Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B

Percentage Accurate: 98.2% → 98.2%

Time: 8.0s

Alternatives: 10

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x + y \cdot \frac{z - t}{a - t} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (a - t)));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (y * ((z - t) / (a - t)))
end function

Java

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

Python

def code(x, y, z, t, a):
	return x + (y * ((z - t) / (a - t)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (y * ((z - t) / (a - t)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \frac{z - t}{a - t} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (a - t)));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (y * ((z - t) / (a - t)))
end function

Java

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

Python

def code(x, y, z, t, a):
	return x + (y * ((z - t) / (a - t)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (y * ((z - t) / (a - t)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \frac{z - t}{a - t} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (a - t)));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (y * ((z - t) / (a - t)))
end function

Java

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

Python

def code(x, y, z, t, a):
	return x + (y * ((z - t) / (a - t)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (y * ((z - t) / (a - t)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.4%

   \[x + y \cdot \frac{z - t}{a - t} \]

2. Final simplification 98.4%

   \[\leadsto x + y \cdot \frac{z - t}{a - t} \]

Alternative 2: 82.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.65 \cdot 10^{+208} \lor \neg \left(t \leq 1.9 \cdot 10^{+212}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.65e+208) (not (<= t 1.9e+212)))
   (+ x y)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.65e+208) || !(t <= 1.9e+212)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.65d+208)) .or. (.not. (t <= 1.9d+212))) then
        tmp = x + y
    else
        tmp = x + (y * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.65e+208) || !(t <= 1.9e+212)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.65e+208) or not (t <= 1.9e+212):
		tmp = x + y
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.65e+208) || !(t <= 1.9e+212))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.65e+208) || ~((t <= 1.9e+212)))
		tmp = x + y;
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.65e+208], N[Not[LessEqual[t, 1.9e+212]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.64999999999999996e208 or 1.89999999999999994e212 < t

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{a - t} \]

   2. Taylor expanded in t around inf 90.9%

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

   if -3.64999999999999996e208 < t < 1.89999999999999994e212

   1. Initial program 98.1%

      \[x + y \cdot \frac{z - t}{a - t} \]

   2. Taylor expanded in z around inf 88.8%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.65 \cdot 10^{+208} \lor \neg \left(t \leq 1.9 \cdot 10^{+212}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 3: 82.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+208} \lor \neg \left(t \leq 1.9 \cdot 10^{+212}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7e+208) (not (<= t 1.9e+212)))
   (+ x y)
   (+ x (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7e+208) || !(t <= 1.9e+212)) {
		tmp = x + y;
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-7d+208)) .or. (.not. (t <= 1.9d+212))) then
        tmp = x + y
    else
        tmp = x + (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7e+208) || !(t <= 1.9e+212)) {
		tmp = x + y;
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7e+208) or not (t <= 1.9e+212):
		tmp = x + y
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7e+208) || !(t <= 1.9e+212))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7e+208) || ~((t <= 1.9e+212)))
		tmp = x + y;
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7e+208], N[Not[LessEqual[t, 1.9e+212]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.00000000000000033e208 or 1.89999999999999994e212 < t

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{a - t} \]

   2. Taylor expanded in t around inf 90.9%

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

   if -7.00000000000000033e208 < t < 1.89999999999999994e212

   1. Initial program 98.1%

      \[x + y \cdot \frac{z - t}{a - t} \]

   2. Taylor expanded in z around inf 83.3%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a - t}} \]
   3. Step-by-step derivation

      1. associate-/l* 88.8%

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

   4. Simplified 88.8%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+208} \lor \neg \left(t \leq 1.9 \cdot 10^{+212}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]

Alternative 4: 82.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+208} \lor \neg \left(t \leq 2.3 \cdot 10^{+212}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7e+208) (not (<= t 2.3e+212)))
   (+ x y)
   (+ x (/ z (/ (- a t) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7e+208) || !(t <= 2.3e+212)) {
		tmp = x + y;
	} else {
		tmp = x + (z / ((a - t) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-7d+208)) .or. (.not. (t <= 2.3d+212))) then
        tmp = x + y
    else
        tmp = x + (z / ((a - t) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7e+208) || !(t <= 2.3e+212)) {
		tmp = x + y;
	} else {
		tmp = x + (z / ((a - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7e+208) or not (t <= 2.3e+212):
		tmp = x + y
	else:
		tmp = x + (z / ((a - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7e+208) || !(t <= 2.3e+212))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7e+208) || ~((t <= 2.3e+212)))
		tmp = x + y;
	else
		tmp = x + (z / ((a - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7e+208], N[Not[LessEqual[t, 2.3e+212]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.00000000000000033e208 or 2.2999999999999998e212 < t

