= y 6.5e+56) t_3 t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * (1.0 + (x / z)));
	double t_1 = z * (-1.0 - (x / y));
	double t_2 = 1.0 - (y / z);
	double t_3 = x / t_2;
	double tmp;
	if (y <= -3.6e+38) {
		tmp = t_1;
	} else if (y <= -2.15e-9) {
		tmp = t_0;
	} else if (y <= -4.5e-54) {
		tmp = t_1;
	} else if (y <= -1.85e-200) {
		tmp = t_0;
	} else if (y <= 4000000000.0) {
		tmp = t_3;
	} else if (y <= 1.45e+41) {
		tmp = y / t_2;
	} else if (y <= 6.5e+56) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	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) :: t_3
    real(8) :: tmp
    t_0 = x + (y * (1.0d0 + (x / z)))
    t_1 = z * ((-1.0d0) - (x / y))
    t_2 = 1.0d0 - (y / z)
    t_3 = x / t_2
    if (y <= (-3.6d+38)) then
        tmp = t_1
    else if (y <= (-2.15d-9)) then
        tmp = t_0
    else if (y <= (-4.5d-54)) then
        tmp = t_1
    else if (y <= (-1.85d-200)) then
        tmp = t_0
    else if (y <= 4000000000.0d0) then
        tmp = t_3
    else if (y <= 1.45d+41) then
        tmp = y / t_2
    else if (y <= 6.5d+56) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * (1.0 + (x / z)));
	double t_1 = z * (-1.0 - (x / y));
	double t_2 = 1.0 - (y / z);
	double t_3 = x / t_2;
	double tmp;
	if (y <= -3.6e+38) {
		tmp = t_1;
	} else if (y <= -2.15e-9) {
		tmp = t_0;
	} else if (y <= -4.5e-54) {
		tmp = t_1;
	} else if (y <= -1.85e-200) {
		tmp = t_0;
	} else if (y <= 4000000000.0) {
		tmp = t_3;
	} else if (y <= 1.45e+41) {
		tmp = y / t_2;
	} else if (y <= 6.5e+56) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * (1.0 + (x / z)))
	t_1 = z * (-1.0 - (x / y))
	t_2 = 1.0 - (y / z)
	t_3 = x / t_2
	tmp = 0
	if y <= -3.6e+38:
		tmp = t_1
	elif y <= -2.15e-9:
		tmp = t_0
	elif y <= -4.5e-54:
		tmp = t_1
	elif y <= -1.85e-200:
		tmp = t_0
	elif y <= 4000000000.0:
		tmp = t_3
	elif y <= 1.45e+41:
		tmp = y / t_2
	elif y <= 6.5e+56:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * Float64(1.0 + Float64(x / z))))
	t_1 = Float64(z * Float64(-1.0 - Float64(x / y)))
	t_2 = Float64(1.0 - Float64(y / z))
	t_3 = Float64(x / t_2)
	tmp = 0.0
	if (y <= -3.6e+38)
		tmp = t_1;
	elseif (y <= -2.15e-9)
		tmp = t_0;
	elseif (y <= -4.5e-54)
		tmp = t_1;
	elseif (y <= -1.85e-200)
		tmp = t_0;
	elseif (y <= 4000000000.0)
		tmp = t_3;
	elseif (y <= 1.45e+41)
		tmp = Float64(y / t_2);
	elseif (y <= 6.5e+56)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * (1.0 + (x / z)));
	t_1 = z * (-1.0 - (x / y));
	t_2 = 1.0 - (y / z);
	t_3 = x / t_2;
	tmp = 0.0;
	if (y <= -3.6e+38)
		tmp = t_1;
	elseif (y <= -2.15e-9)
		tmp = t_0;
	elseif (y <= -4.5e-54)
		tmp = t_1;
	elseif (y <= -1.85e-200)
		tmp = t_0;
	elseif (y <= 4000000000.0)
		tmp = t_3;
	elseif (y <= 1.45e+41)
		tmp = y / t_2;
	elseif (y <= 6.5e+56)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * N[(1.0 + N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / t$95$2), $MachinePrecision]}, If[LessEqual[y, -3.6e+38], t$95$1, If[LessEqual[y, -2.15e-9], t$95$0, If[LessEqual[y, -4.5e-54], t$95$1, If[LessEqual[y, -1.85e-200], t$95$0, If[LessEqual[y, 4000000000.0], t$95$3, If[LessEqual[y, 1.45e+41], N[(y / t$95$2), $MachinePrecision], If[LessEqual[y, 6.5e+56], t$95$3, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.59999999999999969e38 or -2.14999999999999981e-9 < y < -4.4999999999999998e-54 or 6.5000000000000001e56 < y

