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

Percentage Accurate: 85.6% → 98.0%

Time: 7.5s

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: 85.6% 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: 98.0% accurate, 1.0× speedup

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 81.2%

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

   1. associate-*l/ 96.6%

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

3. Simplified 96.6%

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

4. Taylor expanded in y around 0 81.2%

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

   1. associate-*r/ 98.2%

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

6. Simplified 98.2%

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

7. Final simplification 98.2%

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

Alternative 2: 82.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-21} \lor \neg \left(z \leq 1.1 \cdot 10^{-54}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.6e-21) (not (<= z 1.1e-54)))
   (+ x (* y (- 1.0 (/ t z))))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.6e-21) || !(z <= 1.1e-54)) {
		tmp = x + (y * (1.0 - (t / z)));
	} 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 <= (-3.6d-21)) .or. (.not. (z <= 1.1d-54))) then
        tmp = x + (y * (1.0d0 - (t / z)))
    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 <= -3.6e-21) || !(z <= 1.1e-54)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.6e-21) or not (z <= 1.1e-54):
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.6e-21) || !(z <= 1.1e-54))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	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 <= -3.6e-21) || ~((z <= 1.1e-54)))
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.6e-21], N[Not[LessEqual[z, 1.1e-54]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.59999999999999989e-21 or 1.1e-54 < z

   1. Initial program 72.4%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in y around 0 72.4%

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

      1. associate-*r/ 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in a around 0 84.6%

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

      1. div-sub 84.6%

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

      2. *-inverses 84.6%

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

   9. Simplified 84.6%

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

   if -3.59999999999999989e-21 < z < 1.1e-54

   1. Initial program 90.2%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in y around 0 90.2%

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

      1. associate-*r/ 96.5%

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

   6. Simplified 96.5%

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

   7. Taylor expanded in z around 0 86.2%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-21} \lor \neg \left(z \leq 1.1 \cdot 10^{-54}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 3: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+42} \lor \neg \left(t \leq 7.5 \cdot 10^{-27}\right):\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.4e+42) (not (<= t 7.5e-27)))
   (- x (* y (/ t (- z a))))
   (+ x (* z (/ y (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e+42) || !(t <= 7.5e-27)) {
		tmp = x - (y * (t / (z - a)));
	} else {
		tmp = x + (z * (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 <= (-2.4d+42)) .or. (.not. (t <= 7.5d-27))) then
        tmp = x - (y * (t / (z - a)))
    else
        tmp = x + (z * (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 <= -2.4e+42) || !(t <= 7.5e-27)) {
		tmp = x - (y * (t / (z - a)));
	} else {
		tmp = x + (z * (y / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.4e+42) or not (t <= 7.5e-27):
		tmp = x - (y * (t / (z - a)))
	else:
		tmp = x + (z * (y / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.4e+42) || !(t <= 7.5e-27))
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.4e+42) || ~((t <= 7.5e-27)))
		tmp = x - (y * (t / (z - a)));
	else
		tmp = x + (z * (y / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.4e+42], N[Not[LessEqual[t, 7.5e-27]], $MachinePrecision]], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.3999999999999999e42 or 7.50000000000000029e-27 < t

   1. Initial program 78.9%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in t around inf 76.1%

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

      1. associate-*r/ 76.1%

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

      2. mul-1-neg 76.1%

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

      3. distribute-lft-neg-out 76.1%

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

      4. *-commutative 76.1%

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

   6. Simplified 76.1%

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

   7. Taylor expanded in x around 0 76.1%

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

      1. mul-1-neg 76.1%

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

      2. *-commutative 76.1%

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

      3. associate-*r/ 87.9%

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

      4. sub-neg 87.9%

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

   9. Simplified 87.9%

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

   if -2.3999999999999999e42 < t < 7.50000000000000029e-27

   1. Initial program 83.2%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in t around 0 76.9%

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

      1. associate-*l/ 92.2%

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

      2. *-commutative 92.2%

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

   6. Simplified 92.2%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+42} \lor \neg \left(t \leq 7.5 \cdot 10^{-27}\right):\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \]

Alternative 4: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+42} \lor \neg \left(t \leq 3.2 \cdot 10^{-32}\right):\\ \;\;\;\;x - \frac{y}{\frac{z - a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.8e+42) (not (<= t 3.2e-32)))
   (- x (/ y (/ (- z a) t)))
   (+ x (* z (/ y (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.8e+42) || !(t <= 3.2e-32)) {
		tmp = x - (y / ((z - a) / t));
	} else {
		tmp = x + (z * (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 <= (-6.8d+42)) .or. (.not. (t <= 3.2d-32))) then
        tmp = x - (y / ((z - a) / t))
    else
        tmp = x + (z * (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 <= -6.8e+42) || !(t <= 3.2e-32)) {
		tmp = x - (y / ((z - a) / t));
	} else {
		tmp = x + (z * (y / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.8e+42) or not (t <= 3.2e-32):
		tmp = x - (y / ((z - a) / t))
	else:
		tmp = x + (z * (y / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.8e+42) || !(t <= 3.2e-32))
		tmp = Float64(x - Float64(y / Float64(Float64(z - a) / t)));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.8e+42) || ~((t <= 3.2e-32)))
		tmp = x - (y / ((z - a) / t));
	else
		tmp = x + (z * (y / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.8e+42], N[Not[LessEqual[t, 3.2e-32]], $MachinePrecision]], N[(x - N[(y / N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.7999999999999995e42 or 3.2000000000000002e-32 < t

