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

Percentage Accurate: 85.3% → 98.3%

Time: 9.5s

Alternatives: 13

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: 85.3% 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: 98.3% 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 85.0%

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

   1. *-commutative 85.0%

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

   2. associate-*l/ 98.8%

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

4. Applied egg-rr 98.8%

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

5. Final simplification 98.8%

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

Alternative 2: 82.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{z - a}\\ \mathbf{if}\;t_1 \leq -10000000000 \lor \neg \left(t_1 \leq 10^{+43}\right):\\ \;\;\;\;\frac{z - t}{z - a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) y) (- z a))))
   (if (or (<= t_1 -10000000000.0) (not (<= t_1 1e+43)))
     (* (/ (- z t) (- z a)) y)
     (+ x (* z (/ y (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (z - a);
	double tmp;
	if ((t_1 <= -10000000000.0) || !(t_1 <= 1e+43)) {
		tmp = ((z - t) / (z - a)) * y;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = ((z - t) * y) / (z - a)
    if ((t_1 <= (-10000000000.0d0)) .or. (.not. (t_1 <= 1d+43))) then
        tmp = ((z - t) / (z - a)) * y
    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 t_1 = ((z - t) * y) / (z - a);
	double tmp;
	if ((t_1 <= -10000000000.0) || !(t_1 <= 1e+43)) {
		tmp = ((z - t) / (z - a)) * y;
	} else {
		tmp = x + (z * (y / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((z - t) * y) / (z - a)
	tmp = 0
	if (t_1 <= -10000000000.0) or not (t_1 <= 1e+43):
		tmp = ((z - t) / (z - a)) * y
	else:
		tmp = x + (z * (y / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) * y) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= -10000000000.0) || !(t_1 <= 1e+43))
		tmp = Float64(Float64(Float64(z - t) / Float64(z - a)) * y);
	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)
	t_1 = ((z - t) * y) / (z - a);
	tmp = 0.0;
	if ((t_1 <= -10000000000.0) || ~((t_1 <= 1e+43)))
		tmp = ((z - t) / (z - a)) * y;
	else
		tmp = x + (z * (y / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -10000000000.0], N[Not[LessEqual[t$95$1, 1e+43]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -1e10 or 1.00000000000000001e43 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 68.3%

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

   3. Taylor expanded in x around 0 60.7%

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

      1. *-commutative 68.3%

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

      2. associate-*l/ 97.4%

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

   5. Applied egg-rr 84.6%

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

   if -1e10 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 1.00000000000000001e43

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 90.5%

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

      1. +-commutative 90.5%

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

      2. associate-*l/ 88.4%

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

      3. *-commutative 88.4%

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

   5. Simplified 88.4%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{z - a} \leq -10000000000 \lor \neg \left(\frac{\left(z - t\right) \cdot y}{z - a} \leq 10^{+43}\right):\\ \;\;\;\;\frac{z - t}{z - a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{z - t}{z - a} \cdot y\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z t) (/ z y)))))
   (if (<= z -1.35e+60)
     t_1
     (if (<= z -3.2e+14)
       x
       (if (<= z -4.5e-29)
         (* (/ (- z t) (- z a)) y)
         (if (<= z 2.5e-18) (+ x (/ t (/ a y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) / (z / y));
	double tmp;
	if (z <= -1.35e+60) {
		tmp = t_1;
	} else if (z <= -3.2e+14) {
		tmp = x;
	} else if (z <= -4.5e-29) {
		tmp = ((z - t) / (z - a)) * y;
	} else if (z <= 2.5e-18) {
		tmp = x + (t / (a / y));
	} 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 + ((z - t) / (z / y))
    if (z <= (-1.35d+60)) then
        tmp = t_1
    else if (z <= (-3.2d+14)) then
        tmp = x
    else if (z <= (-4.5d-29)) then
        tmp = ((z - t) / (z - a)) * y
    else if (z <= 2.5d-18) then
        tmp = x + (t / (a / y))
    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 + ((z - t) / (z / y));
	double tmp;
	if (z <= -1.35e+60) {
		tmp = t_1;
	} else if (z <= -3.2e+14) {
		tmp = x;
	} else if (z <= -4.5e-29) {
		tmp = ((z - t) / (z - a)) * y;
	} else if (z <= 2.5e-18) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) / (z / y))
	tmp = 0
	if z <= -1.35e+60:
		tmp = t_1
	elif z <= -3.2e+14:
		tmp = x
	elif z <= -4.5e-29:
		tmp = ((z - t) / (z - a)) * y
	elif z <= 2.5e-18:
		tmp = x + (t / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) / Float64(z / y)))
	tmp = 0.0
	if (z <= -1.35e+60)
		tmp = t_1;
	elseif (z <= -3.2e+14)
		tmp = x;
	elseif (z <= -4.5e-29)
		tmp = Float64(Float64(Float64(z - t) / Float64(z - a)) * y);
	elseif (z <= 2.5e-18)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) / (z / y));
	tmp = 0.0;
	if (z <= -1.35e+60)
		tmp = t_1;
	elseif (z <= -3.2e+14)
		tmp = x;
	elseif (z <= -4.5e-29)
		tmp = ((z - t) / (z - a)) * y;
	elseif (z <= 2.5e-18)
		tmp = x + (t / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+60], t$95$1, If[LessEqual[z, -3.2e+14], x, If[LessEqual[z, -4.5e-29], N[(N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 2.5e-18], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.35e60 or 2.50000000000000018e-18 < z

