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

Percentage Accurate: 98.0% → 98.0%

Time: 10.2s

Alternatives: 11

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: 98.0% 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]

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 99.2%

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

2. Final simplification 99.2%

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

Alternative 2: 81.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+82}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -2.16 \cdot 10^{-72}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e+82)
   (+ x (* y (- 1.0 (/ t z))))
   (if (<= z -2.16e-72)
     (+ x (* z (/ y (- z a))))
     (if (<= z 4e-107) (+ x (/ y (/ a t))) (+ x (* y (/ z (- z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+82) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= -2.16e-72) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= 4e-107) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.2d+82)) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else if (z <= (-2.16d-72)) then
        tmp = x + (z * (y / (z - a)))
    else if (z <= 4d-107) then
        tmp = x + (y / (a / t))
    else
        tmp = x + (y * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+82) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= -2.16e-72) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= 4e-107) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.2e+82:
		tmp = x + (y * (1.0 - (t / z)))
	elif z <= -2.16e-72:
		tmp = x + (z * (y / (z - a)))
	elif z <= 4e-107:
		tmp = x + (y / (a / t))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e+82)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	elseif (z <= -2.16e-72)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	elseif (z <= 4e-107)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.2e+82)
		tmp = x + (y * (1.0 - (t / z)));
	elseif (z <= -2.16e-72)
		tmp = x + (z * (y / (z - a)));
	elseif (z <= 4e-107)
		tmp = x + (y / (a / t));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e+82], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.16e-72], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-107], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.1999999999999997e82

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 91.4%

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

      1. div-sub 91.4%

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

      2. *-inverses 91.4%

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

   4. Simplified 91.4%

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

   if -5.1999999999999997e82 < z < -2.15999999999999996e-72

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 78.0%

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

      1. associate-/l* 83.2%

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

   4. Simplified 83.2%

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

      1. associate-/r/ 86.3%

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

   6. Applied egg-rr 86.3%

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

   if -2.15999999999999996e-72 < z < 4e-107

   1. Initial program 97.8%

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

   2. Taylor expanded in z around 0 84.3%

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

      1. associate-/l* 80.0%

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

      2. associate-/r/ 84.3%

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

   4. Applied egg-rr 84.3%

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

      1. *-commutative 84.3%

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

      2. clear-num 84.2%

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

      3. un-div-inv 84.4%

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

   6. Applied egg-rr 84.4%

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

   if 4e-107 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 89.1%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+82}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -2.16 \cdot 10^{-72}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 3: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-86} \lor \neg \left(z \leq 32500\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.75e-86) (not (<= z 32500.0)))
   (+ x (* y (- 1.0 (/ t z))))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.75e-86) || !(z <= 32500.0)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.75d-86)) .or. (.not. (z <= 32500.0d0))) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.75e-86) || !(z <= 32500.0)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.75e-86) or not (z <= 32500.0):
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.75e-86) || !(z <= 32500.0))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.75e-86) || ~((z <= 32500.0)))
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.75e-86], N[Not[LessEqual[z, 32500.0]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7500000000000001e-86 or 32500 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 86.8%

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

      1. div-sub 86.8%

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

      2. *-inverses 86.8%

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

   4. Simplified 86.8%

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

   if -1.7500000000000001e-86 < z < 32500

   1. Initial program 98.2%

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

   2. Taylor expanded in z around 0 84.5%

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

      1. associate-/l* 81.0%

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

      2. associate-/r/ 83.7%

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

   4. Applied egg-rr 83.7%

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

      1. *-commutative 83.7%

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

      2. clear-num 83.6%

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

      3. un-div-inv 84.5%

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

   6. Applied egg-rr 84.5%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-86} \lor \neg \left(z \leq 32500\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 4: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+52} \lor \neg \left(t \leq 6 \cdot 10^{+37}\right):\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.1e+52) (not (<= t 6e+37)))
   (- 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 <= -4.1e+52) || !(t <= 6e+37)) {
		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 <= (-4.1d+52)) .or. (.not. (t <= 6d+37))) 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 <= -4.1e+52) || !(t <= 6e+37)) {
		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 <= -4.1e+52) or not (t <= 6e+37):
		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 <= -4.1e+52) || !(t <= 6e+37))
		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 <= -4.1e+52) || ~((t <= 6e+37)))
		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, -4.1e+52], N[Not[LessEqual[t, 6e+37]], $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 < -4.1e52 or 6.00000000000000043e37 < t

