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

Percentage Accurate: 88.4% → 99.6%

Time: 10.6s

Alternatives: 11

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: 88.4% 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: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-260} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-260) (not (<= t_0 0.0))) t_0 (/ (- z) (/ y (+ x y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-260) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-1d-260)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = -z / (y / (x + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-260) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -1e-260) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = -z / (y / (x + y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -1e-260) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) / Float64(y / Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -1e-260) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = -z / (y / (x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -1e-260], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -9.99999999999999961e-261 or -0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

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

   if -9.99999999999999961e-261 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -0.0

   1. Initial program 9.6%

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

   2. Taylor expanded in z around 0 97.0%

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

      1. mul-1-neg 97.0%

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

      2. associate-/l* 100.0%

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

      3. distribute-neg-frac 100.0%

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

      4. +-commutative 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-260} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \]

Alternative 2: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{y}{t_0}\\ t_2 := \left(-z\right) - \frac{x}{\frac{y}{z}}\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+202}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.3:\\ \;\;\;\;\frac{x}{t_0}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ y t_0)) (t_2 (- (- z) (/ x (/ y z)))))
   (if (<= y -1.45e+202)
     t_2
     (if (<= y -4.5e-9)
       t_1
       (if (<= y 5.3) (/ x t_0) (if (<= y 4.3e+114) t_1 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 - (x / (y / z));
	double tmp;
	if (y <= -1.45e+202) {
		tmp = t_2;
	} else if (y <= -4.5e-9) {
		tmp = t_1;
	} else if (y <= 5.3) {
		tmp = x / t_0;
	} else if (y <= 4.3e+114) {
		tmp = t_1;
	} 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 = y / t_0
    t_2 = -z - (x / (y / z))
    if (y <= (-1.45d+202)) then
        tmp = t_2
    else if (y <= (-4.5d-9)) then
        tmp = t_1
    else if (y <= 5.3d0) then
        tmp = x / t_0
    else if (y <= 4.3d+114) then
        tmp = t_1
    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 - (x / (y / z));
	double tmp;
	if (y <= -1.45e+202) {
		tmp = t_2;
	} else if (y <= -4.5e-9) {
		tmp = t_1;
	} else if (y <= 5.3) {
		tmp = x / t_0;
	} else if (y <= 4.3e+114) {
		tmp = t_1;
	} 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 - (x / (y / z))
	tmp = 0
	if y <= -1.45e+202:
		tmp = t_2
	elif y <= -4.5e-9:
		tmp = t_1
	elif y <= 5.3:
		tmp = x / t_0
	elif y <= 4.3e+114:
		tmp = t_1
	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(x / Float64(y / z)))
	tmp = 0.0
	if (y <= -1.45e+202)
		tmp = t_2;
	elseif (y <= -4.5e-9)
		tmp = t_1;
	elseif (y <= 5.3)
		tmp = Float64(x / t_0);
	elseif (y <= 4.3e+114)
		tmp = t_1;
	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 - (x / (y / z));
	tmp = 0.0;
	if (y <= -1.45e+202)
		tmp = t_2;
	elseif (y <= -4.5e-9)
		tmp = t_1;
	elseif (y <= 5.3)
		tmp = x / t_0;
	elseif (y <= 4.3e+114)
		tmp = t_1;
	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[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e+202], t$95$2, If[LessEqual[y, -4.5e-9], t$95$1, If[LessEqual[y, 5.3], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 4.3e+114], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45e202 or 4.3000000000000001e114 < y

   1. Initial program 71.0%

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

   2. Taylor expanded in z around 0 52.9%

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

      1. mul-1-neg 52.9%

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

      2. +-commutative 52.9%

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

   4. Simplified 52.9%

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

   5. Taylor expanded in y around 0 80.8%

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

      1. associate-/l* 84.3%

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

   7. Simplified 84.3%

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

   if -1.45e202 < y < -4.49999999999999976e-9 or 5.29999999999999982 < y < 4.3000000000000001e114

   1. Initial program 88.0%

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

   2. Taylor expanded in x around 0 67.1%

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

   if -4.49999999999999976e-9 < y < 5.29999999999999982

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 87.0%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+202}:\\ \;\;\;\;\left(-z\right) - \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-9}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 5.3:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+114}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{x}{\frac{y}{z}}\\ \end{array} \]

