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

Percentage Accurate: 87.9% → 99.1%

Time: 5.4s

Alternatives: 10

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 87.9% 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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-274} \lor \neg \left(t_0 \leq 3 \cdot 10^{-241}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-274) (not (<= t_0 3e-241)))
     t_0
     (* z (- -1.0 (/ 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-274) || !(t_0 <= 3e-241)) {
		tmp = t_0;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-1d-274)) .or. (.not. (t_0 <= 3d-241))) then
        tmp = t_0
    else
        tmp = z * ((-1.0d0) - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-274) || !(t_0 <= 3e-241)) {
		tmp = t_0;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -1e-274) or not (t_0 <= 3e-241):
		tmp = t_0
	else:
		tmp = z * (-1.0 - (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-274) || !(t_0 <= 3e-241))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(-1.0 - 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-274) || ~((t_0 <= 3e-241)))
		tmp = t_0;
	else
		tmp = z * (-1.0 - (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-274], N[Not[LessEqual[t$95$0, 3e-241]], $MachinePrecision]], t$95$0, N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -9.99999999999999966e-275 or 2.9999999999999999e-241 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

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

   if -9.99999999999999966e-275 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 2.9999999999999999e-241

   1. Initial program 12.2%

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

   2. Taylor expanded in y around inf 99.9%

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

      1. sub-neg 99.9%

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

      2. mul-1-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. associate-+l- 99.9%

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

      5. mul-1-neg 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. mul-1-neg 99.9%

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

      8. div-sub 99.9%

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

      9. sub-neg 99.9%

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

      10. mul-1-neg 99.9%

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

      11. remove-double-neg 99.9%

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

      12. unpow2 99.9%

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

      13. distribute-lft-out 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. mul-1-neg 100.0%

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

      5. distribute-lft-in 100.0%

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

      6. metadata-eval 100.0%

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

      7. mul-1-neg 100.0%

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

      8. distribute-neg-frac 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-274} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 3 \cdot 10^{-241}\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 2: 66.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - \frac{y}{z}}\\ \mathbf{if}\;y \leq -1.52 \cdot 10^{+153}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-266}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 190:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+105}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 (/ y z)))))
   (if (<= y -1.52e+153)
     (- z)
     (if (<= y -1e-266)
       t_0
       (if (<= y 190.0) (+ x y) (if (<= y 2.4e+105) t_0 (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -1.52e+153) {
		tmp = -z;
	} else if (y <= -1e-266) {
		tmp = t_0;
	} else if (y <= 190.0) {
		tmp = x + y;
	} else if (y <= 2.4e+105) {
		tmp = t_0;
	} 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 <= (-1.52d+153)) then
        tmp = -z
    else if (y <= (-1d-266)) then
        tmp = t_0
    else if (y <= 190.0d0) then
        tmp = x + y
    else if (y <= 2.4d+105) then
        tmp = t_0
    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 <= -1.52e+153) {
		tmp = -z;
	} else if (y <= -1e-266) {
		tmp = t_0;
	} else if (y <= 190.0) {
		tmp = x + y;
	} else if (y <= 2.4e+105) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (1.0 - (y / z))
	tmp = 0
	if y <= -1.52e+153:
		tmp = -z
	elif y <= -1e-266:
		tmp = t_0
	elif y <= 190.0:
		tmp = x + y
	elif y <= 2.4e+105:
		tmp = t_0
	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 <= -1.52e+153)
		tmp = Float64(-z);
	elseif (y <= -1e-266)
		tmp = t_0;
	elseif (y <= 190.0)
		tmp = Float64(x + y);
	elseif (y <= 2.4e+105)
		tmp = t_0;
	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 <= -1.52e+153)
		tmp = -z;
	elseif (y <= -1e-266)
		tmp = t_0;
	elseif (y <= 190.0)
		tmp = x + y;
	elseif (y <= 2.4e+105)
		tmp = t_0;
	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, -1.52e+153], (-z), If[LessEqual[y, -1e-266], t$95$0, If[LessEqual[y, 190.0], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.4e+105], t$95$0, (-z)]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.52e153 or 2.39999999999999975e105 < y