   1. Initial program 79.1%

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

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -3.59999999999999969e38 < y < -2.14999999999999981e-9 or -4.4999999999999998e-54 < y < -1.85000000000000005e-200

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.85000000000000005e-200 < y < 4e9 or 1.44999999999999994e41 < y < 6.5000000000000001e56

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 4e9 < y < 1.44999999999999994e41

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 73.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ t_1 := 1 - \frac{y}{z}\\ t_2 := \frac{x}{t\_1}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+39}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-6}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-55}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-200}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 17000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+41}:\\ \;\;\;\;\frac{y}{t\_1}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 -2.3e+39)
     t_0
     (if (<= y -4.6e-6)
       (+ y x)
       (if (<= y -2e-55)
         t_0
         (if (<= y -1.45e-200)
           (+ y x)
           (if (<= y 17000000000.0)
             t_2
             (if (<= y 3.3e+41) (/ y t_1) (if (<= y 7.2e+55) 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 <= -2.3e+39) {
		tmp = t_0;
	} else if (y <= -4.6e-6) {
		tmp = y + x;
	} else if (y <= -2e-55) {
		tmp = t_0;
	} else if (y <= -1.45e-200) {
		tmp = y + x;
	} else if (y <= 17000000000.0) {
		tmp = t_2;
	} else if (y <= 3.3e+41) {
		tmp = y / t_1;
	} else if (y <= 7.2e+55) {
		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 <= (-2.3d+39)) then
        tmp = t_0
    else if (y <= (-4.6d-6)) then
        tmp = y + x
    else if (y <= (-2d-55)) then
        tmp = t_0
    else if (y <= (-1.45d-200)) then
        tmp = y + x
    else if (y <= 17000000000.0d0) then
        tmp = t_2
    else if (y <= 3.3d+41) then
        tmp = y / t_1
    else if (y <= 7.2d+55) 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 <= -2.3e+39) {
		tmp = t_0;
	} else if (y <= -4.6e-6) {
		tmp = y + x;
	} else if (y <= -2e-55) {
		tmp = t_0;
	} else if (y <= -1.45e-200) {
		tmp = y + x;
	} else if (y <= 17000000000.0) {
		tmp = t_2;
	} else if (y <= 3.3e+41) {
		tmp = y / t_1;
	} else if (y <= 7.2e+55) {
		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 <= -2.3e+39:
		tmp = t_0
	elif y <= -4.6e-6:
		tmp = y + x
	elif y <= -2e-55:
		tmp = t_0
	elif y <= -1.45e-200:
		tmp = y + x
	elif y <= 17000000000.0:
		tmp = t_2
	elif y <= 3.3e+41:
		tmp = y / t_1
	elif y <= 7.2e+55:
		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 <= -2.3e+39)
		tmp = t_0;
	elseif (y <= -4.6e-6)
		tmp = Float64(y + x);
	elseif (y <= -2e-55)
		tmp = t_0;
	elseif (y <= -1.45e-200)
		tmp = Float64(y + x);
	elseif (y <= 17000000000.0)
		tmp = t_2;
	elseif (y <= 3.3e+41)
		tmp = Float64(y / t_1);
	elseif (y <= 7.2e+55)
		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 <= -2.3e+39)
		tmp = t_0;
	elseif (y <= -4.6e-6)
		tmp = y + x;
	elseif (y <= -2e-55)
		tmp = t_0;
	elseif (y <= -1.45e-200)
		tmp = y + x;
	elseif (y <= 17000000000.0)
		tmp = t_2;
	elseif (y <= 3.3e+41)
		tmp = y / t_1;
	elseif (y <= 7.2e+55)
		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, -2.3e+39], t$95$0, If[LessEqual[y, -4.6e-6], N[(y + x), $MachinePrecision], If[LessEqual[y, -2e-55], t$95$0, If[LessEqual[y, -1.45e-200], N[(y + x), $MachinePrecision], If[LessEqual[y, 17000000000.0], t$95$2, If[LessEqual[y, 3.3e+41], N[(y / t$95$1), $MachinePrecision], If[LessEqual[y, 7.2e+55], t$95$2, t$95$0]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.30000000000000012e39 or -4.6e-6 < y < -1.99999999999999999e-55 or 7.19999999999999975e55 < y