   1. Initial program 72.9%

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

      1. *-commutative 72.9%

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

      2. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in z around inf 84.6%

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

   if -1.35e60 < z < -3.2e14

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 91.8%

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

   if -3.2e14 < z < -4.4999999999999998e-29

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 85.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l/ 99.6%

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

   5. Applied egg-rr 85.7%

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

   if -4.4999999999999998e-29 < z < 2.50000000000000018e-18

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0 78.6%

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

      1. +-commutative 78.6%

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

      2. associate-/l* 82.3%

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

   5. Simplified 82.3%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+60}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{z - t}{z - a} \cdot y\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+118} \lor \neg \left(t \leq 2.15 \cdot 10^{-16}\right):\\ \;\;\;\;x - \frac{t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.05e+118) (not (<= t 2.15e-16)))
   (- x (/ t (/ (- z a) y)))
   (+ x (* z (/ y (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+118) || !(t <= 2.15e-16)) {
		tmp = x - (t / ((z - a) / y));
	} 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 <= (-1.05d+118)) .or. (.not. (t <= 2.15d-16))) then
        tmp = x - (t / ((z - a) / y))
    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 <= -1.05e+118) || !(t <= 2.15e-16)) {
		tmp = x - (t / ((z - a) / y));
	} else {
		tmp = x + (z * (y / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.05e+118) or not (t <= 2.15e-16):
		tmp = x - (t / ((z - a) / y))
	else:
		tmp = x + (z * (y / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.05e+118) || !(t <= 2.15e-16))
		tmp = Float64(x - Float64(t / Float64(Float64(z - a) / y)));
	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 <= -1.05e+118) || ~((t <= 2.15e-16)))
		tmp = x - (t / ((z - a) / y));
	else
		tmp = x + (z * (y / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.05e+118], N[Not[LessEqual[t, 2.15e-16]], $MachinePrecision]], N[(x - N[(t / N[(N[(z - a), $MachinePrecision] / y), $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 < -1.05e118 or 2.1499999999999999e-16 < t

