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

Percentage Accurate: 88.3% → 99.3%

Time: 8.5s

Alternatives: 8

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{-249} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -5e-249) (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 <= -5e-249) || !(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 <= (-5d-249)) .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 <= -5e-249) || !(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 <= -5e-249) 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 <= -5e-249) || !(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 <= -5e-249) || ~((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, -5e-249], 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 1 (/.f64 y z))) < -4.9999999999999999e-249 or -0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.8%

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

   if -4.9999999999999999e-249 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -0.0

   1. Initial program 9.0%

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

   2. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{z \cdot x}{y}\right) - \frac{{z}^{2}}{y}} \]
   3. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-+l- 100.0%

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

      5. mul-1-neg 100.0%

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

      6. distribute-frac-neg 100.0%

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

      7. mul-1-neg 100.0%

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

      8. div-sub 100.0%

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

      9. sub-neg 100.0%

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

      10. mul-1-neg 100.0%

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

      11. remove-double-neg 100.0%

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

      12. unpow2 100.0%

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

      13. distribute-lft-out 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-249} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \end{array} \]

Alternative 2: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{x}{t_0}\\ t_2 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-132}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-44}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.00038:\\ \;\;\;\;\frac{y}{t_0}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+64}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ x t_0)) (t_2 (* z (- -1.0 (/ x y)))))
   (if (<= y -5.6e-18)
     t_2
     (if (<= y -2.5e-132)
       (+ x y)
       (if (<= y 4.9e-108)
         t_1
         (if (<= y 1.8e-44)
           (+ x y)
           (if (<= y 4e-25)
             t_2
             (if (<= y 3.3e-16)
               t_1
               (if (<= y 0.00038)
                 (/ y t_0)
                 (if (<= y 2e+64) (+ x y) t_2))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = x / t_0;
	double t_2 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -5.6e-18) {
		tmp = t_2;
	} else if (y <= -2.5e-132) {
		tmp = x + y;
	} else if (y <= 4.9e-108) {
		tmp = t_1;
	} else if (y <= 1.8e-44) {
		tmp = x + y;
	} else if (y <= 4e-25) {
		tmp = t_2;
	} else if (y <= 3.3e-16) {
		tmp = t_1;
	} else if (y <= 0.00038) {
		tmp = y / t_0;
	} else if (y <= 2e+64) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = x / t_0
    t_2 = z * ((-1.0d0) - (x / y))
    if (y <= (-5.6d-18)) then
        tmp = t_2
    else if (y <= (-2.5d-132)) then
        tmp = x + y
    else if (y <= 4.9d-108) then
        tmp = t_1
    else if (y <= 1.8d-44) then
        tmp = x + y
    else if (y <= 4d-25) then
        tmp = t_2
    else if (y <= 3.3d-16) then
        tmp = t_1
    else if (y <= 0.00038d0) then
        tmp = y / t_0
    else if (y <= 2d+64) then
        tmp = x + y
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = x / t_0;
	double t_2 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -5.6e-18) {
		tmp = t_2;
	} else if (y <= -2.5e-132) {
		tmp = x + y;
	} else if (y <= 4.9e-108) {
		tmp = t_1;
	} else if (y <= 1.8e-44) {
		tmp = x + y;
	} else if (y <= 4e-25) {
		tmp = t_2;
	} else if (y <= 3.3e-16) {
		tmp = t_1;
	} else if (y <= 0.00038) {
		tmp = y / t_0;
	} else if (y <= 2e+64) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = x / t_0
	t_2 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -5.6e-18:
		tmp = t_2
	elif y <= -2.5e-132:
		tmp = x + y
	elif y <= 4.9e-108:
		tmp = t_1
	elif y <= 1.8e-44:
		tmp = x + y
	elif y <= 4e-25:
		tmp = t_2
	elif y <= 3.3e-16:
		tmp = t_1
	elif y <= 0.00038:
		tmp = y / t_0
	elif y <= 2e+64:
		tmp = x + y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(x / t_0)
	t_2 = Float64(z * Float64(-1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -5.6e-18)
		tmp = t_2;
	elseif (y <= -2.5e-132)
		tmp = Float64(x + y);
	elseif (y <= 4.9e-108)
		tmp = t_1;
	elseif (y <= 1.8e-44)
		tmp = Float64(x + y);
	elseif (y <= 4e-25)
		tmp = t_2;
	elseif (y <= 3.3e-16)
		tmp = t_1;
	elseif (y <= 0.00038)
		tmp = Float64(y / t_0);
	elseif (y <= 2e+64)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = x / t_0;
	t_2 = z * (-1.0 - (x / y));
	tmp = 0.0;
	if (y <= -5.6e-18)
		tmp = t_2;
	elseif (y <= -2.5e-132)
		tmp = x + y;
	elseif (y <= 4.9e-108)
		tmp = t_1;
	elseif (y <= 1.8e-44)
		tmp = x + y;
	elseif (y <= 4e-25)
		tmp = t_2;
	elseif (y <= 3.3e-16)
		tmp = t_1;
	elseif (y <= 0.00038)
		tmp = y / t_0;
	elseif (y <= 2e+64)
		tmp = x + y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.6e-18], t$95$2, If[LessEqual[y, -2.5e-132], N[(x + y), $MachinePrecision], If[LessEqual[y, 4.9e-108], t$95$1, If[LessEqual[y, 1.8e-44], N[(x + y), $MachinePrecision], If[LessEqual[y, 4e-25], t$95$2, If[LessEqual[y, 3.3e-16], t$95$1, If[LessEqual[y, 0.00038], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, 2e+64], N[(x + y), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.60000000000000025e-18 or 1.7999999999999999e-44 < y < 4.00000000000000015e-25 or 2.00000000000000004e64 < y

