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

Percentage Accurate: 98.2% → 95.9%

Time: 7.3s

Alternatives: 10

Speedup: 1.0×

Specification

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]

Initial Program: 98.2% 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]

Alternative 1: 95.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. +-commutative 97.6%

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

   2. associate-*r/ 84.7%

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

   3. associate-*l/ 98.3%

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

   4. *-commutative 98.3%

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

   5. fma-def 98.3%

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

3. Simplified 98.3%

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

4. Final simplification 98.3%

   \[\leadsto \mathsf{fma}\left(z - t, \frac{y}{z - a}, x\right) \]

Alternative 2: 82.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{\frac{a}{z - t}}\\ t_2 := x + y \cdot \frac{z - t}{z}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-74}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-273}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ y (/ a (- z t))))) (t_2 (+ x (* y (/ (- z t) z)))))
   (if (<= z -2.6e+43)
     t_2
     (if (<= z -3.5e-55)
       t_1
       (if (<= z -3.6e-74)
         (+ x (/ (- z t) (/ z y)))
         (if (<= z -5e-273)
           (+ x (* t (/ y a)))
           (if (<= z 8.2e-60) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (a / (z - t)));
	double t_2 = x + (y * ((z - t) / z));
	double tmp;
	if (z <= -2.6e+43) {
		tmp = t_2;
	} else if (z <= -3.5e-55) {
		tmp = t_1;
	} else if (z <= -3.6e-74) {
		tmp = x + ((z - t) / (z / y));
	} else if (z <= -5e-273) {
		tmp = x + (t * (y / a));
	} else if (z <= 8.2e-60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x - (y / (a / (z - t)))
    t_2 = x + (y * ((z - t) / z))
    if (z <= (-2.6d+43)) then
        tmp = t_2
    else if (z <= (-3.5d-55)) then
        tmp = t_1
    else if (z <= (-3.6d-74)) then
        tmp = x + ((z - t) / (z / y))
    else if (z <= (-5d-273)) then
        tmp = x + (t * (y / a))
    else if (z <= 8.2d-60) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (a / (z - t)));
	double t_2 = x + (y * ((z - t) / z));
	double tmp;
	if (z <= -2.6e+43) {
		tmp = t_2;
	} else if (z <= -3.5e-55) {
		tmp = t_1;
	} else if (z <= -3.6e-74) {
		tmp = x + ((z - t) / (z / y));
	} else if (z <= -5e-273) {
		tmp = x + (t * (y / a));
	} else if (z <= 8.2e-60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y / (a / (z - t)))
	t_2 = x + (y * ((z - t) / z))
	tmp = 0
	if z <= -2.6e+43:
		tmp = t_2
	elif z <= -3.5e-55:
		tmp = t_1
	elif z <= -3.6e-74:
		tmp = x + ((z - t) / (z / y))
	elif z <= -5e-273:
		tmp = x + (t * (y / a))
	elif z <= 8.2e-60:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y / Float64(a / Float64(z - t))))
	t_2 = Float64(x + Float64(y * Float64(Float64(z - t) / z)))
	tmp = 0.0
	if (z <= -2.6e+43)
		tmp = t_2;
	elseif (z <= -3.5e-55)
		tmp = t_1;
	elseif (z <= -3.6e-74)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(z / y)));
	elseif (z <= -5e-273)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 8.2e-60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y / (a / (z - t)));
	t_2 = x + (y * ((z - t) / z));
	tmp = 0.0;
	if (z <= -2.6e+43)
		tmp = t_2;
	elseif (z <= -3.5e-55)
		tmp = t_1;
	elseif (z <= -3.6e-74)
		tmp = x + ((z - t) / (z / y));
	elseif (z <= -5e-273)
		tmp = x + (t * (y / a));
	elseif (z <= 8.2e-60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+43], t$95$2, If[LessEqual[z, -3.5e-55], t$95$1, If[LessEqual[z, -3.6e-74], N[(x + N[(N[(z - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5e-273], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-60], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.60000000000000021e43 or 8.20000000000000025e-60 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 86.6%

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

   if -2.60000000000000021e43 < z < -3.50000000000000025e-55 or -4.99999999999999965e-273 < z < 8.20000000000000025e-60

   1. Initial program 98.8%

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

   2. Taylor expanded in a around inf 83.3%

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

      1. +-commutative 83.3%

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

      2. mul-1-neg 83.3%

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

      3. *-commutative 83.3%

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

      4. unsub-neg 83.3%

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

      5. associate-/l* 88.0%

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

   4. Simplified 88.0%

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

   if -3.50000000000000025e-55 < z < -3.6000000000000002e-74

   1. Initial program 84.4%

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

      1. *-commutative 84.4%

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

      2. associate-*l/ 99.2%

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

      3. associate-/l* 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in z around inf 84.1%