   1. Initial program 72.9%

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

   2. Taylor expanded in y around inf 70.6%

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

      1. mul-1-neg 70.6%

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

   4. Simplified 70.6%

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

   if -1.52e153 < y < -9.9999999999999998e-267 or 190 < y < 2.39999999999999975e105

   1. Initial program 94.4%

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

   2. Taylor expanded in x around inf 71.2%

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

   if -9.9999999999999998e-267 < y < 190

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 77.3%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{+153}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-266}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 190:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+105}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 3: 66.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{x}{t_0}\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-90}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-164}:\\ \;\;\;\;\frac{y}{t_0}\\ \mathbf{elif}\;x \leq 86000000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ x t_0)))
   (if (<= x -2.6e+59)
     t_1
     (if (<= x -1.85e-90)
       (- z)
       (if (<= x 1.9e-164) (/ y t_0) (if (<= x 86000000000.0) (+ 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 <= -2.6e+59) {
		tmp = t_1;
	} else if (x <= -1.85e-90) {
		tmp = -z;
	} else if (x <= 1.9e-164) {
		tmp = y / t_0;
	} else if (x <= 86000000000.0) {
		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 <= (-2.6d+59)) then
        tmp = t_1
    else if (x <= (-1.85d-90)) then
        tmp = -z
    else if (x <= 1.9d-164) then
        tmp = y / t_0
    else if (x <= 86000000000.0d0) 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 <= -2.6e+59) {
		tmp = t_1;
	} else if (x <= -1.85e-90) {
		tmp = -z;
	} else if (x <= 1.9e-164) {
		tmp = y / t_0;
	} else if (x <= 86000000000.0) {
		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 <= -2.6e+59:
		tmp = t_1
	elif x <= -1.85e-90:
		tmp = -z
	elif x <= 1.9e-164:
		tmp = y / t_0
	elif x <= 86000000000.0:
		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 <= -2.6e+59)
		tmp = t_1;
	elseif (x <= -1.85e-90)
		tmp = Float64(-z);
	elseif (x <= 1.9e-164)
		tmp = Float64(y / t_0);
	elseif (x <= 86000000000.0)
		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 <= -2.6e+59)
		tmp = t_1;
	elseif (x <= -1.85e-90)
		tmp = -z;
	elseif (x <= 1.9e-164)
		tmp = y / t_0;
	elseif (x <= 86000000000.0)
		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, -2.6e+59], t$95$1, If[LessEqual[x, -1.85e-90], (-z), If[LessEqual[x, 1.9e-164], N[(y / t$95$0), $MachinePrecision], If[LessEqual[x, 86000000000.0], N[(x + y), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.59999999999999999e59 or 8.6e10 < x

   1. Initial program 89.6%

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

   2. Taylor expanded in x around inf 75.5%

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

   if -2.59999999999999999e59 < x < -1.85000000000000009e-90

   1. Initial program 83.1%

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

   2. Taylor expanded in y around inf 59.4%

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

      1. mul-1-neg 59.4%

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

   4. Simplified 59.4%

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

   if -1.85000000000000009e-90 < x < 1.89999999999999995e-164

   1. Initial program 90.5%

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

   2. Taylor expanded in x around 0 77.3%

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

   if 1.89999999999999995e-164 < x < 8.6e10

   1. Initial program 92.6%

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

   2. Taylor expanded in z around inf 76.9%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-90}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-164}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;x \leq 86000000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]

Alternative 4: 73.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-5} \lor \neg \left(z \leq 4.6\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.2e-5) (not (<= z 4.6))) (+ x y) (- (- z) (/ z (/ y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.2e-5) || !(z <= 4.6)) {
		tmp = x + y;
	} else {
		tmp = -z - (z / (y / 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 ((z <= (-6.2d-5)) .or. (.not. (z <= 4.6d0))) then
        tmp = x + y
    else
        tmp = -z - (z / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.2e-5) || !(z <= 4.6)) {
		tmp = x + y;
	} else {
		tmp = -z - (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.2e-5) or not (z <= 4.6):
		tmp = x + y
	else:
		tmp = -z - (z / (y / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.2e-5) || !(z <= 4.6))
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(-z) - Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6.2e-5) || ~((z <= 4.6)))
		tmp = x + y;
	else
		tmp = -z - (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.2e-5], N[Not[LessEqual[z, 4.6]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[((-z) - N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.20000000000000027e-5 or 4.5999999999999996 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 77.5%