   1. Initial program 98.2%

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

   2. Taylor expanded in t around inf 86.9%

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

      1. neg-mul-1 86.9%

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

      2. distribute-neg-frac 86.9%

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

   4. Simplified 86.9%

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

      1. *-commutative 86.9%

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

      2. add-sqr-sqrt 43.7%

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

      3. sqrt-unprod 38.1%

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

      4. sqr-neg 38.1%

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

      5. sqrt-unprod 19.8%

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

      6. add-sqr-sqrt 37.2%

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

      7. cancel-sign-sub 37.2%

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

      8. distribute-frac-neg 37.2%

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

      9. *-commutative 37.2%

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

      10. add-sqr-sqrt 17.4%

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

      11. sqrt-unprod 37.9%

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

      12. sqr-neg 37.9%

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

      13. sqrt-unprod 43.1%

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

      14. add-sqr-sqrt 86.9%

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

   6. Applied egg-rr 86.9%

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

   if -4.1e52 < t < 6.00000000000000043e37

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 77.3%

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

      1. associate-/l* 92.3%

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

   4. Simplified 92.3%

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

      1. associate-/r/ 94.3%

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

   6. Applied egg-rr 94.3%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+52} \lor \neg \left(t \leq 6 \cdot 10^{+37}\right):\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \]

Alternative 5: 81.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-85}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.4e-85)
   (+ x (* y (- 1.0 (/ t z))))
   (if (<= z 2.1e-107) (+ x (/ y (/ a t))) (+ x (* y (/ z (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e-85) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 2.1e-107) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.4d-85)) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else if (z <= 2.1d-107) then
        tmp = x + (y / (a / t))
    else
        tmp = x + (y * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e-85) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 2.1e-107) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.4e-85:
		tmp = x + (y * (1.0 - (t / z)))
	elif z <= 2.1e-107:
		tmp = x + (y / (a / t))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.4e-85)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	elseif (z <= 2.1e-107)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.4e-85)
		tmp = x + (y * (1.0 - (t / z)));
	elseif (z <= 2.1e-107)
		tmp = x + (y / (a / t));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.4e-85], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-107], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.40000000000000008e-85

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 82.6%

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

      1. div-sub 82.6%

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

      2. *-inverses 82.6%

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

   4. Simplified 82.6%

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

   if -1.40000000000000008e-85 < z < 2.0999999999999999e-107

   1. Initial program 97.7%

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

   2. Taylor expanded in z around 0 86.1%

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

      1. associate-/l* 81.6%

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

      2. associate-/r/ 86.1%

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

   4. Applied egg-rr 86.1%

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

      1. *-commutative 86.1%

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

      2. clear-num 86.0%

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

      3. un-div-inv 86.1%

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

   6. Applied egg-rr 86.1%

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

   if 2.0999999999999999e-107 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 89.1%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-85}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 6: 87.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-27}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 66000:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - t \cdot \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.3e-27)
   (+ x (* y (- 1.0 (/ t z))))
   (if (<= z 66000.0) (+ x (/ t (/ (- a z) y))) (+ x (- y (* t (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e-27) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 66000.0) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x + (y - (t * (y / 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 <= (-3.3d-27)) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else if (z <= 66000.0d0) then
        tmp = x + (t / ((a - z) / y))
    else
        tmp = x + (y - (t * (y / 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 <= -3.3e-27) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 66000.0) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x + (y - (t * (y / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.3e-27:
		tmp = x + (y * (1.0 - (t / z)))
	elif z <= 66000.0:
		tmp = x + (t / ((a - z) / y))
	else:
		tmp = x + (y - (t * (y / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.3e-27)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	elseif (z <= 66000.0)
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	else
		tmp = Float64(x + Float64(y - Float64(t * Float64(y / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.3e-27)
		tmp = x + (y * (1.0 - (t / z)));
	elseif (z <= 66000.0)
		tmp = x + (t / ((a - z) / y));
	else
		tmp = x + (y - (t * (y / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.3e-27], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 66000.0], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.29999999999999998e-27