   1. Initial program 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-*l/ 98.0%

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

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in t around inf 81.7%

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

      1. mul-1-neg 81.7%

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

      2. associate-/l* 92.7%

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

   7. Simplified 92.7%

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

   if -1.05e118 < t < 2.1499999999999999e-16

   1. Initial program 87.3%

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

   3. Taylor expanded in t around 0 78.3%

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

      1. +-commutative 78.3%

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

      2. associate-*l/ 88.1%

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

      3. *-commutative 88.1%

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

   5. Simplified 88.1%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+118} \lor \neg \left(t \leq 2.15 \cdot 10^{-16}\right):\\ \;\;\;\;x - \frac{t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z - a}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+118}:\\ \;\;\;\;x - \frac{t}{\frac{z - a}{y}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-16}:\\ \;\;\;\;x + z \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- z a))))
   (if (<= t -1.05e+118)
     (- x (/ t (/ (- z a) y)))
     (if (<= t 2.2e-16) (+ x (* z t_1)) (- x (* t t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (z - a);
	double tmp;
	if (t <= -1.05e+118) {
		tmp = x - (t / ((z - a) / y));
	} else if (t <= 2.2e-16) {
		tmp = x + (z * t_1);
	} else {
		tmp = x - (t * 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 = y / (z - a)
    if (t <= (-1.05d+118)) then
        tmp = x - (t / ((z - a) / y))
    else if (t <= 2.2d-16) then
        tmp = x + (z * t_1)
    else
        tmp = x - (t * 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 = y / (z - a);
	double tmp;
	if (t <= -1.05e+118) {
		tmp = x - (t / ((z - a) / y));
	} else if (t <= 2.2e-16) {
		tmp = x + (z * t_1);
	} else {
		tmp = x - (t * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (z - a)
	tmp = 0
	if t <= -1.05e+118:
		tmp = x - (t / ((z - a) / y))
	elif t <= 2.2e-16:
		tmp = x + (z * t_1)
	else:
		tmp = x - (t * t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(z - a))
	tmp = 0.0
	if (t <= -1.05e+118)
		tmp = Float64(x - Float64(t / Float64(Float64(z - a) / y)));
	elseif (t <= 2.2e-16)
		tmp = Float64(x + Float64(z * t_1));
	else
		tmp = Float64(x - Float64(t * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (z - a);
	tmp = 0.0;
	if (t <= -1.05e+118)
		tmp = x - (t / ((z - a) / y));
	elseif (t <= 2.2e-16)
		tmp = x + (z * t_1);
	else
		tmp = x - (t * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e+118], N[(x - N[(t / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e-16], N[(x + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05e118

   1. Initial program 77.2%

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

      1. *-commutative 77.2%

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

      2. associate-*l/ 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around inf 77.2%

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

      1. mul-1-neg 77.2%

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

      2. associate-/l* 93.4%

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

   7. Simplified 93.4%

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

   if -1.05e118 < t < 2.2e-16

   1. Initial program 87.3%

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

   3. Taylor expanded in t around 0 78.3%

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

      1. +-commutative 78.3%

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

      2. associate-*l/ 88.1%

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

      3. *-commutative 88.1%

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

   5. Simplified 88.1%

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

   if 2.2e-16 < t

   1. Initial program 83.3%

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

   3. Taylor expanded in t around inf 83.5%

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

      1. associate-*r/ 93.6%

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

      2. neg-mul-1 93.6%

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

      3. distribute-rgt-neg-in 93.6%

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

      4. distribute-neg-frac 93.6%

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

   5. Simplified 93.6%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+118}:\\ \;\;\;\;x - \frac{t}{\frac{z - a}{y}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-16}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+63} \lor \neg \left(z \leq 5 \cdot 10^{-15}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.8e+63) (not (<= z 5e-15))) (+ x y) (+ x (/ (* t y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.8e+63) || !(z <= 5e-15)) {
		tmp = x + y;
	} else {
		tmp = x + ((t * y) / 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 <= (-9.8d+63)) .or. (.not. (z <= 5d-15))) then
        tmp = x + y
    else
        tmp = x + ((t * y) / 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 <= -9.8e+63) || !(z <= 5e-15)) {
		tmp = x + y;
	} else {
		tmp = x + ((t * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.8e+63) or not (z <= 5e-15):
		tmp = x + y
	else:
		tmp = x + ((t * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.8e+63) || !(z <= 5e-15))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(t * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.8e+63) || ~((z <= 5e-15)))
		tmp = x + y;
	else
		tmp = x + ((t * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.8e+63], N[Not[LessEqual[z, 5e-15]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.7999999999999994e63 or 4.99999999999999999e-15 < z