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

   if -6.20000000000000027e-5 < z < 4.5999999999999996

   1. Initial program 77.5%

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

   2. Taylor expanded in y around inf 77.1%

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

      1. sub-neg 77.1%

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

      2. mul-1-neg 77.1%

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

      3. unsub-neg 77.1%

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

      4. associate-+l- 77.1%

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

      5. mul-1-neg 77.1%

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

      6. distribute-frac-neg 77.1%

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

      7. mul-1-neg 77.1%

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

      8. div-sub 77.1%

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

      9. sub-neg 77.1%

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

      10. mul-1-neg 77.1%

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

      11. remove-double-neg 77.1%

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

      12. unpow2 77.1%

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

      13. distribute-lft-out 77.1%

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

   4. Simplified 77.1%

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

   5. Taylor expanded in z around 0 77.1%

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

      1. associate-/l* 72.4%

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

   7. Simplified 72.4%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-5} \lor \neg \left(z \leq 4.6\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 5: 73.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-6}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 0.021:\\ \;\;\;\;\frac{z \cdot \left(\left(-y\right) - x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.8e-6) (+ x y) (if (<= z 0.021) (/ (* z (- (- y) x)) y) (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.8e-6) {
		tmp = x + y;
	} else if (z <= 0.021) {
		tmp = (z * (-y - x)) / y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.8d-6)) then
        tmp = x + y
    else if (z <= 0.021d0) then
        tmp = (z * (-y - x)) / y
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.8e-6) {
		tmp = x + y;
	} else if (z <= 0.021) {
		tmp = (z * (-y - x)) / y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.8e-6:
		tmp = x + y
	elif z <= 0.021:
		tmp = (z * (-y - x)) / y
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.8e-6)
		tmp = Float64(x + y);
	elseif (z <= 0.021)
		tmp = Float64(Float64(z * Float64(Float64(-y) - x)) / y);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.8e-6)
		tmp = x + y;
	elseif (z <= 0.021)
		tmp = (z * (-y - x)) / y;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.8e-6], N[(x + y), $MachinePrecision], If[LessEqual[z, 0.021], N[(N[(z * N[((-y) - x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.79999999999999992e-6 or 0.0210000000000000013 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 77.5%

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

   if -1.79999999999999992e-6 < z < 0.0210000000000000013

   1. Initial program 77.5%

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

   2. Taylor expanded in z around 0 73.9%

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

      1. associate-*r/ 73.9%

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

      2. +-commutative 73.9%

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

      3. *-commutative 73.9%

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

      4. associate-*r* 73.9%

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

      5. mul-1-neg 73.9%

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

      6. +-commutative 73.9%

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

   4. Simplified 73.9%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-6}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 0.021:\\ \;\;\;\;\frac{z \cdot \left(\left(-y\right) - x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6: 73.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.000105:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 19:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.000105) (+ x y) (if (<= z 19.0) (* z (- -1.0 (/ x y))) (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.000105) {
		tmp = x + y;
	} else if (z <= 19.0) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.000105d0)) then
        tmp = x + y
    else if (z <= 19.0d0) then
        tmp = z * ((-1.0d0) - (x / y))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.000105) {
		tmp = x + y;
	} else if (z <= 19.0) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.000105:
		tmp = x + y
	elif z <= 19.0:
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.000105)
		tmp = Float64(x + y);
	elseif (z <= 19.0)
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.000105)
		tmp = x + y;
	elseif (z <= 19.0)
		tmp = z * (-1.0 - (x / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.000105], N[(x + y), $MachinePrecision], If[LessEqual[z, 19.0], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e-4 or 19 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 77.5%