Alternative 3: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{y}{t_0}\\ t_2 := z \cdot \frac{-\left(x + y\right)}{y}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.3:\\ \;\;\;\;\frac{x}{t_0}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ y t_0)) (t_2 (* z (/ (- (+ x y)) y))))
   (if (<= y -1.6e+75)
     t_2
     (if (<= y -2.4e-8)
       t_1
       (if (<= y 4.3) (/ x t_0) (if (<= y 6.2e+113) t_1 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 * (-(x + y) / y);
	double tmp;
	if (y <= -1.6e+75) {
		tmp = t_2;
	} else if (y <= -2.4e-8) {
		tmp = t_1;
	} else if (y <= 4.3) {
		tmp = x / t_0;
	} else if (y <= 6.2e+113) {
		tmp = t_1;
	} 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 = y / t_0
    t_2 = z * (-(x + y) / y)
    if (y <= (-1.6d+75)) then
        tmp = t_2
    else if (y <= (-2.4d-8)) then
        tmp = t_1
    else if (y <= 4.3d0) then
        tmp = x / t_0
    else if (y <= 6.2d+113) then
        tmp = t_1
    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 * (-(x + y) / y);
	double tmp;
	if (y <= -1.6e+75) {
		tmp = t_2;
	} else if (y <= -2.4e-8) {
		tmp = t_1;
	} else if (y <= 4.3) {
		tmp = x / t_0;
	} else if (y <= 6.2e+113) {
		tmp = t_1;
	} 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 * (-(x + y) / y)
	tmp = 0
	if y <= -1.6e+75:
		tmp = t_2
	elif y <= -2.4e-8:
		tmp = t_1
	elif y <= 4.3:
		tmp = x / t_0
	elif y <= 6.2e+113:
		tmp = t_1
	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(z * Float64(Float64(-Float64(x + y)) / y))
	tmp = 0.0
	if (y <= -1.6e+75)
		tmp = t_2;
	elseif (y <= -2.4e-8)
		tmp = t_1;
	elseif (y <= 4.3)
		tmp = Float64(x / t_0);
	elseif (y <= 6.2e+113)
		tmp = t_1;
	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 * (-(x + y) / y);
	tmp = 0.0;
	if (y <= -1.6e+75)
		tmp = t_2;
	elseif (y <= -2.4e-8)
		tmp = t_1;
	elseif (y <= 4.3)
		tmp = x / t_0;
	elseif (y <= 6.2e+113)
		tmp = t_1;
	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[((-N[(x + y), $MachinePrecision]) / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+75], t$95$2, If[LessEqual[y, -2.4e-8], t$95$1, If[LessEqual[y, 4.3], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 6.2e+113], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.59999999999999992e75 or 6.19999999999999982e113 < y

   1. Initial program 73.6%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Step-by-step derivation

      1. clear-num 73.4%

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

      2. inv-pow 73.4%

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

   3. Applied egg-rr 73.4%

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

   4. Taylor expanded in z around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. +-commutative 57.9%

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

      3. neg-mul-1 57.9%

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

      4. distribute-neg-frac 57.9%

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

      5. associate-*r/ 84.3%

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

      6. distribute-lft-neg-in 84.3%

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

      7. +-commutative 84.3%

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

   6. Simplified 84.3%

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

   if -1.59999999999999992e75 < y < -2.39999999999999998e-8 or 4.29999999999999982 < y < 6.19999999999999982e113

   1. Initial program 94.1%

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

   2. Taylor expanded in x around 0 69.5%

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

   if -2.39999999999999998e-8 < y < 4.29999999999999982

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 87.0%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+75}:\\ \;\;\;\;z \cdot \frac{-\left(x + y\right)}{y}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 4.3:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+113}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-\left(x + y\right)}{y}\\ \end{array} \]