   1. Initial program 73.5%

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

   3. Taylor expanded in z around inf 76.0%

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

      1. +-commutative 76.0%

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

   5. Simplified 76.0%

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

   if -9.7999999999999994e63 < z < 4.99999999999999999e-15

   1. Initial program 94.3%

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

   3. Taylor expanded in z around 0 75.6%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+63} \lor \neg \left(z \leq 5 \cdot 10^{-15}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+64} \lor \neg \left(z \leq 7.5 \cdot 10^{-13}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.25e+64) (not (<= z 7.5e-13))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.25e+64) || !(z <= 7.5e-13)) {
		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 <= (-1.25d+64)) .or. (.not. (z <= 7.5d-13))) 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 <= -1.25e+64) || !(z <= 7.5e-13)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.25e+64) or not (z <= 7.5e-13):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.25e+64) || !(z <= 7.5e-13))
		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 <= -1.25e+64) || ~((z <= 7.5e-13)))
		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, -1.25e+64], N[Not[LessEqual[z, 7.5e-13]], $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 < -1.25e64 or 7.5000000000000004e-13 < z

   1. Initial program 73.5%

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

   3. Taylor expanded in z around inf 76.0%

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

      1. +-commutative 76.0%

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

   5. Simplified 76.0%

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

   if -1.25e64 < z < 7.5000000000000004e-13

   1. Initial program 94.3%

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

   3. Taylor expanded in z around 0 75.6%

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

      1. +-commutative 75.6%

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

      2. associate-/l* 78.8%

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

   5. Simplified 78.8%

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

      1. associate-/r/ 33.6%

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

   7. Applied egg-rr 78.5%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+64} \lor \neg \left(z \leq 7.5 \cdot 10^{-13}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+63} \lor \neg \left(z \leq 1.65 \cdot 10^{-15}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.2e+63) (not (<= z 1.65e-15))) (+ x y) (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.2e+63) || !(z <= 1.65e-15)) {
		tmp = x + y;
	} else {
		tmp = x + (t / (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 ((z <= (-8.2d+63)) .or. (.not. (z <= 1.65d-15))) then
        tmp = x + y
    else
        tmp = x + (t / (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 ((z <= -8.2e+63) || !(z <= 1.65e-15)) {
		tmp = x + y;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.2e+63) or not (z <= 1.65e-15):
		tmp = x + y
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.2e+63) || !(z <= 1.65e-15))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.2e+63) || ~((z <= 1.65e-15)))
		tmp = x + y;
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.2e+63], N[Not[LessEqual[z, 1.65e-15]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.19999999999999985e63 or 1.65e-15 < z

   1. Initial program 73.5%

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

   3. Taylor expanded in z around inf 76.0%

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

      1. +-commutative 76.0%

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

   5. Simplified 76.0%

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

   if -8.19999999999999985e63 < z < 1.65e-15

   1. Initial program 94.3%

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

   3. Taylor expanded in z around 0 75.6%

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

      1. +-commutative 75.6%

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

      2. associate-/l* 78.8%

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

   5. Simplified 78.8%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+63} \lor \neg \left(z \leq 1.65 \cdot 10^{-15}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+136} \lor \neg \left(t \leq 7.2 \cdot 10^{+195}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2e+136) (not (<= t 7.2e+195))) (* y (/ t a)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2e+136) || !(t <= 7.2e+195)) {
		tmp = 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 ((t <= (-2d+136)) .or. (.not. (t <= 7.2d+195))) then
        tmp = 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 ((t <= -2e+136) || !(t <= 7.2e+195)) {
		tmp = y * (t / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2e+136) or not (t <= 7.2e+195):
		tmp = y * (t / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2e+136) || !(t <= 7.2e+195))
		tmp = 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 ((t <= -2e+136) || ~((t <= 7.2e+195)))
		tmp = y * (t / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2e+136], N[Not[LessEqual[t, 7.2e+195]], $MachinePrecision]], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.00000000000000012e136 or 7.1999999999999997e195 < t

