Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A

Percentage Accurate: 85.1% → 98.1%

Time: 8.4s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (((z - t) / (z - a)) * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.0%

   \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. associate-/l* 99.1%

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

   2. *-commutative 99.1%

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

4. Applied egg-rr 99.1%

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

5. Final simplification 99.1%

   \[\leadsto x + \frac{z - t}{z - a} \cdot y \]
6. Add Preprocessing

Alternative 2: 81.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-103} \lor \neg \left(z \leq 3.4 \cdot 10^{-94}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.4e-103) (not (<= z 3.4e-94)))
   (+ x (* y (/ z (- z a))))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.4e-103) || !(z <= 3.4e-94)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y * (t / 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 ((z <= (-3.4d-103)) .or. (.not. (z <= 3.4d-94))) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x + (y * (t / 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 ((z <= -3.4e-103) || !(z <= 3.4e-94)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.4e-103) or not (z <= 3.4e-94):
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.4e-103) || !(z <= 3.4e-94))
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.4e-103) || ~((z <= 3.4e-94)))
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.4e-103], N[Not[LessEqual[z, 3.4e-94]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.40000000000000003e-103 or 3.3999999999999998e-94 < z

   1. Initial program 78.4%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 66.2%

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

      1. associate-/l* 81.2%

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

   5. Simplified 81.2%

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

   if -3.40000000000000003e-103 < z < 3.3999999999999998e-94

   1. Initial program 94.6%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l* 97.2%

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

      2. *-commutative 97.2%

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

   4. Applied egg-rr 97.2%

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

   5. Taylor expanded in z around 0 85.1%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-103} \lor \neg \left(z \leq 3.4 \cdot 10^{-94}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+34} \lor \neg \left(t \leq 1.65 \cdot 10^{-10}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.02e+34) (not (<= t 1.65e-10)))
   (+ x (* y (/ t (- a z))))
   (+ x (* y (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.02e+34) || !(t <= 1.65e-10)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (y * (z / (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 <= (-1.02d+34)) .or. (.not. (t <= 1.65d-10))) then
        tmp = x + (y * (t / (a - z)))
    else
        tmp = x + (y * (z / (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 <= -1.02e+34) || !(t <= 1.65e-10)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.02e+34) or not (t <= 1.65e-10):
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.02e+34) || !(t <= 1.65e-10))
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.02e+34) || ~((t <= 1.65e-10)))
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.02e+34], N[Not[LessEqual[t, 1.65e-10]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.02e34 or 1.65e-10 < t

   1. Initial program 82.0%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l* 98.1%

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

      2. *-commutative 98.1%

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

   4. Applied egg-rr 98.1%

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

   5. Taylor expanded in t around inf 86.1%

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

      1. neg-mul-1 86.1%

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

      2. distribute-neg-frac2 86.1%

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

      3. sub-neg 86.1%

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

      4. distribute-neg-in 86.1%

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

      5. remove-double-neg 86.1%

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

   7. Simplified 86.1%

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

   8. Taylor expanded in t around 0 86.1%

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

   if -1.02e34 < t < 1.65e-10

   1. Initial program 83.8%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 76.5%

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

      1. associate-/l* 92.6%

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

   5. Simplified 92.6%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+34} \lor \neg \left(t \leq 1.65 \cdot 10^{-10}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-232}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-265}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.5e-232)
   (+ x y)
   (if (<= z 4.1e-265) (* (/ y a) (- t z)) (if (<= z 2.35e-38) x (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e-232) {
		tmp = x + y;
	} else if (z <= 4.1e-265) {
		tmp = (y / a) * (t - z);
	} else if (z <= 2.35e-38) {
		tmp = x;
	} else {
		tmp = x + 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 (z <= (-3.5d-232)) then
        tmp = x + y
    else if (z <= 4.1d-265) then
        tmp = (y / a) * (t - z)
    else if (z <= 2.35d-38) then
        tmp = x
    else
        tmp = x + 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 (z <= -3.5e-232) {
		tmp = x + y;
	} else if (z <= 4.1e-265) {
		tmp = (y / a) * (t - z);
	} else if (z <= 2.35e-38) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.5e-232:
		tmp = x + y
	elif z <= 4.1e-265:
		tmp = (y / a) * (t - z)
	elif z <= 2.35e-38:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.5e-232)
		tmp = Float64(x + y);
	elseif (z <= 4.1e-265)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	elseif (z <= 2.35e-38)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.5e-232)
		tmp = x + y;
	elseif (z <= 4.1e-265)
		tmp = (y / a) * (t - z);
	elseif (z <= 2.35e-38)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.5e-232], N[(x + y), $MachinePrecision], If[LessEqual[z, 4.1e-265], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e-38], x, N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4999999999999998e-232 or 2.34999999999999999e-38 < z