Alternative 4: 69.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{y}{t_0}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.2:\\ \;\;\;\;\frac{x}{t_0}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+170}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ y t_0)))
   (if (<= y -9.5e-11)
     t_1
     (if (<= y 6.2) (/ x t_0) (if (<= y 2.2e+170) 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 tmp;
	if (y <= -9.5e-11) {
		tmp = t_1;
	} else if (y <= 6.2) {
		tmp = x / t_0;
	} else if (y <= 2.2e+170) {
		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) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = y / t_0
    if (y <= (-9.5d-11)) then
        tmp = t_1
    else if (y <= 6.2d0) then
        tmp = x / t_0
    else if (y <= 2.2d+170) 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 tmp;
	if (y <= -9.5e-11) {
		tmp = t_1;
	} else if (y <= 6.2) {
		tmp = x / t_0;
	} else if (y <= 2.2e+170) {
		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
	tmp = 0
	if y <= -9.5e-11:
		tmp = t_1
	elif y <= 6.2:
		tmp = x / t_0
	elif y <= 2.2e+170:
		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)
	tmp = 0.0
	if (y <= -9.5e-11)
		tmp = t_1;
	elseif (y <= 6.2)
		tmp = Float64(x / t_0);
	elseif (y <= 2.2e+170)
		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;
	tmp = 0.0;
	if (y <= -9.5e-11)
		tmp = t_1;
	elseif (y <= 6.2)
		tmp = x / t_0;
	elseif (y <= 2.2e+170)
		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]}, If[LessEqual[y, -9.5e-11], t$95$1, If[LessEqual[y, 6.2], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 2.2e+170], t$95$1, (-z)]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.49999999999999951e-11 or 6.20000000000000018 < y < 2.19999999999999989e170

   1. Initial program 85.1%

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

   2. Taylor expanded in x around 0 65.8%

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

   if -9.49999999999999951e-11 < y < 6.20000000000000018

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 87.0%

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

   if 2.19999999999999989e170 < y

   1. Initial program 66.0%

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

   2. Taylor expanded in y around inf 79.4%

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

      1. mul-1-neg 79.4%

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

   4. Simplified 79.4%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 6.2:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+170}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 5: 64.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+82}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-59}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-142}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+171}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.9e+82)
   (- z)
   (if (<= y -2.4e-59)
     (+ x y)
     (if (<= y -1.3e-142)
       (/ (* x (- z)) y)
       (if (<= y 8.8e+171) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e+82) {
		tmp = -z;
	} else if (y <= -2.4e-59) {
		tmp = x + y;
	} else if (y <= -1.3e-142) {
		tmp = (x * -z) / y;
	} else if (y <= 8.8e+171) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.9d+82)) then
        tmp = -z
    else if (y <= (-2.4d-59)) then
        tmp = x + y
    else if (y <= (-1.3d-142)) then
        tmp = (x * -z) / y
    else if (y <= 8.8d+171) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e+82) {
		tmp = -z;
	} else if (y <= -2.4e-59) {
		tmp = x + y;
	} else if (y <= -1.3e-142) {
		tmp = (x * -z) / y;
	} else if (y <= 8.8e+171) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.9e+82:
		tmp = -z
	elif y <= -2.4e-59:
		tmp = x + y
	elif y <= -1.3e-142:
		tmp = (x * -z) / y
	elif y <= 8.8e+171:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.9e+82)
		tmp = Float64(-z);
	elseif (y <= -2.4e-59)
		tmp = Float64(x + y);
	elseif (y <= -1.3e-142)
		tmp = Float64(Float64(x * Float64(-z)) / y);
	elseif (y <= 8.8e+171)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.9e+82)
		tmp = -z;
	elseif (y <= -2.4e-59)
		tmp = x + y;
	elseif (y <= -1.3e-142)
		tmp = (x * -z) / y;
	elseif (y <= 8.8e+171)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.9e+82], (-z), If[LessEqual[y, -2.4e-59], N[(x + y), $MachinePrecision], If[LessEqual[y, -1.3e-142], N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 8.8e+171], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.90000000000000017e82 or 8.7999999999999998e171 < y

   1. Initial program 72.2%

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

   2. Taylor expanded in y around inf 73.5%

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

      1. mul-1-neg 73.5%

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

   4. Simplified 73.5%

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

   if -1.90000000000000017e82 < y < -2.40000000000000015e-59 or -1.3e-142 < y < 8.7999999999999998e171