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

   if -3.6000000000000002e-74 < z < -4.99999999999999965e-273

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

      2. associate-*l/ 86.7%

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

      3. associate-/l* 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around 0 77.5%

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

      1. *-commutative 77.5%

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

      2. associate-*r/ 90.6%

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

   6. Simplified 90.6%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+43}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-55}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-74}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-273}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-60}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]

Alternative 3: 81.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+44} \lor \neg \left(z \leq 2.22 \cdot 10^{-60}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.2e+44) (not (<= z 2.22e-60)))
   (+ x (* y (/ (- z t) z)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e+44) || !(z <= 2.22e-60)) {
		tmp = x + (y * ((z - t) / z));
	} 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 <= (-4.2d+44)) .or. (.not. (z <= 2.22d-60))) then
        tmp = x + (y * ((z - t) / z))
    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 <= -4.2e+44) || !(z <= 2.22e-60)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.2e+44) or not (z <= 2.22e-60):
		tmp = x + (y * ((z - t) / z))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.2e+44) || !(z <= 2.22e-60))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.2e+44) || ~((z <= 2.22e-60)))
		tmp = x + (y * ((z - t) / z));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.2e+44], N[Not[LessEqual[z, 2.22e-60]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999974e44 or 2.21999999999999998e-60 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 86.6%

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

   if -4.19999999999999974e44 < z < 2.21999999999999998e-60

   1. Initial program 95.9%

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

      1. *-commutative 95.9%

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

      2. associate-*l/ 92.8%

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

      3. associate-/l* 98.6%

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

   3. Applied egg-rr 98.6%

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

   4. Taylor expanded in z around 0 75.2%

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

      1. *-commutative 75.2%

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

      2. associate-*r/ 81.0%

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

   6. Simplified 81.0%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+44} \lor \neg \left(z \leq 2.22 \cdot 10^{-60}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 4: 82.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-74} \lor \neg \left(z \leq 3.8 \cdot 10^{-91}\right):\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.4e-74) (not (<= z 3.8e-91)))
   (+ x (/ y (- 1.0 (/ a z))))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.4e-74) || !(z <= 3.8e-91)) {
		tmp = x + (y / (1.0 - (a / z)));
	} 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 <= (-3.4d-74)) .or. (.not. (z <= 3.8d-91))) then
        tmp = x + (y / (1.0d0 - (a / z)))
    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 <= -3.4e-74) || !(z <= 3.8e-91)) {
		tmp = x + (y / (1.0 - (a / z)));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.4e-74) or not (z <= 3.8e-91):
		tmp = x + (y / (1.0 - (a / z)))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.4e-74) || !(z <= 3.8e-91))
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.4e-74) || ~((z <= 3.8e-91)))
		tmp = x + (y / (1.0 - (a / z)));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.4e-74], N[Not[LessEqual[z, 3.8e-91]], $MachinePrecision]], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4000000000000001e-74 or 3.79999999999999978e-91 < z

   1. Initial program 99.3%

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

   2. Taylor expanded in t around 0 66.3%

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

      1. associate-/l* 80.2%

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

      2. div-sub 80.2%

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

      3. *-inverses 80.2%

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

   4. Simplified 80.2%

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

   if -3.4000000000000001e-74 < z < 3.79999999999999978e-91

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-*l/ 91.3%

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

      3. associate-/l* 98.9%

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

   3. Applied egg-rr 98.9%

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

   4. Taylor expanded in z around 0 81.4%

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

      1. *-commutative 81.4%

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

      2. associate-*r/ 89.1%

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

   6. Simplified 89.1%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-74} \lor \neg \left(z \leq 3.8 \cdot 10^{-91}\right):\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 5: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+56}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-60}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.5e+56) (+ y x) (if (<= z 1.95e-60) (+ x (* t (/ y a))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+56) {
		tmp = y + x;
	} else if (z <= 1.95e-60) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + 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 <= (-1.5d+56)) then
        tmp = y + x
    else if (z <= 1.95d-60) then
        tmp = x + (t * (y / a))
    else
        tmp = y + 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 <= -1.5e+56) {
		tmp = y + x;
	} else if (z <= 1.95e-60) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.5e+56:
		tmp = y + x
	elif z <= 1.95e-60:
		tmp = x + (t * (y / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.5e+56)
		tmp = Float64(y + x);
	elseif (z <= 1.95e-60)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.5e+56)
		tmp = y + x;
	elseif (z <= 1.95e-60)
		tmp = x + (t * (y / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.5e+56], N[(y + x), $MachinePrecision], If[LessEqual[z, 1.95e-60], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000003e56 or 1.9500000000000001e-60 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 76.7%