   1. Initial program 79.1%

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

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.30000000000000012e39 < y < -4.6e-6 or -1.99999999999999999e-55 < y < -1.45e-200

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.45e-200 < y < 1.7e10 or 3.3e41 < y < 7.19999999999999975e55

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.7e10 < y < 3.3e41

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 4: 73.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot \left(1 + \frac{x}{z}\right)\\ t_1 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.3 \cdot 10^{-9}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-55}:\\ \;\;\;\;\left(0 - z\right) - \frac{z \cdot x}{y}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-200}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+56}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y (+ 1.0 (/ x z))))) (t_1 (* z (- -1.0 (/ x y)))))
   (if (<= y -1e+39)
     t_1
     (if (<= y -6.3e-9)
       t_0
       (if (<= y -2e-55)
         (- (- 0.0 z) (/ (* z x) y))
         (if (<= y -1.8e-200)
           t_0
           (if (<= y 1.1e+56) (/ x (- 1.0 (/ y z))) t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * (1.0 + (x / z)));
	double t_1 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -1e+39) {
		tmp = t_1;
	} else if (y <= -6.3e-9) {
		tmp = t_0;
	} else if (y <= -2e-55) {
		tmp = (0.0 - z) - ((z * x) / y);
	} else if (y <= -1.8e-200) {
		tmp = t_0;
	} else if (y <= 1.1e+56) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x + (y * (1.0d0 + (x / z)))
    t_1 = z * ((-1.0d0) - (x / y))
    if (y <= (-1d+39)) then
        tmp = t_1
    else if (y <= (-6.3d-9)) then
        tmp = t_0
    else if (y <= (-2d-55)) then
        tmp = (0.0d0 - z) - ((z * x) / y)
    else if (y <= (-1.8d-200)) then
        tmp = t_0
    else if (y <= 1.1d+56) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * (1.0 + (x / z)));
	double t_1 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -1e+39) {
		tmp = t_1;
	} else if (y <= -6.3e-9) {
		tmp = t_0;
	} else if (y <= -2e-55) {
		tmp = (0.0 - z) - ((z * x) / y);
	} else if (y <= -1.8e-200) {
		tmp = t_0;
	} else if (y <= 1.1e+56) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * (1.0 + (x / z)))
	t_1 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -1e+39:
		tmp = t_1
	elif y <= -6.3e-9:
		tmp = t_0
	elif y <= -2e-55:
		tmp = (0.0 - z) - ((z * x) / y)
	elif y <= -1.8e-200:
		tmp = t_0
	elif y <= 1.1e+56:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * Float64(1.0 + Float64(x / z))))
	t_1 = Float64(z * Float64(-1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -1e+39)
		tmp = t_1;
	elseif (y <= -6.3e-9)
		tmp = t_0;
	elseif (y <= -2e-55)
		tmp = Float64(Float64(0.0 - z) - Float64(Float64(z * x) / y));
	elseif (y <= -1.8e-200)
		tmp = t_0;
	elseif (y <= 1.1e+56)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * (1.0 + (x / z)));
	t_1 = z * (-1.0 - (x / y));
	tmp = 0.0;
	if (y <= -1e+39)
		tmp = t_1;
	elseif (y <= -6.3e-9)
		tmp = t_0;
	elseif (y <= -2e-55)
		tmp = (0.0 - z) - ((z * x) / y);
	elseif (y <= -1.8e-200)
		tmp = t_0;
	elseif (y <= 1.1e+56)
		tmp = x / (1.0 - (y / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * N[(1.0 + N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+39], t$95$1, If[LessEqual[y, -6.3e-9], t$95$0, If[LessEqual[y, -2e-55], N[(N[(0.0 - z), $MachinePrecision] - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.8e-200], t$95$0, If[LessEqual[y, 1.1e+56], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.9999999999999994e38 or 1.10000000000000008e56 < y

   1. Initial program 77.0%

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

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -9.9999999999999994e38 < y < -6.3000000000000002e-9 or -1.99999999999999999e-55 < y < -1.8000000000000001e-200