   1. Initial program 76.8%

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

   2. Taylor expanded in y around inf 73.0%

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{z \cdot x}{y}\right) - \frac{{z}^{2}}{y}} \]
   3. Step-by-step derivation

      1. mul-1-neg 73.0%

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

      2. unsub-neg 73.0%

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

      3. mul-1-neg 73.0%

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

      4. associate-/l* 74.7%

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

      5. associate-/r/ 72.2%

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

      6. unpow2 72.2%

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

      7. associate-/l* 80.8%

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

   4. Simplified 80.8%

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

   5. Taylor expanded in z around 0 83.4%

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

      1. mul-1-neg 83.4%

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

      2. *-commutative 83.4%

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

      3. distribute-lft-neg-in 83.4%

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

   7. Simplified 83.4%

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

   if -5.60000000000000025e-18 < y < -2.5e-132 or 4.8999999999999998e-108 < y < 1.7999999999999999e-44 or 3.8000000000000002e-4 < y < 2.00000000000000004e64

   1. Initial program 98.3%

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

   2. Taylor expanded in z around inf 74.3%

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

   if -2.5e-132 < y < 4.8999999999999998e-108 or 4.00000000000000015e-25 < y < 3.29999999999999988e-16

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 87.8%

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

   if 3.29999999999999988e-16 < y < 3.8000000000000002e-4

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0 88.3%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-18}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-132}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-44}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-25}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 0.00038:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+64}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 3: 67.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{y}{t_0}\\ t_2 := \frac{x}{t_0}\\ \mathbf{if}\;y \leq -6 \cdot 10^{+93}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ y t_0)) (t_2 (/ x t_0)))
   (if (<= y -6e+93)
     (- z)
     (if (<= y -1.7e-55)
       t_2
       (if (<= y -1.6e-116)
         t_1
         (if (<= y 1.2e-16) t_2 (if (<= y 3.6e+164) t_1 (- z))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = y / t_0;
	double t_2 = x / t_0;
	double tmp;
	if (y <= -6e+93) {
		tmp = -z;
	} else if (y <= -1.7e-55) {
		tmp = t_2;
	} else if (y <= -1.6e-116) {
		tmp = t_1;
	} else if (y <= 1.2e-16) {
		tmp = t_2;
	} else if (y <= 3.6e+164) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = y / t_0
    t_2 = x / t_0
    if (y <= (-6d+93)) then
        tmp = -z
    else if (y <= (-1.7d-55)) then
        tmp = t_2
    else if (y <= (-1.6d-116)) then
        tmp = t_1
    else if (y <= 1.2d-16) then
        tmp = t_2
    else if (y <= 3.6d+164) then
        tmp = t_1
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = y / t_0;
	double t_2 = x / t_0;
	double tmp;
	if (y <= -6e+93) {
		tmp = -z;
	} else if (y <= -1.7e-55) {
		tmp = t_2;
	} else if (y <= -1.6e-116) {
		tmp = t_1;
	} else if (y <= 1.2e-16) {
		tmp = t_2;
	} else if (y <= 3.6e+164) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = y / t_0
	t_2 = x / t_0
	tmp = 0
	if y <= -6e+93:
		tmp = -z
	elif y <= -1.7e-55:
		tmp = t_2
	elif y <= -1.6e-116:
		tmp = t_1
	elif y <= 1.2e-16:
		tmp = t_2
	elif y <= 3.6e+164:
		tmp = t_1
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(y / t_0)
	t_2 = Float64(x / t_0)
	tmp = 0.0
	if (y <= -6e+93)
		tmp = Float64(-z);
	elseif (y <= -1.7e-55)
		tmp = t_2;
	elseif (y <= -1.6e-116)
		tmp = t_1;
	elseif (y <= 1.2e-16)
		tmp = t_2;
	elseif (y <= 3.6e+164)
		tmp = t_1;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = y / t_0;
	t_2 = x / t_0;
	tmp = 0.0;
	if (y <= -6e+93)
		tmp = -z;
	elseif (y <= -1.7e-55)
		tmp = t_2;
	elseif (y <= -1.6e-116)
		tmp = t_1;
	elseif (y <= 1.2e-16)
		tmp = t_2;
	elseif (y <= 3.6e+164)
		tmp = t_1;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y / t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(x / t$95$0), $MachinePrecision]}, If[LessEqual[y, -6e+93], (-z), If[LessEqual[y, -1.7e-55], t$95$2, If[LessEqual[y, -1.6e-116], t$95$1, If[LessEqual[y, 1.2e-16], t$95$2, If[LessEqual[y, 3.6e+164], t$95$1, (-z)]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.99999999999999957e93 or 3.5999999999999999e164 < y

