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

Percentage Accurate: 87.7% → 99.1%

Time: 5.9s

Alternatives: 9

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: 87.7% 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: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{-262} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + y\right) \cdot \left(-z\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -5e-262) (not (<= t_0 0.0))) t_0 (/ (* (+ x y) (- 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-262) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = ((x + y) * -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-262)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = ((x + y) * -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-262) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = ((x + y) * -z) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -5e-262) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = ((x + y) * -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-262) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(x + y) * Float64(-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-262) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = ((x + y) * -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-262], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(N[(N[(x + y), $MachinePrecision] * (-z)), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -4.99999999999999992e-262 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 -4.99999999999999992e-262 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 0.0

   1. Initial program 8.5%

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

   2. Taylor expanded in z around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. +-commutative 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 99.8%

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

Alternative 2: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{y}{t_0}\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{+118}:\\ \;\;\;\;\left(-z\right) - \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{t_0}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.098:\\ \;\;\;\;x \cdot \frac{1}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ y t_0)))
   (if (<= y -3.3e+118)
     (- (- z) (/ z (/ y x)))
     (if (<= y -1.4e+15)
       t_1
       (if (<= y -3.25e-15)
         (/ x t_0)
         (if (<= y -6e-88)
           t_1
           (if (<= y 0.098) (* x (/ 1.0 t_0)) (- (- z) (* z (/ x y))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = y / t_0;
	double tmp;
	if (y <= -3.3e+118) {
		tmp = -z - (z / (y / x));
	} else if (y <= -1.4e+15) {
		tmp = t_1;
	} else if (y <= -3.25e-15) {
		tmp = x / t_0;
	} else if (y <= -6e-88) {
		tmp = t_1;
	} else if (y <= 0.098) {
		tmp = x * (1.0 / 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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = y / t_0
    if (y <= (-3.3d+118)) then
        tmp = -z - (z / (y / x))
    else if (y <= (-1.4d+15)) then
        tmp = t_1
    else if (y <= (-3.25d-15)) then
        tmp = x / t_0
    else if (y <= (-6d-88)) then
        tmp = t_1
    else if (y <= 0.098d0) then
        tmp = x * (1.0d0 / 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 = 1.0 - (y / z);
	double t_1 = y / t_0;
	double tmp;
	if (y <= -3.3e+118) {
		tmp = -z - (z / (y / x));
	} else if (y <= -1.4e+15) {
		tmp = t_1;
	} else if (y <= -3.25e-15) {
		tmp = x / t_0;
	} else if (y <= -6e-88) {
		tmp = t_1;
	} else if (y <= 0.098) {
		tmp = x * (1.0 / t_0);
	} else {
		tmp = -z - (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = y / t_0
	tmp = 0
	if y <= -3.3e+118:
		tmp = -z - (z / (y / x))
	elif y <= -1.4e+15:
		tmp = t_1
	elif y <= -3.25e-15:
		tmp = x / t_0
	elif y <= -6e-88:
		tmp = t_1
	elif y <= 0.098:
		tmp = x * (1.0 / t_0)
	else:
		tmp = -z - (z * (x / y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(y / t_0)
	tmp = 0.0
	if (y <= -3.3e+118)
		tmp = Float64(Float64(-z) - Float64(z / Float64(y / x)));
	elseif (y <= -1.4e+15)
		tmp = t_1;
	elseif (y <= -3.25e-15)
		tmp = Float64(x / t_0);
	elseif (y <= -6e-88)
		tmp = t_1;
	elseif (y <= 0.098)
		tmp = Float64(x * Float64(1.0 / 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 = 1.0 - (y / z);
	t_1 = y / t_0;
	tmp = 0.0;
	if (y <= -3.3e+118)
		tmp = -z - (z / (y / x));
	elseif (y <= -1.4e+15)
		tmp = t_1;
	elseif (y <= -3.25e-15)
		tmp = x / t_0;
	elseif (y <= -6e-88)
		tmp = t_1;
	elseif (y <= 0.098)
		tmp = x * (1.0 / t_0);
	else
		tmp = -z - (z * (x / y));
	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]}, If[LessEqual[y, -3.3e+118], N[((-z) - N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.4e+15], t$95$1, If[LessEqual[y, -3.25e-15], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, -6e-88], t$95$1, If[LessEqual[y, 0.098], N[(x * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision], N[((-z) - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.3e118