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{a - t} \]

   2. Taylor expanded in t around inf 90.9%

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

   if -7.00000000000000033e208 < t < 2.2999999999999998e212

   1. Initial program 98.1%

      \[x + y \cdot \frac{z - t}{a - t} \]

   2. Taylor expanded in z around inf 88.8%

      \[\leadsto x + y \cdot \color{blue}{\frac{z}{a - t}} \]
   3. Step-by-step derivation

      1. *-commutative 88.8%

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

      2. associate-/r/ 89.3%

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

   4. Applied egg-rr 89.3%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+208} \lor \neg \left(t \leq 2.3 \cdot 10^{+212}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \end{array} \]

Alternative 5: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{z}{t_1}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-110}:\\ \;\;\;\;x - \frac{t}{t_1}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- a t) y)))
   (if (<= z -2.7e-65)
     (+ x (/ z t_1))
     (if (<= z 1.22e-110) (- x (/ t t_1)) (+ x (* y (/ z (- a t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a - t) / y;
	double tmp;
	if (z <= -2.7e-65) {
		tmp = x + (z / t_1);
	} else if (z <= 1.22e-110) {
		tmp = x - (t / t_1);
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - t) / y
    if (z <= (-2.7d-65)) then
        tmp = x + (z / t_1)
    else if (z <= 1.22d-110) then
        tmp = x - (t / t_1)
    else
        tmp = x + (y * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a - t) / y;
	double tmp;
	if (z <= -2.7e-65) {
		tmp = x + (z / t_1);
	} else if (z <= 1.22e-110) {
		tmp = x - (t / t_1);
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a - t) / y
	tmp = 0
	if z <= -2.7e-65:
		tmp = x + (z / t_1)
	elif z <= 1.22e-110:
		tmp = x - (t / t_1)
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a - t) / y)
	tmp = 0.0
	if (z <= -2.7e-65)
		tmp = Float64(x + Float64(z / t_1));
	elseif (z <= 1.22e-110)
		tmp = Float64(x - Float64(t / t_1));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a - t) / y;
	tmp = 0.0;
	if (z <= -2.7e-65)
		tmp = x + (z / t_1);
	elseif (z <= 1.22e-110)
		tmp = x - (t / t_1);
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -2.7e-65], N[(x + N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e-110], N[(x - N[(t / t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6999999999999999e-65

   1. Initial program 97.6%

      \[x + y \cdot \frac{z - t}{a - t} \]

   2. Taylor expanded in z around inf 87.3%

      \[\leadsto x + y \cdot \color{blue}{\frac{z}{a - t}} \]
   3. Step-by-step derivation

      1. *-commutative 87.3%

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

      2. associate-/r/ 88.5%

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

   4. Applied egg-rr 88.5%

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

   if -2.6999999999999999e-65 < z < 1.22e-110

   1. Initial program 98.8%

      \[x + y \cdot \frac{z - t}{a - t} \]

   2. Taylor expanded in z around 0 82.8%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{t \cdot y}{a - t}} \]
   3. Step-by-step derivation

      1. mul-1-neg 82.8%

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

      2. associate-/l* 94.1%

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

      3. distribute-neg-frac 94.1%

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

   4. Simplified 94.1%

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

   if 1.22e-110 < z

   1. Initial program 98.8%

      \[x + y \cdot \frac{z - t}{a - t} \]

   2. Taylor expanded in z around inf 90.8%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-110}:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 6: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+90} \lor \neg \left(t \leq 7.5\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.05e+90) (not (<= t 7.5))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+90) || !(t <= 7.5)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.05d+90)) .or. (.not. (t <= 7.5d0))) then
        tmp = x + y
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+90) || !(t <= 7.5)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.05e+90) or not (t <= 7.5):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.05e+90) || !(t <= 7.5))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.05e+90) || ~((t <= 7.5)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.05e+90], N[Not[LessEqual[t, 7.5]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.0499999999999999e90 or 7.5 < t

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{a - t} \]

   2. Taylor expanded in t around inf 79.0%

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

   if -1.0499999999999999e90 < t < 7.5

   1. Initial program 97.2%

      \[x + y \cdot \frac{z - t}{a - t} \]