   1. Initial program 64.9%

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

   2. Taylor expanded in y around inf 80.7%

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

      1. mul-1-neg 80.7%

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

   4. Simplified 80.7%

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

   if -5.99999999999999957e93 < y < -1.69999999999999986e-55 or -1.60000000000000005e-116 < y < 1.20000000000000002e-16

   1. Initial program 98.6%

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

   2. Taylor expanded in x around inf 75.3%

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

   if -1.69999999999999986e-55 < y < -1.60000000000000005e-116 or 1.20000000000000002e-16 < y < 3.5999999999999999e164

   1. Initial program 95.5%

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

   2. Taylor expanded in x around 0 71.9%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+93}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-116}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+164}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 67.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - \frac{y}{z}}\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+93}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-28}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-132}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-107}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+70}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 (/ y z)))))
   (if (<= y -6.2e+93)
     (- z)
     (if (<= y -5.1e-28)
       t_0
       (if (<= y -2.75e-132)
         (+ x y)
         (if (<= y 3.7e-107) t_0 (if (<= y 2.25e+70) (+ x y) (- z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -6.2e+93) {
		tmp = -z;
	} else if (y <= -5.1e-28) {
		tmp = t_0;
	} else if (y <= -2.75e-132) {
		tmp = x + y;
	} else if (y <= 3.7e-107) {
		tmp = t_0;
	} else if (y <= 2.25e+70) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x / (1.0d0 - (y / z))
    if (y <= (-6.2d+93)) then
        tmp = -z
    else if (y <= (-5.1d-28)) then
        tmp = t_0
    else if (y <= (-2.75d-132)) then
        tmp = x + y
    else if (y <= 3.7d-107) then
        tmp = t_0
    else if (y <= 2.25d+70) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -6.2e+93) {
		tmp = -z;
	} else if (y <= -5.1e-28) {
		tmp = t_0;
	} else if (y <= -2.75e-132) {
		tmp = x + y;
	} else if (y <= 3.7e-107) {
		tmp = t_0;
	} else if (y <= 2.25e+70) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (1.0 - (y / z))
	tmp = 0
	if y <= -6.2e+93:
		tmp = -z
	elif y <= -5.1e-28:
		tmp = t_0
	elif y <= -2.75e-132:
		tmp = x + y
	elif y <= 3.7e-107:
		tmp = t_0
	elif y <= 2.25e+70:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (y <= -6.2e+93)
		tmp = Float64(-z);
	elseif (y <= -5.1e-28)
		tmp = t_0;
	elseif (y <= -2.75e-132)
		tmp = Float64(x + y);
	elseif (y <= 3.7e-107)
		tmp = t_0;
	elseif (y <= 2.25e+70)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (1.0 - (y / z));
	tmp = 0.0;
	if (y <= -6.2e+93)
		tmp = -z;
	elseif (y <= -5.1e-28)
		tmp = t_0;
	elseif (y <= -2.75e-132)
		tmp = x + y;
	elseif (y <= 3.7e-107)
		tmp = t_0;
	elseif (y <= 2.25e+70)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+93], (-z), If[LessEqual[y, -5.1e-28], t$95$0, If[LessEqual[y, -2.75e-132], N[(x + y), $MachinePrecision], If[LessEqual[y, 3.7e-107], t$95$0, If[LessEqual[y, 2.25e+70], N[(x + y), $MachinePrecision], (-z)]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.20000000000000038e93 or 2.25e70 < y