   1. Initial program 97.5%

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

   2. Taylor expanded in z around inf 62.6%

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

      1. +-commutative 62.6%

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

   4. Simplified 62.6%

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

   if -2.40000000000000015e-59 < y < -1.3e-142

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 93.1%

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

   3. Taylor expanded in y around inf 65.2%

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

      1. mul-1-neg 65.2%

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

   5. Simplified 65.2%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+82}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-59}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-142}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+171}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 6: 64.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+85}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.86 \cdot 10^{-59}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-142}:\\ \;\;\;\;\frac{-x}{\frac{y}{z}}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+171}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1e+85)
   (- z)
   (if (<= y -1.86e-59)
     (+ x y)
     (if (<= y -1.3e-142)
       (/ (- x) (/ y z))
       (if (<= y 8.8e+171) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1e+85) {
		tmp = -z;
	} else if (y <= -1.86e-59) {
		tmp = x + y;
	} else if (y <= -1.3e-142) {
		tmp = -x / (y / z);
	} else if (y <= 8.8e+171) {
		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 <= (-1d+85)) then
        tmp = -z
    else if (y <= (-1.86d-59)) then
        tmp = x + y
    else if (y <= (-1.3d-142)) then
        tmp = -x / (y / z)
    else if (y <= 8.8d+171) 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 <= -1e+85) {
		tmp = -z;
	} else if (y <= -1.86e-59) {
		tmp = x + y;
	} else if (y <= -1.3e-142) {
		tmp = -x / (y / z);
	} else if (y <= 8.8e+171) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1e+85:
		tmp = -z
	elif y <= -1.86e-59:
		tmp = x + y
	elif y <= -1.3e-142:
		tmp = -x / (y / z)
	elif y <= 8.8e+171:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1e+85)
		tmp = Float64(-z);
	elseif (y <= -1.86e-59)
		tmp = Float64(x + y);
	elseif (y <= -1.3e-142)
		tmp = Float64(Float64(-x) / Float64(y / z));
	elseif (y <= 8.8e+171)
		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 <= -1e+85)
		tmp = -z;
	elseif (y <= -1.86e-59)
		tmp = x + y;
	elseif (y <= -1.3e-142)
		tmp = -x / (y / z);
	elseif (y <= 8.8e+171)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1e+85], (-z), If[LessEqual[y, -1.86e-59], N[(x + y), $MachinePrecision], If[LessEqual[y, -1.3e-142], N[((-x) / N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.8e+171], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1e85 or 8.7999999999999998e171 < y

   1. Initial program 72.2%

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

   2. Taylor expanded in y around inf 73.5%

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

      1. mul-1-neg 73.5%

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

   4. Simplified 73.5%

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

   if -1e85 < y < -1.86000000000000004e-59 or -1.3e-142 < y < 8.7999999999999998e171

   1. Initial program 97.5%

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

   2. Taylor expanded in z around inf 62.6%

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

      1. +-commutative 62.6%

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

   4. Simplified 62.6%

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

   if -1.86000000000000004e-59 < y < -1.3e-142

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 93.1%

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

   3. Taylor expanded in y around inf 65.2%

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

      1. mul-1-neg 65.2%

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

      2. associate-/l* 65.5%

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

      3. distribute-neg-frac 65.5%

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

   5. Simplified 65.5%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+85}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.86 \cdot 10^{-59}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-142}:\\ \;\;\;\;\frac{-x}{\frac{y}{z}}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+171}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 7: 68.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+14}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.5e+14) (- z) (if (<= y 9e+48) (/ x (- 1.0 (/ y z))) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.5e+14) {
		tmp = -z;
	} else if (y <= 9e+48) {
		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 <= (-8.5d+14)) then
        tmp = -z
    else if (y <= 9d+48) 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 <= -8.5e+14) {
		tmp = -z;
	} else if (y <= 9e+48) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.5e+14:
		tmp = -z
	elif y <= 9e+48:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.5e+14)
		tmp = Float64(-z);
	elseif (y <= 9e+48)
		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 <= -8.5e+14)
		tmp = -z;
	elseif (y <= 9e+48)
		tmp = x / (1.0 - (y / z));
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.5e+14], (-z), If[LessEqual[y, 9e+48], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5e14 or 8.99999999999999991e48 < y