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -6.3000000000000002e-9 < y < -1.99999999999999999e-55

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -1.8000000000000001e-200 < y < 1.10000000000000008e56

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 5: 73.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-7}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-57}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-200}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))))
   (if (<= y -2.5e+38)
     t_0
     (if (<= y -5.5e-7)
       (+ y x)
       (if (<= y -8.5e-57)
         t_0
         (if (<= y -1.25e-200)
           (+ y x)
           (if (<= y 8.8e+55) (/ 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 <= -5.5e-7) {
		tmp = y + x;
	} else if (y <= -8.5e-57) {
		tmp = t_0;
	} else if (y <= -1.25e-200) {
		tmp = y + x;
	} else if (y <= 8.8e+55) {
		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 <= (-5.5d-7)) then
        tmp = y + x
    else if (y <= (-8.5d-57)) then
        tmp = t_0
    else if (y <= (-1.25d-200)) then
        tmp = y + x
    else if (y <= 8.8d+55) 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 <= -5.5e-7) {
		tmp = y + x;
	} else if (y <= -8.5e-57) {
		tmp = t_0;
	} else if (y <= -1.25e-200) {
		tmp = y + x;
	} else if (y <= 8.8e+55) {
		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 <= -5.5e-7:
		tmp = y + x
	elif y <= -8.5e-57:
		tmp = t_0
	elif y <= -1.25e-200:
		tmp = y + x
	elif y <= 8.8e+55:
		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 <= -5.5e-7)
		tmp = Float64(y + x);
	elseif (y <= -8.5e-57)
		tmp = t_0;
	elseif (y <= -1.25e-200)
		tmp = Float64(y + x);
	elseif (y <= 8.8e+55)
		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 <= -5.5e-7)
		tmp = y + x;
	elseif (y <= -8.5e-57)
		tmp = t_0;
	elseif (y <= -1.25e-200)
		tmp = y + x;
	elseif (y <= 8.8e+55)
		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, -5.5e-7], N[(y + x), $MachinePrecision], If[LessEqual[y, -8.5e-57], t$95$0, If[LessEqual[y, -1.25e-200], N[(y + x), $MachinePrecision], If[LessEqual[y, 8.8e+55], 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 -5.5000000000000003e-7 < y < -8.49999999999999955e-57 or 8.80000000000000042e55 < y

   1. Initial program 79.1%

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

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.49999999999999985e38 < y < -5.5000000000000003e-7 or -8.49999999999999955e-57 < y < -1.24999999999999998e-200

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.24999999999999998e-200 < y < 8.80000000000000042e55

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 74.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+38}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-7}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+40}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))))
   (if (<= y -5.6e+38)
     t_0
     (if (<= y -1.95e-7)
       (+ y x)
       (if (<= y -3.4e-54) t_0 (if (<= y 7.8e+40) (+ y x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -5.6e+38) {
		tmp = t_0;
	} else if (y <= -1.95e-7) {
		tmp = y + x;
	} else if (y <= -3.4e-54) {
		tmp = t_0;
	} else if (y <= 7.8e+40) {
		tmp = y + x;
	} 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 <= (-5.6d+38)) then
        tmp = t_0
    else if (y <= (-1.95d-7)) then
        tmp = y + x
    else if (y <= (-3.4d-54)) then
        tmp = t_0
    else if (y <= 7.8d+40) then
        tmp = y + x
    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 <= -5.6e+38) {
		tmp = t_0;
	} else if (y <= -1.95e-7) {
		tmp = y + x;
	} else if (y <= -3.4e-54) {
		tmp = t_0;
	} else if (y <= 7.8e+40) {
		tmp = y + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -5.6e+38:
		tmp = t_0
	elif y <= -1.95e-7:
		tmp = y + x
	elif y <= -3.4e-54:
		tmp = t_0
	elif y <= 7.8e+40:
		tmp = y + x
	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 <= -5.6e+38)
		tmp = t_0;
	elseif (y <= -1.95e-7)
		tmp = Float64(y + x);
	elseif (y <= -3.4e-54)
		tmp = t_0;
	elseif (y <= 7.8e+40)
		tmp = Float64(y + x);
	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 <= -5.6e+38)
		tmp = t_0;
	elseif (y <= -1.95e-7)
		tmp = y + x;
	elseif (y <= -3.4e-54)
		tmp = t_0;
	elseif (y <= 7.8e+40)
		tmp = y + x;
	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, -5.6e+38], t$95$0, If[LessEqual[y, -1.95e-7], N[(y + x), $MachinePrecision], If[LessEqual[y, -3.4e-54], t$95$0, If[LessEqual[y, 7.8e+40], N[(y + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.6e38 or -1.95000000000000012e-7 < y < -3.39999999999999987e-54 or 7.8000000000000002e40 < y