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

   if -1.50000000000000003e56 < z < 1.9500000000000001e-60

   1. Initial program 95.9%

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

      1. *-commutative 95.9%

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

      2. associate-*l/ 92.9%

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

      3. associate-/l* 98.0%

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

   3. Applied egg-rr 98.0%

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

   4. Taylor expanded in z around 0 74.7%

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

      1. *-commutative 74.7%

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

      2. associate-*r/ 80.5%

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

   6. Simplified 80.5%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+56}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-60}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 6: 98.2% 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 97.6%

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

2. Final simplification 97.6%

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

Alternative 7: 95.9% accurate, 1.0× speedup

Math

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

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

Derivation

1. Initial program 97.6%

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

   1. *-commutative 97.6%

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

   2. associate-*l/ 84.7%

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

   3. associate-/l* 98.0%

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

3. Applied egg-rr 98.0%

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

4. Final simplification 98.0%

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

Alternative 8: 50.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{+106}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+207}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+296}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.16e+106)
   y
   (if (<= y 4.6e-16) x (if (<= y 1.75e+207) y (if (<= y 1.26e+296) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.16e+106) {
		tmp = y;
	} else if (y <= 4.6e-16) {
		tmp = x;
	} else if (y <= 1.75e+207) {
		tmp = y;
	} else if (y <= 1.26e+296) {
		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 <= (-1.16d+106)) then
        tmp = y
    else if (y <= 4.6d-16) then
        tmp = x
    else if (y <= 1.75d+207) then
        tmp = y
    else if (y <= 1.26d+296) 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 <= -1.16e+106) {
		tmp = y;
	} else if (y <= 4.6e-16) {
		tmp = x;
	} else if (y <= 1.75e+207) {
		tmp = y;
	} else if (y <= 1.26e+296) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.16e+106:
		tmp = y
	elif y <= 4.6e-16:
		tmp = x
	elif y <= 1.75e+207:
		tmp = y
	elif y <= 1.26e+296:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.16e+106)
		tmp = y;
	elseif (y <= 4.6e-16)
		tmp = x;
	elseif (y <= 1.75e+207)
		tmp = y;
	elseif (y <= 1.26e+296)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.16e+106)
		tmp = y;
	elseif (y <= 4.6e-16)
		tmp = x;
	elseif (y <= 1.75e+207)
		tmp = y;
	elseif (y <= 1.26e+296)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.16e+106], y, If[LessEqual[y, 4.6e-16], x, If[LessEqual[y, 1.75e+207], y, If[LessEqual[y, 1.26e+296], x, y]]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.16000000000000004e106 or 4.5999999999999998e-16 < y < 1.75000000000000014e207 or 1.25999999999999992e296 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 38.9%

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

      1. associate-/l* 58.0%

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

      2. div-sub 58.0%

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

      3. *-inverses 58.0%

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

   4. Simplified 58.0%

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

   5. Taylor expanded in y around inf 44.9%

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

   6. Taylor expanded in a around 0 37.2%

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

   if -1.16000000000000004e106 < y < 4.5999999999999998e-16 or 1.75000000000000014e207 < y < 1.25999999999999992e296

   1. Initial program 96.4%

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

   2. Taylor expanded in x around inf 66.2%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{+106}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+207}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+296}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9: 62.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{-185}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.4e-185) (+ y x) (if (<= z 3e-96) x (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.4e-185) {
		tmp = y + x;
	} else if (z <= 3e-96) {
		tmp = x;
	} else {
		tmp = y + 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 <= (-9.4d-185)) then
        tmp = y + x
    else if (z <= 3d-96) then
        tmp = x
    else
        tmp = y + 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 <= -9.4e-185) {
		tmp = y + x;
	} else if (z <= 3e-96) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.4e-185:
		tmp = y + x
	elif z <= 3e-96:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.4e-185)
		tmp = Float64(y + x);
	elseif (z <= 3e-96)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.4e-185)
		tmp = y + x;
	elseif (z <= 3e-96)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.4e-185], N[(y + x), $MachinePrecision], If[LessEqual[z, 3e-96], x, N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.4000000000000004e-185 or 3e-96 < z

   1. Initial program 98.8%

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

   2. Taylor expanded in z around inf 65.5%

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

   if -9.4000000000000004e-185 < z < 3e-96

   1. Initial program 94.7%

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

   2. Taylor expanded in x around inf 53.0%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{-185}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 10: 51.1% 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 97.6%

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

2. Taylor expanded in x around inf 47.7%

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

3. Final simplification 47.7%

   \[\leadsto x \]

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 2023238 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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