   1. Initial program 78.5%

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

   2. Taylor expanded in y around inf 62.4%

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

      1. mul-1-neg 62.4%

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

   4. Simplified 62.4%

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

   if -8.5e14 < y < 8.99999999999999991e48

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 82.1%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+14}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 8: 66.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+84}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+171}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.8e+84) (- z) (if (<= y 8.8e+171) (+ x y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.8e+84) {
		tmp = -z;
	} else if (y <= 8.8e+171) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-6.8d+84)) then
        tmp = -z
    else if (y <= 8.8d+171) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.8e+84) {
		tmp = -z;
	} else if (y <= 8.8e+171) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.8e+84:
		tmp = -z
	elif y <= 8.8e+171:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.8e+84)
		tmp = Float64(-z);
	elseif (y <= 8.8e+171)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.8e+84)
		tmp = -z;
	elseif (y <= 8.8e+171)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.8e+84], (-z), If[LessEqual[y, 8.8e+171], N[(x + y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -6.7999999999999996e84 or 8.7999999999999998e171 < y

   1. Initial program 72.2%

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

   2. Taylor expanded in y around inf 73.5%

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

      1. mul-1-neg 73.5%

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

   4. Simplified 73.5%

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

   if -6.7999999999999996e84 < y < 8.7999999999999998e171

   1. Initial program 97.7%

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

   2. Taylor expanded in z around inf 59.9%

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

      1. +-commutative 59.9%

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

   4. Simplified 59.9%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+84}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+171}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 9: 59.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -13000000000000:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 10^{+35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -13000000000000.0) (- z) (if (<= y 1e+35) x (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -13000000000000.0) {
		tmp = -z;
	} else if (y <= 1e+35) {
		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 <= (-13000000000000.0d0)) then
        tmp = -z
    else if (y <= 1d+35) 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 <= -13000000000000.0) {
		tmp = -z;
	} else if (y <= 1e+35) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -13000000000000.0:
		tmp = -z
	elif y <= 1e+35:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -13000000000000.0)
		tmp = Float64(-z);
	elseif (y <= 1e+35)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -13000000000000.0)
		tmp = -z;
	elseif (y <= 1e+35)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -13000000000000.0], (-z), If[LessEqual[y, 1e+35], x, (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e13 or 9.9999999999999997e34 < y

   1. Initial program 79.1%

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

   2. Taylor expanded in y around inf 61.4%

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

      1. mul-1-neg 61.4%

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

   4. Simplified 61.4%

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

   if -1.3e13 < y < 9.9999999999999997e34

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 52.5%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -13000000000000:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 10^{+35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 10: 39.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-41}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.4e-35) x (if (<= x 5.6e-41) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.4e-35) {
		tmp = x;
	} else if (x <= 5.6e-41) {
		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 <= (-5.4d-35)) then
        tmp = x
    else if (x <= 5.6d-41) 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 <= -5.4e-35) {
		tmp = x;
	} else if (x <= 5.6e-41) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.4e-35:
		tmp = x
	elif x <= 5.6e-41:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.4e-35)
		tmp = x;
	elseif (x <= 5.6e-41)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.4e-35)
		tmp = x;
	elseif (x <= 5.6e-41)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.4e-35], x, If[LessEqual[x, 5.6e-41], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.3999999999999995e-35 or 5.6000000000000003e-41 < x

   1. Initial program 90.6%

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

   2. Taylor expanded in y around 0 40.1%

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

   if -5.3999999999999995e-35 < x < 5.6000000000000003e-41

   1. Initial program 86.4%

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

   2. Taylor expanded in z around inf 40.8%

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

      1. associate-+r+ 40.8%

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

      2. *-lft-identity 40.8%

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

      3. associate-/l* 43.6%

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

      4. associate-/r/ 43.6%

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

      5. distribute-rgt-in 43.6%

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

      6. +-commutative 43.6%

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

   4. Simplified 43.6%

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

   5. Taylor expanded in x around 0 30.3%

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

      1. distribute-lft-in 30.3%

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

      2. *-rgt-identity 30.3%

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

   7. Simplified 30.3%

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

   8. Taylor expanded in y around 0 31.1%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-41}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 34.9% 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 88.9%

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

2. Taylor expanded in y around 0 30.5%

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

3. Final simplification 30.5%

   \[\leadsto x \]

Developer target: 94.0% 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 2023280 
(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))))