   1. Initial program 78.9%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in t around inf 76.1%

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

      1. associate-*r/ 76.1%

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

      2. mul-1-neg 76.1%

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

      3. distribute-lft-neg-out 76.1%

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

      4. *-commutative 76.1%

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

   6. Simplified 76.1%

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

   7. Taylor expanded in x around 0 76.1%

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

      1. mul-1-neg 76.1%

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

      2. *-commutative 76.1%

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

      3. associate-*r/ 87.9%

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

      4. sub-neg 87.9%

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

   9. Simplified 87.9%

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

       1. clear-num 88.0%

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

       2. un-div-inv 88.1%

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

   11. Applied egg-rr 88.1%

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

   if -6.7999999999999995e42 < t < 3.2000000000000002e-32

   1. Initial program 83.2%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in t around 0 76.9%

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

      1. associate-*l/ 92.2%

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

      2. *-commutative 92.2%

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

   6. Simplified 92.2%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+42} \lor \neg \left(t \leq 3.2 \cdot 10^{-32}\right):\\ \;\;\;\;x - \frac{y}{\frac{z - a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \]

Alternative 5: 82.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-53}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.55e-22)
   (+ x (/ y (/ z (- z t))))
   (if (<= z 3.2e-53) (+ x (* y (/ t a))) (+ x (* y (- 1.0 (/ t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.55e-22) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 3.2e-53) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + (y * (1.0 - (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 (z <= (-1.55d-22)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= 3.2d-53) then
        tmp = x + (y * (t / a))
    else
        tmp = x + (y * (1.0d0 - (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 (z <= -1.55e-22) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 3.2e-53) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.55e-22:
		tmp = x + (y / (z / (z - t)))
	elif z <= 3.2e-53:
		tmp = x + (y * (t / a))
	else:
		tmp = x + (y * (1.0 - (t / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.55e-22)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= 3.2e-53)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.55e-22)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= 3.2e-53)
		tmp = x + (y * (t / a));
	else
		tmp = x + (y * (1.0 - (t / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.55e-22], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-53], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55000000000000006e-22

   1. Initial program 72.4%

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

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in a around 0 63.3%

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

      1. +-commutative 63.3%

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

      2. associate-/l* 84.5%

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

   6. Simplified 84.5%

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

   if -1.55000000000000006e-22 < z < 3.2000000000000001e-53

   1. Initial program 90.2%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in y around 0 90.2%

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

      1. associate-*r/ 96.5%

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

   6. Simplified 96.5%

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

   7. Taylor expanded in z around 0 86.2%

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

   if 3.2000000000000001e-53 < z

   1. Initial program 72.5%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in y around 0 72.5%

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

      1. associate-*r/ 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in a around 0 84.8%

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

      1. div-sub 84.8%

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

      2. *-inverses 84.8%

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

   9. Simplified 84.8%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-53}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]

Alternative 6: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+58}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-8}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e+58) (+ x y) (if (<= z 1.36e-8) (+ x (* y (/ t a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+58) {
		tmp = x + y;
	} else if (z <= 1.36e-8) {
		tmp = x + (y * (t / a));
	} 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 <= (-1.9d+58)) then
        tmp = x + y
    else if (z <= 1.36d-8) then
        tmp = x + (y * (t / a))
    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 <= -1.9e+58) {
		tmp = x + y;
	} else if (z <= 1.36e-8) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e+58:
		tmp = x + y
	elif z <= 1.36e-8:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e+58)
		tmp = Float64(x + y);
	elseif (z <= 1.36e-8)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.9e+58)
		tmp = x + y;
	elseif (z <= 1.36e-8)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e+58], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.36e-8], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8999999999999999e58 or 1.3599999999999999e-8 < z

   1. Initial program 67.4%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in z around inf 79.0%

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

      1. +-commutative 79.0%

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

   6. Simplified 79.0%

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

   if -1.8999999999999999e58 < z < 1.3599999999999999e-8

   1. Initial program 90.2%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in y around 0 90.2%

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

      1. associate-*r/ 97.1%

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

   6. Simplified 97.1%

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

   7. Taylor expanded in z around 0 80.5%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+58}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-8}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 63.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-59}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.4e-59) (+ x y) (if (<= z 9.6e-23) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e-59) {
		tmp = x + y;
	} else if (z <= 9.6e-23) {
		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 <= (-4.4d-59)) then
        tmp = x + y
    else if (z <= 9.6d-23) 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 <= -4.4e-59) {
		tmp = x + y;
	} else if (z <= 9.6e-23) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.4e-59:
		tmp = x + y
	elif z <= 9.6e-23:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.4e-59)
		tmp = Float64(x + y);
	elseif (z <= 9.6e-23)
		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 <= -4.4e-59)
		tmp = x + y;
	elseif (z <= 9.6e-23)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.4e-59], N[(x + y), $MachinePrecision], If[LessEqual[z, 9.6e-23], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3999999999999998e-59 or 9.59999999999999986e-23 < z

   1. Initial program 70.5%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in z around inf 71.7%

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

      1. +-commutative 71.7%

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

   6. Simplified 71.7%

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

   if -4.3999999999999998e-59 < z < 9.59999999999999986e-23

   1. Initial program 91.3%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in x around inf 54.6%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-59}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8: 50.3% 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 81.2%

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

   1. associate-*l/ 96.6%

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

3. Simplified 96.6%

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

4. Taylor expanded in x around inf 48.2%

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

5. Final simplification 48.2%

   \[\leadsto x \]

Developer target: 98.2% 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 2023290 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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