   1. Initial program 63.5%

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

   2. Taylor expanded in z around 0 59.3%

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

      1. mul-1-neg 59.3%

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

      2. +-commutative 59.3%

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

      3. *-commutative 59.3%

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

      4. +-commutative 59.3%

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

   4. Simplified 59.3%

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

   5. Taylor expanded in y around 0 78.3%

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

      1. +-commutative 78.3%

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

      2. associate-/l* 81.9%

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

   7. Simplified 81.9%

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

   if -3.3e118 < y < -1.4e15 or -3.24999999999999996e-15 < y < -5.9999999999999999e-88

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 69.7%

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

   if -1.4e15 < y < -3.24999999999999996e-15

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 87.0%

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

   if -5.9999999999999999e-88 < y < 0.098000000000000004

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 81.2%

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

      1. *-un-lft-identity 81.2%

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

      2. associate-*l/ 81.3%

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

   4. Applied egg-rr 81.3%

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

   if 0.098000000000000004 < y

   1. Initial program 73.3%

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

   2. Taylor expanded in z around 0 64.5%

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

      1. mul-1-neg 64.5%

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

      2. +-commutative 64.5%

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

      3. *-commutative 64.5%

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

      4. +-commutative 64.5%

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

   4. Simplified 64.5%

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

   5. Taylor expanded in y around 0 74.3%

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

      1. +-commutative 74.3%

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

      2. associate-/l* 77.4%

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

   7. Simplified 77.4%

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

      1. div-inv 77.5%

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

      2. clear-num 77.4%

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

      3. *-commutative 77.4%

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

   9. Applied egg-rr 77.4%

      \[\leadsto -\left(z + \color{blue}{\frac{x}{y} \cdot z}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+118}:\\ \;\;\;\;\left(-z\right) - \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-88}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 0.098:\\ \;\;\;\;x \cdot \frac{1}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \]

Alternative 3: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{y}{t_0}\\ t_2 := \left(-z\right) - z \cdot \frac{x}{y}\\ t_3 := \frac{x}{t_0}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-23}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.0058:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z)))
        (t_1 (/ y t_0))
        (t_2 (- (- z) (* z (/ x y))))
        (t_3 (/ x t_0)))
   (if (<= y -4.5e+118)
     t_2
     (if (<= y -1e+15)
       t_1
       (if (<= y -3.5e-23)
         t_3
         (if (<= y -1.28e-82) t_1 (if (<= y 0.0058) t_3 t_2)))))))

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 = -z - (z * (x / y));
	double t_3 = x / t_0;
	double tmp;
	if (y <= -4.5e+118) {
		tmp = t_2;
	} else if (y <= -1e+15) {
		tmp = t_1;
	} else if (y <= -3.5e-23) {
		tmp = t_3;
	} else if (y <= -1.28e-82) {
		tmp = t_1;
	} else if (y <= 0.0058) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = y / t_0
    t_2 = -z - (z * (x / y))
    t_3 = x / t_0
    if (y <= (-4.5d+118)) then
        tmp = t_2
    else if (y <= (-1d+15)) then
        tmp = t_1
    else if (y <= (-3.5d-23)) then
        tmp = t_3
    else if (y <= (-1.28d-82)) then
        tmp = t_1
    else if (y <= 0.0058d0) then
        tmp = t_3
    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 = y / t_0;
	double t_2 = -z - (z * (x / y));
	double t_3 = x / t_0;
	double tmp;
	if (y <= -4.5e+118) {
		tmp = t_2;
	} else if (y <= -1e+15) {
		tmp = t_1;
	} else if (y <= -3.5e-23) {
		tmp = t_3;
	} else if (y <= -1.28e-82) {
		tmp = t_1;
	} else if (y <= 0.0058) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = y / t_0
	t_2 = -z - (z * (x / y))
	t_3 = x / t_0
	tmp = 0
	if y <= -4.5e+118:
		tmp = t_2
	elif y <= -1e+15:
		tmp = t_1
	elif y <= -3.5e-23:
		tmp = t_3
	elif y <= -1.28e-82:
		tmp = t_1
	elif y <= 0.0058:
		tmp = t_3
	else:
		tmp = t_2
	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(Float64(-z) - Float64(z * Float64(x / y)))
	t_3 = Float64(x / t_0)
	tmp = 0.0
	if (y <= -4.5e+118)
		tmp = t_2;
	elseif (y <= -1e+15)
		tmp = t_1;
	elseif (y <= -3.5e-23)
		tmp = t_3;
	elseif (y <= -1.28e-82)
		tmp = t_1;
	elseif (y <= 0.0058)
		tmp = t_3;
	else
		tmp = t_2;
	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 = -z - (z * (x / y));
	t_3 = x / t_0;
	tmp = 0.0;
	if (y <= -4.5e+118)
		tmp = t_2;
	elseif (y <= -1e+15)
		tmp = t_1;
	elseif (y <= -3.5e-23)
		tmp = t_3;
	elseif (y <= -1.28e-82)
		tmp = t_1;
	elseif (y <= 0.0058)
		tmp = t_3;
	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[(y / t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[((-z) - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / t$95$0), $MachinePrecision]}, If[LessEqual[y, -4.5e+118], t$95$2, If[LessEqual[y, -1e+15], t$95$1, If[LessEqual[y, -3.5e-23], t$95$3, If[LessEqual[y, -1.28e-82], t$95$1, If[LessEqual[y, 0.0058], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.50000000000000002e118 or 0.0058 < y