   2. Taylor expanded in t around 0 76.6%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+90} \lor \neg \left(t \leq 7.5\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 7: 77.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+90} \lor \neg \left(t \leq 100\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.45e+90) (not (<= t 100.0))) (+ x y) (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.45e+90) || !(t <= 100.0)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.45d+90)) .or. (.not. (t <= 100.0d0))) then
        tmp = x + y
    else
        tmp = x + (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.45e+90) || !(t <= 100.0)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.45e+90) or not (t <= 100.0):
		tmp = x + y
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.45e+90) || !(t <= 100.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.45e+90) || ~((t <= 100.0)))
		tmp = x + y;
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.45e+90], N[Not[LessEqual[t, 100.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4500000000000001e90 or 100 < t

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{a - t} \]

   2. Taylor expanded in t around inf 79.0%

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

   if -1.4500000000000001e90 < t < 100

   1. Initial program 97.2%

      \[x + y \cdot \frac{z - t}{a - t} \]

   2. Taylor expanded in t around 0 71.9%

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

      1. associate-/l* 76.6%

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

   4. Simplified 76.6%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+90} \lor \neg \left(t \leq 100\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 8: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+89} \lor \neg \left(t \leq 250\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9.8e+89) (not (<= t 250.0))) (+ x y) (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.8e+89) || !(t <= 250.0)) {
		tmp = x + y;
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-9.8d+89)) .or. (.not. (t <= 250.0d0))) then
        tmp = x + y
    else
        tmp = x + (z / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.8e+89) || !(t <= 250.0)) {
		tmp = x + y;
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9.8e+89) or not (t <= 250.0):
		tmp = x + y
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9.8e+89) || !(t <= 250.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -9.8e+89) || ~((t <= 250.0)))
		tmp = x + y;
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9.8e+89], N[Not[LessEqual[t, 250.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.79999999999999992e89 or 250 < t

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{a - t} \]

   2. Taylor expanded in t around inf 79.0%

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

   if -9.79999999999999992e89 < t < 250

   1. Initial program 97.2%

      \[x + y \cdot \frac{z - t}{a - t} \]

   2. Taylor expanded in t around 0 71.9%

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

      1. associate-/l* 76.6%

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

   4. Simplified 76.6%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]
   5. Step-by-step derivation

      1. associate-/r/ 76.3%

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

   6. Applied egg-rr 76.3%

      \[\leadsto x + \color{blue}{\frac{y}{a} \cdot z} \]
   7. Step-by-step derivation

      1. *-commutative 76.3%

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

      2. clear-num 76.3%

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

      3. un-div-inv 76.9%

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

   8. Applied egg-rr 76.9%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+89} \lor \neg \left(t \leq 250\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 9: 63.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+181}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8e+103) x (if (<= a 1.9e+181) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8e+103) {
		tmp = x;
	} else if (a <= 1.9e+181) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8d+103)) then
        tmp = x
    else if (a <= 1.9d+181) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8e+103) {
		tmp = x;
	} else if (a <= 1.9e+181) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8e+103:
		tmp = x
	elif a <= 1.9e+181:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8e+103)
		tmp = x;
	elseif (a <= 1.9e+181)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8e+103)
		tmp = x;
	elseif (a <= 1.9e+181)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8e+103], x, If[LessEqual[a, 1.9e+181], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -8e103 or 1.9000000000000001e181 < a

   1. Initial program 98.4%

      \[x + y \cdot \frac{z - t}{a - t} \]

   2. Taylor expanded in t around 0 76.2%

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

      1. associate-/l* 86.9%

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

   4. Simplified 86.9%

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

   5. Taylor expanded in x around inf 70.3%

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

   if -8e103 < a < 1.9000000000000001e181

   1. Initial program 98.4%

      \[x + y \cdot \frac{z - t}{a - t} \]

   2. Taylor expanded in t around inf 60.4%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+181}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 50.7% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 98.4%

   \[x + y \cdot \frac{z - t}{a - t} \]

2. Taylor expanded in t around 0 61.8%

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

   1. associate-/l* 65.0%

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

4. Simplified 65.0%

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

5. Taylor expanded in x around inf 52.8%

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

6. Final simplification 52.8%

   \[\leadsto x \]

Developer target: 99.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (< y -8.508084860551241e-17)
     t_1
     (if (< y 2.894426862792089e-49)
       (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if y < -8.508084860551241e-17:
		tmp = t_1
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023314 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

  (+ x (* y (/ (- z t) (- a t)))))