   1. Initial program 77.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 68.7%

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

      1. +-commutative 68.7%

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

   5. Simplified 68.7%

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

   if -3.4999999999999998e-232 < z < 4.1e-265

   1. Initial program 95.2%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 71.2%

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

      1. associate-*l/ 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in z around 0 66.9%

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

      1. associate-*r/ 66.9%

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

      2. neg-mul-1 66.9%

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

   8. Simplified 66.9%

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

   9. Taylor expanded in y around 0 67.1%

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

       1. associate-*r/ 66.4%

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

       2. *-rgt-identity 66.4%

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

       3. *-rgt-identity 66.4%

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

       4. div-sub 66.4%

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

       5. sub-neg 66.4%

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

       6. neg-mul-1 66.4%

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

       7. distribute-lft-in 66.4%

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

       8. associate-/l* 66.4%

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

       9. neg-mul-1 66.4%

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

       10. distribute-rgt-neg-in 66.4%

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

       11. associate-*r/ 67.1%

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

       12. *-commutative 67.1%

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

       13. associate-*r/ 66.9%

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

       14. unsub-neg 66.9%

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

       15. distribute-lft-out-- 66.9%

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

       16. neg-mul-1 66.9%

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

       17. distribute-lft-neg-in 66.9%

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

       18. cancel-sign-sub 66.9%

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

       19. +-commutative 66.9%

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

   11. Simplified 66.9%

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

   if 4.1e-265 < z < 2.34999999999999999e-38

   1. Initial program 97.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 61.4%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-232}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-265}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+65} \lor \neg \left(z \leq 1.65 \cdot 10^{+44}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.15e+65) (not (<= z 1.65e+44))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e+65) || !(z <= 1.65e+44)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / 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 ((z <= (-1.15d+65)) .or. (.not. (z <= 1.65d+44))) then
        tmp = x + y
    else
        tmp = x + (y * (t / 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 ((z <= -1.15e+65) || !(z <= 1.65e+44)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.15e+65) or not (z <= 1.65e+44):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.15e+65) || !(z <= 1.65e+44))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.15e+65) || ~((z <= 1.65e+44)))
		tmp = x + y;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.15e+65], N[Not[LessEqual[z, 1.65e+44]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e65 or 1.65000000000000007e44 < z

   1. Initial program 68.0%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 77.5%

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

      1. +-commutative 77.5%

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

   5. Simplified 77.5%

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

   if -1.15e65 < z < 1.65000000000000007e44

   1. Initial program 95.2%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l* 98.5%

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

      2. *-commutative 98.5%

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

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in z around 0 75.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+65} \lor \neg \left(z \leq 1.65 \cdot 10^{+44}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+20} \lor \neg \left(z \leq 2.5 \cdot 10^{-38}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.85e+20) (not (<= z 2.5e-38))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.85e+20) || !(z <= 2.5e-38)) {
		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 ((z <= (-1.85d+20)) .or. (.not. (z <= 2.5d-38))) 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 ((z <= -1.85e+20) || !(z <= 2.5e-38)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.85e+20) or not (z <= 2.5e-38):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.85e+20) || !(z <= 2.5e-38))
		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 ((z <= -1.85e+20) || ~((z <= 2.5e-38)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.85e+20], N[Not[LessEqual[z, 2.5e-38]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.85e20 or 2.50000000000000017e-38 < z

   1. Initial program 73.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 72.9%

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

      1. +-commutative 72.9%

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

   5. Simplified 72.9%

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

   if -1.85e20 < z < 2.50000000000000017e-38

   1. Initial program 95.6%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 55.1%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+20} \lor \neg \left(z \leq 2.5 \cdot 10^{-38}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{-208}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-139}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -5.7e-208) x (if (<= x 1.05e-139) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.7e-208) {
		tmp = x;
	} else if (x <= 1.05e-139) {
		tmp = 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 (x <= (-5.7d-208)) then
        tmp = x
    else if (x <= 1.05d-139) then
        tmp = 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 (x <= -5.7e-208) {
		tmp = x;
	} else if (x <= 1.05e-139) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -5.7e-208:
		tmp = x
	elif x <= 1.05e-139:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -5.7e-208)
		tmp = x;
	elseif (x <= 1.05e-139)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -5.7e-208)
		tmp = x;
	elseif (x <= 1.05e-139)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -5.7e-208], x, If[LessEqual[x, 1.05e-139], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.7000000000000004e-208 or 1.05000000000000004e-139 < x

   1. Initial program 84.5%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 59.5%

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

   if -5.7000000000000004e-208 < x < 1.05000000000000004e-139

   1. Initial program 77.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 68.6%

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

      1. associate-*l/ 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in z around inf 49.4%

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

   7. Taylor expanded in z around inf 43.1%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{-208}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-139}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.2% 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 83.0%

   \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 48.5%

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

4. Final simplification 48.5%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (y / ((z - a) / (z - 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 - a) / (z - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024078 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (+ x (/ y (/ (- z a) (- z t))))

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