   1. Initial program 68.8%

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

   2. Taylor expanded in z around 0 62.1%

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

      1. mul-1-neg 62.1%

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

      2. +-commutative 62.1%

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

      3. *-commutative 62.1%

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

      4. +-commutative 62.1%

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

   4. Simplified 62.1%

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

   5. Taylor expanded in y around 0 76.1%

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

      1. +-commutative 76.1%

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

      2. associate-/l* 79.5%

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

   7. Simplified 79.5%

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

      1. div-inv 79.5%

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

      2. clear-num 79.5%

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

      3. *-commutative 79.5%

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

   9. Applied egg-rr 79.5%

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

   if -4.50000000000000002e118 < y < -1e15 or -3.49999999999999993e-23 < y < -1.28e-82

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 70.6%

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

   if -1e15 < y < -3.49999999999999993e-23 or -1.28e-82 < y < 0.0058

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 81.1%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+118}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{-82}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 0.0058:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \]

Alternative 4: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{y}{t_0}\\ t_2 := \frac{x}{t_0}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+118}:\\ \;\;\;\;\left(-z\right) - \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.054:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

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 -2.4e+118)
     (- (- z) (/ z (/ y x)))
     (if (<= y -1e+15)
       t_1
       (if (<= y -7e-16)
         t_2
         (if (<= y -7.5e-83)
           t_1
           (if (<= y 0.054) t_2 (- (- z) (* z (/ x y))))))))))

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 <= -2.4e+118) {
		tmp = -z - (z / (y / x));
	} else if (y <= -1e+15) {
		tmp = t_1;
	} else if (y <= -7e-16) {
		tmp = t_2;
	} else if (y <= -7.5e-83) {
		tmp = t_1;
	} else if (y <= 0.054) {
		tmp = t_2;
	} 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) :: 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 <= (-2.4d+118)) then
        tmp = -z - (z / (y / x))
    else if (y <= (-1d+15)) then
        tmp = t_1
    else if (y <= (-7d-16)) then
        tmp = t_2
    else if (y <= (-7.5d-83)) then
        tmp = t_1
    else if (y <= 0.054d0) then
        tmp = t_2
    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 = 1.0 - (y / z);
	double t_1 = y / t_0;
	double t_2 = x / t_0;
	double tmp;
	if (y <= -2.4e+118) {
		tmp = -z - (z / (y / x));
	} else if (y <= -1e+15) {
		tmp = t_1;
	} else if (y <= -7e-16) {
		tmp = t_2;
	} else if (y <= -7.5e-83) {
		tmp = t_1;
	} else if (y <= 0.054) {
		tmp = t_2;
	} else {
		tmp = -z - (z * (x / y));
	}
	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 <= -2.4e+118:
		tmp = -z - (z / (y / x))
	elif y <= -1e+15:
		tmp = t_1
	elif y <= -7e-16:
		tmp = t_2
	elif y <= -7.5e-83:
		tmp = t_1
	elif y <= 0.054:
		tmp = t_2
	else:
		tmp = -z - (z * (x / y))
	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 <= -2.4e+118)
		tmp = Float64(Float64(-z) - Float64(z / Float64(y / x)));
	elseif (y <= -1e+15)
		tmp = t_1;
	elseif (y <= -7e-16)
		tmp = t_2;
	elseif (y <= -7.5e-83)
		tmp = t_1;
	elseif (y <= 0.054)
		tmp = t_2;
	else
		tmp = Float64(Float64(-z) - Float64(z * Float64(x / y)));
	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 <= -2.4e+118)
		tmp = -z - (z / (y / x));
	elseif (y <= -1e+15)
		tmp = t_1;
	elseif (y <= -7e-16)
		tmp = t_2;
	elseif (y <= -7.5e-83)
		tmp = t_1;
	elseif (y <= 0.054)
		tmp = t_2;
	else
		tmp = -z - (z * (x / y));
	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, -2.4e+118], N[((-z) - N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1e+15], t$95$1, If[LessEqual[y, -7e-16], t$95$2, If[LessEqual[y, -7.5e-83], t$95$1, If[LessEqual[y, 0.054], t$95$2, N[((-z) - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.4e118