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

   if -1.05e-4 < z < 19

   1. Initial program 77.5%

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

   2. Taylor expanded in y around inf 77.1%

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

      1. sub-neg 77.1%

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

      2. mul-1-neg 77.1%

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

      3. unsub-neg 77.1%

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

      4. associate-+l- 77.1%

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

      5. mul-1-neg 77.1%

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

      6. distribute-frac-neg 77.1%

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

      7. mul-1-neg 77.1%

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

      8. div-sub 77.1%

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

      9. sub-neg 77.1%

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

      10. mul-1-neg 77.1%

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

      11. remove-double-neg 77.1%

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

      12. unpow2 77.1%

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

      13. distribute-lft-out 77.1%

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

   4. Simplified 77.1%

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

   5. Taylor expanded in z around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. *-commutative 72.3%

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

      3. distribute-rgt-neg-in 72.3%

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

      4. mul-1-neg 72.3%

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

      5. distribute-lft-in 72.3%

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

      6. metadata-eval 72.3%

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

      7. mul-1-neg 72.3%

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

      8. distribute-neg-frac 72.3%

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

   7. Simplified 72.3%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.000105:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 19:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 68.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.19 \cdot 10^{+82}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+84}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.19e+82) (- z) (if (<= y 2.6e+84) (+ x y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.19e+82) {
		tmp = -z;
	} else if (y <= 2.6e+84) {
		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 <= (-1.19d+82)) then
        tmp = -z
    else if (y <= 2.6d+84) 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 <= -1.19e+82) {
		tmp = -z;
	} else if (y <= 2.6e+84) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.19e+82:
		tmp = -z
	elif y <= 2.6e+84:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.19e+82)
		tmp = Float64(-z);
	elseif (y <= 2.6e+84)
		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 <= -1.19e+82)
		tmp = -z;
	elseif (y <= 2.6e+84)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.19e+82], (-z), If[LessEqual[y, 2.6e+84], N[(x + y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1899999999999999e82 or 2.6000000000000001e84 < y

   1. Initial program 72.4%

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

   2. Taylor expanded in y around inf 63.4%

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

      1. mul-1-neg 63.4%

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

   4. Simplified 63.4%

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

   if -1.1899999999999999e82 < y < 2.6000000000000001e84

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 71.3%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.19 \cdot 10^{+82}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+84}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 8: 57.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-5}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.1e-5) (- z) (if (<= y 1.18e+83) x (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.1e-5) {
		tmp = -z;
	} else if (y <= 1.18e+83) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.1d-5)) then
        tmp = -z
    else if (y <= 1.18d+83) then
        tmp = x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.1e-5) {
		tmp = -z;
	} else if (y <= 1.18e+83) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.1e-5:
		tmp = -z
	elif y <= 1.18e+83:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.1e-5)
		tmp = Float64(-z);
	elseif (y <= 1.18e+83)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.1e-5)
		tmp = -z;
	elseif (y <= 1.18e+83)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.1e-5], (-z), If[LessEqual[y, 1.18e+83], x, (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -3.10000000000000014e-5 or 1.1799999999999999e83 < y

   1. Initial program 75.5%

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

   2. Taylor expanded in y around inf 60.3%

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

      1. mul-1-neg 60.3%

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

   4. Simplified 60.3%

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

   if -3.10000000000000014e-5 < y < 1.1799999999999999e83

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 57.3%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-5}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 9: 41.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-124}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.6e-90) x (if (<= x 1.35e-124) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.6e-90) {
		tmp = x;
	} else if (x <= 1.35e-124) {
		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 <= (-2.6d-90)) then
        tmp = x
    else if (x <= 1.35d-124) 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 <= -2.6e-90) {
		tmp = x;
	} else if (x <= 1.35e-124) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.6e-90:
		tmp = x
	elif x <= 1.35e-124:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.6e-90)
		tmp = x;
	elseif (x <= 1.35e-124)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.6e-90)
		tmp = x;
	elseif (x <= 1.35e-124)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.6e-90], x, If[LessEqual[x, 1.35e-124], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6e-90 or 1.35000000000000009e-124 < x

   1. Initial program 88.8%

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

   2. Taylor expanded in y around 0 47.4%

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

   if -2.6e-90 < x < 1.35000000000000009e-124

   1. Initial program 91.5%

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

   2. Taylor expanded in x around 0 77.2%

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

   3. Taylor expanded in y around 0 39.9%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-124}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 35.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 89.6%

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

2. Taylor expanded in y around 0 38.0%

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

3. Final simplification 38.0%

   \[\leadsto x \]

Developer target: 93.4% 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 2023199 
(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))))