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 87.7%

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

      1. div-sub 87.7%

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

      2. *-inverses 87.7%

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

   4. Simplified 87.7%

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

   if -3.29999999999999998e-27 < z < 66000

   1. Initial program 98.4%

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

   2. Taylor expanded in t around inf 91.1%

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

      1. neg-mul-1 91.1%

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

      2. distribute-neg-frac 91.1%

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

   4. Simplified 91.1%

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

      1. frac-2neg 91.1%

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

      2. remove-double-neg 91.1%

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

      3. associate-*r/ 91.7%

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

   6. Applied egg-rr 91.7%

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

      1. associate-/l* 91.1%

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

      2. neg-sub0 91.1%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{0 - \left(z - a\right)}}{t}} \]

      3. associate--r- 91.1%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{\left(0 - z\right) + a}}{t}} \]

      4. neg-sub0 91.1%

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

   8. Simplified 91.1%

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

   9. Taylor expanded in x around 0 91.7%

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

       1. +-commutative 91.7%

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

       2. associate-/l* 89.8%

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

   11. Simplified 89.8%

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

   if 66000 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 71.8%

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

      1. associate-/l* 92.2%

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

   4. Simplified 92.2%

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

   5. Taylor expanded in z around 0 83.4%

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

      1. +-commutative 83.4%

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

      2. mul-1-neg 83.4%

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

      3. unsub-neg 83.4%

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

      4. associate-*r/ 92.3%

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

   7. Simplified 92.3%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-27}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 66000:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - t \cdot \frac{y}{z}\right)\\ \end{array} \]

Alternative 7: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+51}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+37}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4e+51)
   (+ x (/ y (/ (- a z) t)))
   (if (<= t 3.1e+37) (+ x (* z (/ y (- z a)))) (- x (* y (/ t (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+51) {
		tmp = x + (y / ((a - z) / t));
	} else if (t <= 3.1e+37) {
		tmp = x + (z * (y / (z - a)));
	} else {
		tmp = x - (y * (t / (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 <= (-4d+51)) then
        tmp = x + (y / ((a - z) / t))
    else if (t <= 3.1d+37) then
        tmp = x + (z * (y / (z - a)))
    else
        tmp = x - (y * (t / (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 <= -4e+51) {
		tmp = x + (y / ((a - z) / t));
	} else if (t <= 3.1e+37) {
		tmp = x + (z * (y / (z - a)));
	} else {
		tmp = x - (y * (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4e+51:
		tmp = x + (y / ((a - z) / t))
	elif t <= 3.1e+37:
		tmp = x + (z * (y / (z - a)))
	else:
		tmp = x - (y * (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4e+51)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	elseif (t <= 3.1e+37)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	else
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4e+51)
		tmp = x + (y / ((a - z) / t));
	elseif (t <= 3.1e+37)
		tmp = x + (z * (y / (z - a)));
	else
		tmp = x - (y * (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4e+51], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e+37], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4e51

   1. Initial program 96.5%

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

   2. Taylor expanded in t around inf 84.4%

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

      1. neg-mul-1 84.4%

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

      2. distribute-neg-frac 84.4%

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

   4. Simplified 84.4%

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

      1. frac-2neg 84.4%

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

      2. remove-double-neg 84.4%

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

      3. associate-*r/ 84.4%

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

   6. Applied egg-rr 84.4%

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

      1. associate-/l* 84.5%

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

      2. neg-sub0 84.5%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{0 - \left(z - a\right)}}{t}} \]

      3. associate--r- 84.5%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{\left(0 - z\right) + a}}{t}} \]

      4. neg-sub0 84.5%

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

   8. Simplified 84.5%

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

   if -4e51 < t < 3.1000000000000002e37

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 77.3%

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

      1. associate-/l* 92.3%

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

   4. Simplified 92.3%

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

      1. associate-/r/ 94.3%

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

   6. Applied egg-rr 94.3%

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

   if 3.1000000000000002e37 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 89.7%