   1. Initial program 63.5%

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

   2. Taylor expanded in z around 0 59.3%

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

      1. mul-1-neg 59.3%

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

      2. +-commutative 59.3%

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

      3. *-commutative 59.3%

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

      4. +-commutative 59.3%

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

   4. Simplified 59.3%

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

   5. Taylor expanded in y around 0 78.3%

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

      1. +-commutative 78.3%

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

      2. associate-/l* 81.9%

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

   7. Simplified 81.9%

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

   if -2.4e118 < y < -1e15 or -7.00000000000000035e-16 < y < -7.4999999999999997e-83

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 70.6%

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

   if -1e15 < y < -7.00000000000000035e-16 or -7.4999999999999997e-83 < y < 0.0539999999999999994

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 81.1%

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

   if 0.0539999999999999994 < y

   1. Initial program 73.3%

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

   2. Taylor expanded in z around 0 64.5%

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

      1. mul-1-neg 64.5%

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

      2. +-commutative 64.5%

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

      3. *-commutative 64.5%

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

      4. +-commutative 64.5%

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

   4. Simplified 64.5%

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

   5. Taylor expanded in y around 0 74.3%

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

      1. +-commutative 74.3%

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

      2. associate-/l* 77.4%

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

   7. Simplified 77.4%

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

      1. div-inv 77.5%

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

      2. clear-num 77.4%

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

      3. *-commutative 77.4%

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

   9. Applied egg-rr 77.4%

      \[\leadsto -\left(z + \color{blue}{\frac{x}{y} \cdot z}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+118}:\\ \;\;\;\;\left(-z\right) - \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-83}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 0.054:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5: 67.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{x}{t_0}\\ \mathbf{if}\;x \leq -9 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-115}:\\ \;\;\;\;\frac{y}{t_0}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-75}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-18}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ x t_0)))
   (if (<= x -9e-18)
     t_1
     (if (<= x 3.9e-115)
       (/ y t_0)
       (if (<= x 8.2e-75) (- z) (if (<= x 4.8e-18) (+ x y) t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = x / t_0;
	double tmp;
	if (x <= -9e-18) {
		tmp = t_1;
	} else if (x <= 3.9e-115) {
		tmp = y / t_0;
	} else if (x <= 8.2e-75) {
		tmp = -z;
	} else if (x <= 4.8e-18) {
		tmp = x + y;
	} 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 = 1.0d0 - (y / z)
    t_1 = x / t_0
    if (x <= (-9d-18)) then
        tmp = t_1
    else if (x <= 3.9d-115) then
        tmp = y / t_0
    else if (x <= 8.2d-75) then
        tmp = -z
    else if (x <= 4.8d-18) then
        tmp = x + y
    else
        tmp = t_1
    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 tmp;
	if (x <= -9e-18) {
		tmp = t_1;
	} else if (x <= 3.9e-115) {
		tmp = y / t_0;
	} else if (x <= 8.2e-75) {
		tmp = -z;
	} else if (x <= 4.8e-18) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = x / t_0
	tmp = 0
	if x <= -9e-18:
		tmp = t_1
	elif x <= 3.9e-115:
		tmp = y / t_0
	elif x <= 8.2e-75:
		tmp = -z
	elif x <= 4.8e-18:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(x / t_0)
	tmp = 0.0
	if (x <= -9e-18)
		tmp = t_1;
	elseif (x <= 3.9e-115)
		tmp = Float64(y / t_0);
	elseif (x <= 8.2e-75)
		tmp = Float64(-z);
	elseif (x <= 4.8e-18)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = x / t_0;
	tmp = 0.0;
	if (x <= -9e-18)
		tmp = t_1;
	elseif (x <= 3.9e-115)
		tmp = y / t_0;
	elseif (x <= 8.2e-75)
		tmp = -z;
	elseif (x <= 4.8e-18)
		tmp = x + y;
	else
		tmp = t_1;
	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]}, If[LessEqual[x, -9e-18], t$95$1, If[LessEqual[x, 3.9e-115], N[(y / t$95$0), $MachinePrecision], If[LessEqual[x, 8.2e-75], (-z), If[LessEqual[x, 4.8e-18], N[(x + y), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.99999999999999987e-18 or 4.79999999999999988e-18 < x