   1. Initial program 70.1%

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

   2. Taylor expanded in y around inf 76.1%

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

      1. mul-1-neg 76.1%

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

   4. Simplified 76.1%

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

   if -6.20000000000000038e93 < y < -5.10000000000000009e-28 or -2.75e-132 < y < 3.7000000000000003e-107

   1. Initial program 98.1%

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

   2. Taylor expanded in x around inf 77.2%

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

   if -5.10000000000000009e-28 < y < -2.75e-132 or 3.7000000000000003e-107 < y < 2.25e70

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 69.9%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+93}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-28}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-132}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-107}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+70}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 5: 57.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-16}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+60}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3e-16) (- z) (if (<= y 1.75e-16) x (if (<= y 8.6e+60) y (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3e-16) {
		tmp = -z;
	} else if (y <= 1.75e-16) {
		tmp = x;
	} else if (y <= 8.6e+60) {
		tmp = y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3d-16)) then
        tmp = -z
    else if (y <= 1.75d-16) then
        tmp = x
    else if (y <= 8.6d+60) then
        tmp = y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3e-16) {
		tmp = -z;
	} else if (y <= 1.75e-16) {
		tmp = x;
	} else if (y <= 8.6e+60) {
		tmp = y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3e-16:
		tmp = -z
	elif y <= 1.75e-16:
		tmp = x
	elif y <= 8.6e+60:
		tmp = y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3e-16)
		tmp = Float64(-z);
	elseif (y <= 1.75e-16)
		tmp = x;
	elseif (y <= 8.6e+60)
		tmp = y;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3e-16)
		tmp = -z;
	elseif (y <= 1.75e-16)
		tmp = x;
	elseif (y <= 8.6e+60)
		tmp = y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3e-16], (-z), If[LessEqual[y, 1.75e-16], x, If[LessEqual[y, 8.6e+60], y, (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.99999999999999994e-16 or 8.59999999999999942e60 < y

   1. Initial program 76.2%

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

   2. Taylor expanded in y around inf 65.6%

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

      1. mul-1-neg 65.6%

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

   4. Simplified 65.6%

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

   if -2.99999999999999994e-16 < y < 1.75000000000000009e-16

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 57.1%

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

   if 1.75000000000000009e-16 < y < 8.59999999999999942e60

   1. Initial program 93.4%

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

   2. Taylor expanded in x around 0 63.3%

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

   3. Taylor expanded in y around 0 55.0%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-16}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+60}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 6: 67.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+82}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+67}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e+82) (- z) (if (<= y 9e+67) (+ x y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+82) {
		tmp = -z;
	} else if (y <= 9e+67) {
		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 <= (-3.8d+82)) then
        tmp = -z
    else if (y <= 9d+67) 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 <= -3.8e+82) {
		tmp = -z;
	} else if (y <= 9e+67) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.8e+82:
		tmp = -z
	elif y <= 9e+67:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e+82)
		tmp = Float64(-z);
	elseif (y <= 9e+67)
		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 <= -3.8e+82)
		tmp = -z;
	elseif (y <= 9e+67)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.8e+82], (-z), If[LessEqual[y, 9e+67], N[(x + y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -3.80000000000000033e82 or 8.9999999999999997e67 < y

   1. Initial program 70.4%

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

   2. Taylor expanded in y around inf 75.0%

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

      1. mul-1-neg 75.0%

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

   4. Simplified 75.0%

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

   if -3.80000000000000033e82 < y < 8.9999999999999997e67

   1. Initial program 98.7%

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

   2. Taylor expanded in z around inf 68.3%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+82}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+67}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 7: 40.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-118}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.2e-39) x (if (<= x 1.3e-118) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.2e-39) {
		tmp = x;
	} else if (x <= 1.3e-118) {
		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 <= (-6.2d-39)) then
        tmp = x
    else if (x <= 1.3d-118) 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 <= -6.2e-39) {
		tmp = x;
	} else if (x <= 1.3e-118) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.2e-39:
		tmp = x
	elif x <= 1.3e-118:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.2e-39)
		tmp = x;
	elseif (x <= 1.3e-118)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.2e-39)
		tmp = x;
	elseif (x <= 1.3e-118)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.2e-39], x, If[LessEqual[x, 1.3e-118], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.1999999999999994e-39 or 1.3e-118 < x

   1. Initial program 88.7%

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

   2. Taylor expanded in y around 0 40.3%

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

   if -6.1999999999999994e-39 < x < 1.3e-118

   1. Initial program 88.0%

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

   2. Taylor expanded in x around 0 70.6%

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

   3. Taylor expanded in y around 0 39.8%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-118}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 34.6% 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 88.4%

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

2. Taylor expanded in y around 0 32.6%

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

3. Final simplification 32.6%

   \[\leadsto x \]

Developer target: 93.6% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023274 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

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

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