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

      1. neg-mul-1 89.7%

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

      2. distribute-neg-frac 89.7%

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

   4. Simplified 89.7%

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

      1. *-commutative 89.7%

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

      2. add-sqr-sqrt 0.0%

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

      3. sqrt-unprod 23.8%

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

      4. sqr-neg 23.8%

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

      5. sqrt-unprod 41.1%

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

      6. add-sqr-sqrt 41.1%

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

      7. cancel-sign-sub 41.1%

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

      8. distribute-frac-neg 41.1%

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

      9. *-commutative 41.1%

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

      10. add-sqr-sqrt 0.0%

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

      11. sqrt-unprod 56.2%

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

      12. sqr-neg 56.2%

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

      13. sqrt-unprod 89.5%

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

      14. add-sqr-sqrt 89.7%

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

   6. Applied egg-rr 89.7%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+51}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+37}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \end{array} \]

Alternative 8: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-26} \lor \neg \left(z \leq 6800000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.35e-26) (not (<= z 6800000.0))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.35e-26) || !(z <= 6800000.0)) {
		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 <= (-2.35d-26)) .or. (.not. (z <= 6800000.0d0))) 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 <= -2.35e-26) || !(z <= 6800000.0)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.35e-26) or not (z <= 6800000.0):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.35e-26) || !(z <= 6800000.0))
		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 <= -2.35e-26) || ~((z <= 6800000.0)))
		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, -2.35e-26], N[Not[LessEqual[z, 6800000.0]], $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 < -2.34999999999999995e-26 or 6.8e6 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 80.9%

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

   if -2.34999999999999995e-26 < z < 6.8e6

   1. Initial program 98.4%

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

   2. Taylor expanded in z around 0 80.4%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-26} \lor \neg \left(z \leq 6800000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 9: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-27} \lor \neg \left(z \leq 75000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.7e-27) (not (<= z 75000.0))) (+ x y) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-27) || !(z <= 75000.0)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.7d-27)) .or. (.not. (z <= 75000.0d0))) then
        tmp = x + y
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-27) || !(z <= 75000.0)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.7e-27) or not (z <= 75000.0):
		tmp = x + y
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.7e-27) || !(z <= 75000.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.7e-27) || ~((z <= 75000.0)))
		tmp = x + y;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.7e-27], N[Not[LessEqual[z, 75000.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.69999999999999989e-27 or 75000 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 80.9%

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

   if -2.69999999999999989e-27 < z < 75000

   1. Initial program 98.4%

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

   2. Taylor expanded in z around 0 80.3%

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

      1. associate-/l* 78.0%

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

      2. associate-/r/ 80.4%

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

   4. Applied egg-rr 80.4%

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

      1. *-commutative 80.4%

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

      2. clear-num 80.3%

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

      3. un-div-inv 81.1%

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

   6. Applied egg-rr 81.1%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-27} \lor \neg \left(z \leq 75000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 10: 62.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+170}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+58}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6e+170) x (if (<= a 3.4e+58) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6e+170) {
		tmp = x;
	} else if (a <= 3.4e+58) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6d+170)) then
        tmp = x
    else if (a <= 3.4d+58) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6e+170) {
		tmp = x;
	} else if (a <= 3.4e+58) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6e+170:
		tmp = x
	elif a <= 3.4e+58:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6e+170)
		tmp = x;
	elseif (a <= 3.4e+58)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6e+170)
		tmp = x;
	elseif (a <= 3.4e+58)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6e+170], x, If[LessEqual[a, 3.4e+58], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.99999999999999994e170 or 3.4000000000000001e58 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 83.5%

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

   3. Taylor expanded in x around inf 75.8%

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

   if -5.99999999999999994e170 < a < 3.4000000000000001e58

   1. Initial program 98.9%

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

   2. Taylor expanded in z around inf 66.5%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+170}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+58}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 49.6% 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 99.2%

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

2. Taylor expanded in z around 0 62.0%

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

3. Taylor expanded in x around inf 52.1%

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

4. Final simplification 52.1%

   \[\leadsto x \]

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 2023308 
(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)))))