   1. Initial program 85.0%

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

   2. Taylor expanded in x around inf 70.5%

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

   if -8.99999999999999987e-18 < x < 3.8999999999999998e-115

   1. Initial program 88.6%

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

   2. Taylor expanded in x around 0 76.0%

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

   if 3.8999999999999998e-115 < x < 8.20000000000000005e-75

   1. Initial program 66.3%

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

   2. Taylor expanded in y around inf 68.7%

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

      1. mul-1-neg 68.7%

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

   4. Simplified 68.7%

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

   if 8.20000000000000005e-75 < x < 4.79999999999999988e-18

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 71.2%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-115}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-75}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-18}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]

Alternative 6: 68.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{+85}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.26e+85) (- z) (if (<= y 1.5e+53) (/ x (- 1.0 (/ y z))) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.26e+85) {
		tmp = -z;
	} else if (y <= 1.5e+53) {
		tmp = x / (1.0 - (y / z));
	} 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 <= (-1.26d+85)) then
        tmp = -z
    else if (y <= 1.5d+53) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.26e+85) {
		tmp = -z;
	} else if (y <= 1.5e+53) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.26e+85:
		tmp = -z
	elif y <= 1.5e+53:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.26e+85)
		tmp = Float64(-z);
	elseif (y <= 1.5e+53)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.26e+85)
		tmp = -z;
	elseif (y <= 1.5e+53)
		tmp = x / (1.0 - (y / z));
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.26e+85], (-z), If[LessEqual[y, 1.5e+53], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -1.26000000000000003e85 or 1.49999999999999999e53 < y

   1. Initial program 69.6%

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

   2. Taylor expanded in y around inf 65.5%

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

      1. mul-1-neg 65.5%

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

   4. Simplified 65.5%

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

   if -1.26000000000000003e85 < y < 1.49999999999999999e53

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 69.8%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{+85}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 7: 68.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+94}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 0.88:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e+94) (- z) (if (<= y 0.88) (+ x y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+94) {
		tmp = -z;
	} else if (y <= 0.88) {
		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 <= (-2d+94)) then
        tmp = -z
    else if (y <= 0.88d0) 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 <= -2e+94) {
		tmp = -z;
	} else if (y <= 0.88) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e+94:
		tmp = -z
	elif y <= 0.88:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e+94)
		tmp = Float64(-z);
	elseif (y <= 0.88)
		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 <= -2e+94)
		tmp = -z;
	elseif (y <= 0.88)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e+94], (-z), If[LessEqual[y, 0.88], N[(x + y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -2e94 or 0.880000000000000004 < y

   1. Initial program 70.6%

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

   2. Taylor expanded in y around inf 63.7%

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

      1. mul-1-neg 63.7%

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

   4. Simplified 63.7%

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

   if -2e94 < y < 0.880000000000000004

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 67.9%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+94}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 0.88:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 8: 58.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-82}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 0.245:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.22e-82) (- z) (if (<= y 0.245) x (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.22e-82) {
		tmp = -z;
	} else if (y <= 0.245) {
		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 <= (-1.22d-82)) then
        tmp = -z
    else if (y <= 0.245d0) 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 <= -1.22e-82) {
		tmp = -z;
	} else if (y <= 0.245) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.22e-82:
		tmp = -z
	elif y <= 0.245:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.22e-82)
		tmp = Float64(-z);
	elseif (y <= 0.245)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.22e-82)
		tmp = -z;
	elseif (y <= 0.245)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.22e-82], (-z), If[LessEqual[y, 0.245], x, (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -1.22000000000000001e-82 or 0.245 < y

   1. Initial program 78.1%

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

   2. Taylor expanded in y around inf 53.0%

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

      1. mul-1-neg 53.0%

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

   4. Simplified 53.0%

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

   if -1.22000000000000001e-82 < y < 0.245

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 67.2%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-82}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 0.245:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 9: 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 86.3%

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

2. Taylor expanded in y around 0 31.3%

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

3. Final simplification 31.3%

   \[\leadsto x \]

Developer target: 94.1% 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 2023176 
(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))))