   1. Initial program 80.7%

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

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -5.6e38 < y < -1.95000000000000012e-7 or -3.39999999999999987e-54 < y < 7.8000000000000002e40

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 57.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+47}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-7}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-54}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.7e+47)
   (- z)
   (if (<= y -8.8e-7)
     y
     (if (<= y -3.8e-54) (- z) (if (<= y 1.25e+56) x (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.7e+47) {
		tmp = -z;
	} else if (y <= -8.8e-7) {
		tmp = y;
	} else if (y <= -3.8e-54) {
		tmp = -z;
	} else if (y <= 1.25e+56) {
		tmp = x;
	} 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 <= (-3.7d+47)) then
        tmp = -z
    else if (y <= (-8.8d-7)) then
        tmp = y
    else if (y <= (-3.8d-54)) then
        tmp = -z
    else if (y <= 1.25d+56) then
        tmp = x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.7e+47) {
		tmp = -z;
	} else if (y <= -8.8e-7) {
		tmp = y;
	} else if (y <= -3.8e-54) {
		tmp = -z;
	} else if (y <= 1.25e+56) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.7e+47:
		tmp = -z
	elif y <= -8.8e-7:
		tmp = y
	elif y <= -3.8e-54:
		tmp = -z
	elif y <= 1.25e+56:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.7e+47)
		tmp = Float64(-z);
	elseif (y <= -8.8e-7)
		tmp = y;
	elseif (y <= -3.8e-54)
		tmp = Float64(-z);
	elseif (y <= 1.25e+56)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.7e+47)
		tmp = -z;
	elseif (y <= -8.8e-7)
		tmp = y;
	elseif (y <= -3.8e-54)
		tmp = -z;
	elseif (y <= 1.25e+56)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.7e+47], (-z), If[LessEqual[y, -8.8e-7], y, If[LessEqual[y, -3.8e-54], (-z), If[LessEqual[y, 1.25e+56], x, (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.70000000000000041e47 or -8.8000000000000004e-7 < y < -3.8000000000000002e-54 or 1.25000000000000006e56 < y

   1. Initial program 78.7%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -3.70000000000000041e47 < y < -8.8000000000000004e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -3.8000000000000002e-54 < y < 1.25000000000000006e56

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 67.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+92}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+81}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.9e+92) (- z) (if (<= y 5.5e+81) (+ y x) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.9e+92) {
		tmp = -z;
	} else if (y <= 5.5e+81) {
		tmp = y + x;
	} 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 <= (-3.9d+92)) then
        tmp = -z
    else if (y <= 5.5d+81) then
        tmp = y + x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.9e+92) {
		tmp = -z;
	} else if (y <= 5.5e+81) {
		tmp = y + x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.9e+92:
		tmp = -z
	elif y <= 5.5e+81:
		tmp = y + x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.9e+92)
		tmp = Float64(-z);
	elseif (y <= 5.5e+81)
		tmp = Float64(y + x);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.9e+92)
		tmp = -z;
	elseif (y <= 5.5e+81)
		tmp = y + x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.9e+92], (-z), If[LessEqual[y, 5.5e+81], N[(y + x), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -3.90000000000000011e92 or 5.5000000000000003e81 < y

   1. Initial program 72.4%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -3.90000000000000011e92 < y < 5.5000000000000003e81

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 39.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-123}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9.2e-9) x (if (<= x 8.5e-123) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.2e-9) {
		tmp = x;
	} else if (x <= 8.5e-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 <= 8.5d-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 <= 8.5e-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 <= 8.5e-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 <= 8.5e-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 <= 8.5e-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, 8.5e-123], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -9.1999999999999997e-9 or 8.4999999999999995e-123 < x

   1. Initial program 90.3%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -9.1999999999999997e-9 < x < 8.4999999999999995e-123

   1. Initial program 92.5%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
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 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. 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))))