   1. Initial program 79.6%

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

   3. Taylor expanded in x around 0 60.2%

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

   4. Taylor expanded in z around 0 42.9%

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

      1. associate-/l* 50.8%

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

   6. Simplified 50.8%

      \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 52.2%

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

   8. Applied egg-rr 52.2%

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

   if -2.00000000000000012e136 < t < 7.1999999999999997e195

   1. Initial program 86.4%

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

   3. Taylor expanded in z around inf 66.1%

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

      1. +-commutative 66.1%

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

   5. Simplified 66.1%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+136} \lor \neg \left(t \leq 7.2 \cdot 10^{+195}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+196}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.5e+135)
   (* y (/ t a))
   (if (<= t 1.7e+196) (+ x y) (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.5e+135) {
		tmp = y * (t / a);
	} else if (t <= 1.7e+196) {
		tmp = x + y;
	} else {
		tmp = t / (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 <= (-5.5d+135)) then
        tmp = y * (t / a)
    else if (t <= 1.7d+196) then
        tmp = x + y
    else
        tmp = t / (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 <= -5.5e+135) {
		tmp = y * (t / a);
	} else if (t <= 1.7e+196) {
		tmp = x + y;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.5e+135:
		tmp = y * (t / a)
	elif t <= 1.7e+196:
		tmp = x + y
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.5e+135)
		tmp = Float64(y * Float64(t / a));
	elseif (t <= 1.7e+196)
		tmp = Float64(x + y);
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.5e+135)
		tmp = y * (t / a);
	elseif (t <= 1.7e+196)
		tmp = x + y;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.5e+135], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+196], N[(x + y), $MachinePrecision], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.4999999999999999e135

   1. Initial program 73.6%

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

   3. Taylor expanded in x around 0 57.1%

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

   4. Taylor expanded in z around 0 41.6%

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

      1. associate-/l* 50.2%

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

   6. Simplified 50.2%

      \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 52.9%

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

   8. Applied egg-rr 52.9%

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

   if -5.4999999999999999e135 < t < 1.7e196

   1. Initial program 86.4%

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

   3. Taylor expanded in z around inf 66.1%

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

      1. +-commutative 66.1%

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

   5. Simplified 66.1%

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

   if 1.7e196 < t

   1. Initial program 85.4%

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

   3. Taylor expanded in x around 0 63.2%

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

   4. Taylor expanded in z around 0 44.1%

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

      1. associate-/l* 51.5%

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

   6. Simplified 51.5%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+196}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+63} \lor \neg \left(z \leq 1.52 \cdot 10^{-22}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.2e+63) (not (<= z 1.52e-22))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.2e+63) || !(z <= 1.52e-22)) {
		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 <= (-8.2d+63)) .or. (.not. (z <= 1.52d-22))) 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 <= -8.2e+63) || !(z <= 1.52e-22)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.2e+63) or not (z <= 1.52e-22):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.2e+63) || !(z <= 1.52e-22))
		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 <= -8.2e+63) || ~((z <= 1.52e-22)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.2e+63], N[Not[LessEqual[z, 1.52e-22]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.19999999999999985e63 or 1.52000000000000005e-22 < z

   1. Initial program 72.9%

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

   3. Taylor expanded in z around inf 75.4%

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

      1. +-commutative 75.4%

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

   5. Simplified 75.4%

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

   if -8.19999999999999985e63 < z < 1.52000000000000005e-22

   1. Initial program 94.9%

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

   3. Taylor expanded in x around inf 49.4%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+63} \lor \neg \left(z \leq 1.52 \cdot 10^{-22}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.2 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= y 4.2e+96) x y))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 4.2e+96) {
		tmp = x;
	} else {
		tmp = 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 (y <= 4.2d+96) then
        tmp = x
    else
        tmp = 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 (y <= 4.2e+96) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 4.2e+96:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 4.2e+96)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 4.2e+96)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 4.2e+96], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 4.2000000000000002e96

   1. Initial program 89.4%

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

   3. Taylor expanded in x around inf 58.1%

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

   if 4.2000000000000002e96 < y

   1. Initial program 68.7%

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

   3. Taylor expanded in x around 0 58.7%

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

   4. Taylor expanded in z around inf 30.2%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.2 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.5% 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 85.0%

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

3. Taylor expanded in x around inf 48.1%

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

4. Final simplification 48.1%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 98.4% 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 2024019 
(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))))